homepage: Dr. Carol JVF Burns


Blog is short for weblog (weBLOG).
Check here to see the latest information about my site (and, occasionally, about my life in general).
It isn't a conventional blog—it just lets you know what I'm currently working on!

Tuesday, December 30, 2014
I finished the web exercises for Fundamental Trigonometric Identities.
I'm still sick—just can't seem to shake this nasty bug.

Thursday, December 25, 2014
Merry Christmas, everyone!
I've been sick for three days—started with a very sore throat, and progressed into lots of congestion and a hacky cough. I didn't go to the family Christmas celebration, so as not to spread germs—am having a quiet, snuggly day with Julia and Tony's three kitties instead! (However, Mr. Nels and Don Paquito seem to be very confused over the ownership of my Christmas poptart!)

I finished the concept discussion for Fundamental Trigonometric Identities.

Wednesday, December 24, 2014
Merry Christmas Eve, everyone!
I've made more progress on Fundamental Trigonometric Identities.
Getting close to being done with the concept discussion.

Tuesday, December 23, 2014
I got a good start to the concept discussion for Fundamental Trigonometric Identities.
There's a lot going on during the holidays, so my progress has been pretty slow.

Thursday, December 18, 2014
I added a new Family Home Evening lesson on developing a Personal Mission Statement.

Monday, December 15, 2014
I finally finished the web exercises for Trigonometric Values of Special Angles. This took me a long time, to get the generality that I wanted. What a nightmare!

Saturday, December 13, 2014
Today is: 12/13/14
What a cool date!!!

Saturday, December 6, 2014
I finished the concept discussion for Trigonometric Values of Special Angles.
Today is Marybelle's birthday celebration! She's $\,18\,$ today. Her birthday dinner request: lasagne, salads (with sprouts), eggnog, and tres leche cake for dessert. (I also made bread, and had clementines for color on the plates. Bethany decorated! We put both leaves in our new table, since Joshua joined us for dinner and we had Marybelle's ‘apartment-starter’ gift on the table.)

Friday, December 5, 2014
I'm almost done with the concept discussion for Trigonometric Values of Special Angles.
My two paper-pieced quilt projects are coming along nicely: a sampler quilt, and my log-cabin blocks for Christmas gifts.

Thursday, December 4, 2014
A user asked for textboxes on worksheets, so answers could be typed in at the computer. Then, users can get a printed hardcopy (or print-to-pdf) with their typed answers in place. I've put a prototype on my most recent exercise: Signs of All the Trigonometric Functions. Scroll down to the worksheet, check the appropriate box, and then create the worksheet. Check it out!

Wednesday, December 3, 2014
I went to start a new section today, and realized I hadn't yet finished the web exercises on Signs of All the Trigonometric Functions! They're now done. Things got so busy with two Thanksgiving celebrations that I lost track of where I was!

Tuesday, December 2, 2014
I just sent a (slightly modified) version of my TeX Commands Available in MathJax document to Peter Krautzberger for use in a github respository. I used a very non-restrictive license that will allow it to be used in the MathJax documentation. (It can also be used commercially.) People just need to retain the link back to my site.

I just chanced across this MathJax Hangout on air—Q&A with Davide Cervone, Peter Jipsen, and David LippmanShare event 2. It's so great to ‘see’ the people who I've been communicating with (on and off) for years! I love Peter Jipsen's vision—extremely similar to my own—at about minute $\,48\,.$ (I like to call this ‘active reading’.)

Here are other MathJax Hangouts I've now found: This is also the first I've heard about XyJax, an extension for MathJax that enables you to draw various graphs and diagrams. (I currently use JSXGraph for all my drawing needs.)

A couple other things I hadn't heard about and want to keep track of here: Monday, December 1, 2014
I updated my monthly stats and website income for November.

Wednesday, November 26, 2014
Our new table arrived yesterday! Palettes by Winesburg, rustic cherry, with two (self-storing) leaves. It's beautiful! My little Flagstaff table served us well for almost three months while we awaited our new table's arrival.

I finished the concept discussion on Signs of All the Trigonometric Functions. I'll likely get started on the web exercises today.

I was just contacted by Dr. Peter Krautzberger, MathJax Manager. He asked for my permission to replicate TeX Commands Available in MathJax in a GitHub repository. He indicated that ‘this would allow others to contribute to your excellent guide and possibly make other forms of delivery (epub3 etc) possible.’ I gave him permission, but indicated that the resource must remain free; that no one may profit from this document without my written permission.

Monday, November 24, 2014
I compiled some convenient links to alto/tenor part practice for Handel's Messiah since we'll be singing it soon.

Saturday, November 22, 2014
I finished the web exercises for the Trigonometric Functions.
This section has some randomly-generated JSXGraph problem types.

Thursday, November 20, 2014
I finished the concept discussion for the Trigonometric Functions.

I'm making a sampler paper-pieced quilt—there are about $\,100\,$ different blocks in the book I have, and I'll use most of them at least once to make a queen-size quilt. There are some I won't use (like the cars and trucks) and there are some I'll double up on (like the log cabin and star designs). I'm trying to do one block per day. They started out easy and are getting harder—but I'm also getting better at the method. It seems to be taking me about one hour per day.

Wednesday, November 19, 2014
I spent a long time deciding how to present the motivations for the names ‘tangent’ and ‘secant’, and creating the graphics. Now, I'm close to being done with the concept discussion for the Trigonometric Functions.

Tuesday, November 18, 2014
I got started on the concept discussion for the Trigonometric Functions—then Ray came home in the middle of the day and we ended up practicing rumba, mambo, and cha-cha for a long time!

A link I don't want to lose: Pentatonix (I had never heard of them before) singing ‘Mary Did You Know’. I cried!! There's a moment when the soprano gets this brief look on her face—the ‘it's so beautiful I can't keep my joy from sneaking onto my face’ look. I know the look. I got it last night while practicing the Messiah with Ray in a tiny church room! Alto and tenor can sound wonderful together!!

Monday, November 17, 2014
What an exciting day for me! This morning, I got a \$50 donation, which is double my biggest donation ever! (It's also more than I've made in many of the months for the past year.) Then, this afternoon, I got another donation, for \$100!! The only thing that has changed is that my biography as a featured speaker for CAMT 2015 went ‘live’. Could it be that news about my site is finally getting out to people who can appreciate its value—or was today just an exceptionally lucky day for me? Whatever—it was a fantastic day for me!

Friday, November 14, 2014
I've finished all the exercises for Relatively Prime Numbers and Related Concepts. After an extended break to improve my Algebra I course, I will now return to trigonometry!

By the way, this sounds great for Christmas gifts: Crazy Quilt Block Pot Holder.

Tuesday, November 11, 2014
I've finished the concept discussion and the timed exercise for a new (optional) Algebra I section, Relatively Prime Numbers and Related Concepts.

Monday, November 10, 2014
The speakers for CAMT 2015 (the Conference for the Advancement of Mathematics Teaching) just went live! (I'm a featured speaker, near the bottom—scroll down.) They didn't end up using the bio I sent (it was likely waaayyyy too long). I spent many hours writing it, though, so I'll include it here:

Since 1999, Carol has put more than 10,000 hours into creating about 350 free online math lessons ranging from arithmetic to calculus, each offering unlimited, randomly-generated exercises and worksheets for both online and offline practice. Carol has a Doctor of Arts in Mathematics (a doctoral-level degree that emphasizes effective teaching), and has taught for about 30 years at both the college and high school levels.

For her entire adult life, Carol has been passionate about the language of mathematics—teaching foundational concepts that empower people to teach themselves mathematics. These skills are woven throughout her sequenced curriculum at http://www.onemathematicalcat.org and her online book: One Mathematical Cat, Please!

From humble beginnings with custom-made IBM selectric typewriter elements, to state-of-the-art dynamic web mathematics made possible by MathJax, Carol's love of mathematics has been complemented by her desire to present it beautifully to the world.

Want more information about Carol and her web site?

• 5-minute YouTube website intro
Vita: Dr. Carol JVF Burns
Carol's teaching philosophy
Slide show: history and philosophy of Carol's site
Fun facts about Carol (like: What does the ‘JVF’ stand for?)
Testimonials and More Testimonials
Review of One Mathematical Cat, Please!

The easiest way to get to Carol's site is to type three words—‘math cat burns’—into any search engine!

Friday, November 7, 2014
As per my ‘bonus daughter's’ request, I added a ‘no variables’ checkbox to
Mixed Basic Add/Subtract Multiply/Divide Practice.
(‘Bonus daughter’ sounds a lot better than ‘stepdaughter’!)

I'll be starting my first paper-pieced quilt soon. I found these two fantastic videos: Thursday, November 6, 2014
I added a new Family Home Evening lesson: Remembering Names.

Tuesday, November 4, 2014
I finished the web exercises for The Prime Factorization Theorem.

Saturday, November 1, 2014
I updated my monthly stats and website income for October.
Also, I downloaded this SkinnyTip JavaScript Tooltip Library for use in a new project of mine.

Friday, October 31, 2014
Happy Halloween, everyone!

I finished the concept discussion for The Prime Factorization Theorem,
a new addition to my Algebra I curriculum.

Thursday, October 30, 2014
I put my ASL (American Sign Language) practice online.

I added a section on Prime Numbers to my Algebra I curriculum.
It has both timed practice (more Algebra Pinball!) and concept questions.

Wednesday, October 29, 2014
Several weeks ago I purchased an annual WolframAlpha PRO subscription (\$65.88), so I could start exploring graph interactivity, which requires their CDF player. Thus began weeks of technical support via email, since the CDF player did not work for me. I have MAC OS X, version 10.6.8, which is stated as a supported system.

As of today, it works! There were several steps in the process: I am very thankful to WolframAlpha Technical Support for working with me on this issue. As my users know, I use WolframAlpha a lot, and I want to be able to share what PRO has to offer!

On a different note, my incredible husband Ray came up with a beautiful derivation of the sum formulas for sine and cosine, which I have his permission to use in my future trig sections. He's amazing!!

Friday, October 23, 2014
I'm giving three talks at the 2015 CAMT conference and have been spending lots of time getting my biography, talk titles, and talk descriptions done. In the process, I'm cleaning up a lot of my online resources, like finally replacing the text math with MathJax in Algebra Pinball!

Tuesday, October 20, 2014
I (finally!) finished the web exercises for
Radian Measure: Associating Real Numbers with Points on the Unit Circle.

Friday, October 17, 2014
The last couple weeks have been crazy, so I've gotten very little web work done.
Hopefully things will settle soon.
I've put a couple more Family Home Evening lessons online:
Table Manners
A Brief Introduction to WolframAlpha

Thursday, October 9, 2014
Based on a user email, I added more info about efficient methods of finding the least common multiple.
In particular, I extended an efficient method for finding the greatest common factor to one for finding the least common multiple.

Wednesday, October 8, 2014
I finished the concept discussion for Radian Measure: Associating Real Numbers with Points on the Unit Circle. This one took a long time to write!

Friday, October 3, 2014
I finished the exercises for Reference Angles. This section took me quite a while, but I'm now pleased with it.

Thursday, October 2, 2014
I added a section to the Algebra I curriculum that discusses an unfortunate order of operations mistake:
Taking PEMDAS Too Literally: Don't Make This Mistake!

Wednesday, October 1, 2014
I updated my monthly stats and website income for September.

Tuesday, September 30, 2014
I added a discussion of size/sign to Reference Angles. I also added a collapsing paragraph that explains why an illustrated technique (to adjust the size of the angle to a size between $\,-180^\circ\,$ and $\,180^\circ\,$) always works.
This has ended up being a pretty long section. I'll need to make a decision about breaking it into two pieces, or keeping it as is.

Monday, September 29, 2014
I edited/finished the concept discussion for Reference Angles. For a newbie, this can be confusing, since three angles make an appearance for every problem: an original angle for which you want to find trig values (like $\,1747^\circ\,$); remove extra rotations to make it easier to work with (giving $\,1747^\circ−5\cdot 360^\circ=−53^\circ\,$); and the reference angle (which is $\,53^\circ\,$).

Saturday, September 27, 2014
I'm not quite done with the concept discussion for Reference Angles, but I'm close!

Thursday, September 25, 2014
I put a fun little saying in Special Triangles and Common Trigonometric Values. It's something I've said quite a few times over my many years of teaching!!

Wednesday, September 24, 2014
I finished the exercises for Special Triangles and Common Trigonometric Values.

Tuesday, September 23, 2014
Today is my third wedding anniversary to Ray Burns! We went for a beautiful hike in the Catalina mountains. While on this hike (of course, without any paper or pencil), Ray (my brilliant husband) came up with a great mathematical model for my ‘years with partners’: $$ f(x) = \left|\frac{30x - 70}{x - 3}\right| $$ Note that: $$\,f(1) = \left|\frac{30(1)-70}{1-3}\right| = \left|\frac{-40}{-2}\right| = 20\,$$ My first marriage lasted $\,20\,$ years. Also, $$\,f(2) = \left|\frac{30(2)-70}{2-3}\right| = \left|\frac{-10}{-1}\right| = 10\,$$ My second ‘marriage’ (not a legal marriage) lasted $\,10\,$ years. So, prediction for my third? Of course, $\,f\,$ is not defined at $\,3\,,$ but $$ \lim_{x\rightarrow 3} f(x) = \infty $$ I like it!!

Monday, September 22, 2014
I finished the concept discussion for Special Triangles and Common Trigonometric Values.

Friday, September 19, 2014
I finished the exercises that go with the new example in the Unit Circle Approach to Trigonometry.

Wednesday, September 17, 2014
I added a second example to the Unit Circle Approach to Trigonometry,
and will be adding web exercise(s) corresponding to this example.

Tuesday, September 16, 2014
I finished the web exercises for Compatibility of the Right Triangle and Unit Circle Approaches.

Monday, September 15, 2014
I finished the web exercises for the Unit Circle Approach to Trigonometry.
As for my health, I haven't taken a pain pill since 11:15AM on Sunday—1.5 days.
I haven't been able to do this since mid-March.
This is real progress for me!

Tuesday, September 9, 2014
I finished the web exercises for the Right Triangle Approach to Trigonometry.
Whenever I try to use JSXGraph in the randomly-generated worksheets, it takes a long time. This was no exception! It just fights me every step of the way!

Wednesday, September 3, 2014
I updated my monthly stats and website income for August.

Wednesday, August 27, 2014
I completed the web exercises for Introduction to Trigonometry.

After 8 months of living in our two tiny trailers (Dew Drop and Morning Mist; a total combined floor space of about 40 square feet), we've decided we need to break down and rent a house. We've made a lot of progress in the past 8 months (mostly cleaning), but estimate that we have at least a year before we'll be able to live in the Rock House. It was a good challenge passing through one Arizona summer and monsoon season in our trailers, but I'm not up for a repeat!

I will miss the serenity and gorgeous stars and all the critters, but I will so appreciate a refrigerator inside the house and a real kitchen to prepare meals for my family! The place we're hoping to get has a large tiled room where Ray and I will be able to dance (as much as my leg will permit). So, house-finding has pre-occupied me this week; the actual move will likely postpone serious progress on trigonometry for yet longer. Also, I'm getting another IVIG treatment for my CIDP the next couple days, since the numbness has started to return to my upper back, and I want to ‘catch’ it before it gets as bad as it was several months ago.

Friday, August 22, 2014
I did end up breaking my one looonnnnggg section into four different sections: Now, to write the exercises for all of them!

Thursday, August 21, 2014
I got a lot more done on the concept discussion for Introduction to Trigonometry.
I'll probably end up breaking this single section into three sections: an introduction, the right triangle approach, and the unit circle approach. It's way too long already, and I'm not done!

Wednesday, August 20, 2014
I got a good start to the concept discussion for Introduction to Trigonometry.
Introductions are always hard. You can't say everything first. And, you shouldn't say everything right away, because it's too overwhelming. I'm fairly pleased with what I have so far.

Monday, August 18, 2014
I've finished the exercises for Doubling Time, Half-Life.
Finally, after all these years, on to trigonometry!!

Saturday, August 16, 2014
I've finished the doubling time and half-life discussion for Doubling Time, Half-Life. Next, I want to include a short section on a general situation.

Friday, August 15, 2014
I've started the concept discussion for Doubling Time, Half-Life.

Thursday, August 14, 2014
I had missed a large donation (\$25.00; received \$23.97 after PayPal fees) when reporting my July income. I've corrected it. I believe this is my largest donation ever!!

I finished the web exercises for Solving Exponential Growth and Decay Problems, and also expanded the concept discussion to include (equal change,constant multiplier) pairs.

Tuesday, August 12, 2014
I finished the concept discussion for Solving Exponential Growth and Decay Problems.
I also had my first ‘dry needling’ session, to see if this will help the pain in my right leg.

Saturday, August 9, 2014
I finished the web exercises in Solving Logarithmic Equations.
These took a long time to code!

Thursday, August 7, 2014
Ray and I thought that it might be helpful to have two differently-styled hyperlinks: one style for intra-page links (in the same page); a different style for links that go to a different page. When we re-do the web site, this is an idea that we might incorporate.

Wednesday, August 6, 2014
I started creating my own Amazon store.
I finished the concept discussion in Solving Logarithmic Equations.

Saturday, August 2, 2014
I updated my monthly stats and website income for July.

Friday, August 1, 2014
How to harvest our sunflower seeds!
In a nutshell, I quote from

Harvest sunflower seeds after the flower begins to die back, and most if not all, of the petals have fallen off. Pull out a seed and open it to see if it is full. Cut off the head, leaving a few inches of stalk. Hang the stalks to dry in a well ventilated area. Do not stack them in a box, as mold can develop during the drying process. As soon as the flowers have dried, extract the seeds by rubbing two flower heads together. They should come off of the flower head fairly easily.

Tuesday, July 29, 2014
I finished the exercises in Solving Exponential Equations.

Thursday, July 24, 2014
I finished the concept discussion in Solving Exponential Equations.
Has it really been more than a week since posting anything new? Sigh!

Tuesday, July 15, 2014
I finished the exercises in Exponential Growth and Decay: Relative Growth Rate.

Monday, July 14, 2014
I finished the concept discussion in Exponential Growth and Decay: Relative Growth Rate.

Friday, July 11, 2014
Now, you can click on a cell in the ‘problem type’ table and it will give you that problem. Check it out in Logarithm Summary: Properties, Formulas, Laws. (I changed the color scheme, too.) So, teachers can say (for example) ‘practice problems 3, 7, and 11’.

Thursday, July 10, 2014
I've finished the exercises in Exponential Growth and Decay Problems—Introduction. Upon suggestion by my brilliant husband, I also created a visual indicator of problem types ‘in progress’, ‘mastered’, and ‘available’. Again, I'm really pleased! I'm hoping this will be useful for my users.
I also went back and updated Logarithm Summary: Properties, Formulas, Laws to this graphical style.

Tuesday, July 8, 2014
I've finished the exercises in Logarithm Summary: Properties, Formulas, Laws. Forty of them! This section is a great thorough review of logarithms (yes I'm biased). Plus, I added a button so you can remove a problem type you've already mastered. Also, you can see just how many problem types you still have to master. I'm very pleased with this section!

Monday, July 7, 2014
In the past few days, we've found a bark scorpion, a western diamondback rattlesnake, a black widow spider and a tarantula near our trailers. I guess the rains must be bringing them all out. A few weeks ago, we saw a gila monster (pronounced HEE-la). I've already had lots of ‘training’ in the dangerous Arizona vegetation, and now I'm getting my training in the dangerous Arizona wildlife!

Following a user's suggestion, I created a couple sketches to help explain why you must change the direction of the inequality symbol when multiplying/dividing by negative number. Search for this text (it's about halfway down the page): Here are a couple sketches to further help you understand this concept.

Friday, July 4, 2014
I've got a good start to the exercises in Logarithm Summary: Properties, Formulas, Laws. I've finished the exercises through the Change of Base Formula. More to come!

Tuesday, July 1, 2014
I updated my monthly stats and website income for June.

Saturday, June 28, 2014
Since we have (no joke) $\,200\,$ wheels and about $\,140\,$ tires on the land we're cleaning, I'm collecting some ideas.
I want to make sure that water isn't going to get inside and breed mosquitoes.
Also, I don't want pack rats to think they've found a new nesting place!
There are also concerns about toxicity (zinc, etc.), and you don't want any chance that they'd burn.

alligator tires

a climbing wall for kids

no-slip stairs
(possibly use for steps down into the mine)

a living retaining wall

planters and raised beds

make a tire sculpture

make a palm-tree-tire forest

flower planters

a tire mountain for the kids

roofing a house

a tire obstacle course

mosaic planters

Friday, June 27, 2014
I finished the exposition for Exponential Growth and Decay Problems—Introduction.
I just realized that I haven't yet written the exercises for the previous lesson, so I'll back up and get that done.

Saturday, June 21, 2014
I finished the exposition on Logarithmic Summary: Properties, Formulas, Laws.

Friday, June 20, 2014
I've finished the web exercises for Logarithmic Functions: Review and Additional Properties.
I'm really pleased with the exercises, particularly solving logarithmic sentences.

My husband Ray and Bethany have gone on a DDD (a Daddy-Daughter-Date) to Patagonia Lake in southern Arizona, fishing!

My bookmarks list has gotten out of control! Here are some links I want to keep track of (but move off the list):

Tuesday, June 17, 2014
I've finished the exposition for Logarithmic Functions: Review and Additional Properties.
Also, I'm on ‘kitty duty’ this week, taking care of three cats!

Thursday, June 11, 2014
I've finished the web exercises for Continuous Compounding. On to logarithmic functions!

Tuesday, June 10, 2014
I've finished the ‘Rock House Story’ (our emerging country home) up to present time.
I've finished the exposition on Continuous Compounding.

Thursday, June 5, 2014
My homemade grow boxes did not work out well. They turned into sewage-smelling, ant-attracting, soggy messes. The plastic containers that I bought from Walmart were brittle and cracking after only a couple months in the Arizona sun. The plants did not do well in them, and I ended up transplanting directly into the soil in our new coop. The genuine Earth Box that I purchased is doing fine—we're getting lots of delicious cherry tomatoes. Well, it was fun to try!

Wednesday, June 4, 2014
[update: June 28, 2014] I will never do this again. To me, it's worth the money to have it done by a professional. I didn't have a cool, protected place to work, so contending with wind and sun was very difficult. I found it near impossible to position the film correctly, and to get out air bubbles and wrinkles. Ah well!

I want to tint the cars on our car, Blossom. The car gets really hot in the Arizona summers.
You're expected to abide by the laws in the states where you're driving, even if you're just visiting.

As of 1994, here are Arizona's requirements:
Here's a helpful video for applying the window tint on your car windows.

Here are the basic steps for applying window tint:

Tuesday, June 3, 2014
I updated my monthly stats and website income for May.

I learned that Google did a Panda 4.0 update on about May 19, and this is precisely the date that my hits started increasing dramatically. This update is “designed to help boost great-quality content sites while pushing down thin or low-quality content sites in the search results”. Finally, there seems to be recognition that I have great content! Woo hoo! I'm hopeful that my Adsense income will start to improve with the additional hits.

Ray (my husband) and I have been working hard at cleaning out the Rock House!! It's very satisfying to have progress that can actually be seen. (Ray has been doing lots of structural engineering and architectural work, but this is all in his head, on paper, and on his computer.) We do a lot of work very early in the morning (5 AM and even earlier) because by 7 AM it's already very hot here in Arizona.

Also, Ray has finished our beautiful chicken-coop-turned-garden-coop. It's lovely! I painted the boards, put a latch on the door, and provided lots of cheerleading—Ray did everything else (and Bethany helped a bit too). We have (some are from seed and have not yet sprouted): lettuce, morning glories, cherry tomatoes, garlic, peas, potatoes, pumpkins, squash, cantaloupe, watermelon, wild flowers, sunflowers, and carrots. My daughter Julia gave me a lovely hanging fabric planter, which I'm using for an herb garden, and it is hung on one wall of the coop. Hopefully, I'll have fresh basil, oregano, parsley, chives, tarragon, rosemary and thyme!

Friday, May 23, 2014
Here's a handy video for getting rid of fruit flies. In a nutshell: put some apple cider vinegar (about an inch) in a mug, cover with plastic wrap, punch many tiny holes in the plastic wrap with (say) a toothpick. The fruit flies will fly in, get trapped inside, and die in the vinegar. It may take several days to completely eliminate the fruit flies.
[update several days later]: Didn't work at all for me! Maybe Arizona fruit flies don't like apple cider vinegar.

Usually, at this time of the year, my hits go down dramatically as school ends. However, I've had 1279, 1229 and 1120 page views in the past three days, which is almost double what I've been getting recently. This is good news—I don't know why, but I'll take it!

Thursday, May 22, 2014
I've finished the web exercises on my newest Precalculus section, Simple versus Compound Interest.

I'm trying an organic spray to keep insects from munching on my plants.
I thoroughly blend all the ingredients below in my Magic Bullet Blender, then pour into a spray bottle to spray on the plants. I'm also going to plant these flowers around the outside of my gardening coop.
They'll look beautiful, and are known to have insect-repelling power:

Tuesday, May 20, 2014
We're back in Arizona! It's great to be home, and I'm returning in better health than when I left.

I just wrote a testimonial for Even Par Auto Sales. This is a new web site for Mike and Michelle Waldbillig. We bought Blossom from them, and it was a fantastic car-buying experience.

Tuesday, May 13, 2014
It has now been just under two weeks since completing my IVIG treatment. I believe my general health has been an upward trend with oscillations, something like this:

(Time is along the horizontal axis;
my general well-being is along the vertical axis.)

I have good days, and I have bad days. I have days when I can forget, for short periods, that I've been so sick. I have days when I can barely walk. However, the upper back pain and headache have been entirely gone for about a week and a half now. I've had physical therapy for the leg pain. The therapist feels my pain is consistent with a herniated disc in the lumbar region. The stretching exercises seem to help a bit. There is no discernable improvement in the pins-and-needles in my hands, feet, and upper back—my greatest fear is that as each day goes by with this numbness, it increases the likelihood of permanent nerve damage. I'm averaging 1-2 percocet per day; one of these is usually to get some sleep at night.

Ray arrives very late tomorrow night, and we'll leave together for Tucson on Monday, May 19th. Overall, I feel it has been a successful trip back here. I'm not going back in perfect health, but I'm definitely not continuing to get worse, and I have more functionality and less pain than when I left Tucson on April 17th.

Monday, May 12, 2014
I just received an email from a friend who mentioned plasmapheresis. Whereas IVIG adds good antibodies, plasmapheresis cleanses the body of bad antibodies.

Friday, May 9, 2014
I bought a Kb sock loom. It was originally $25.00 at Joann's in Pittsfield, MA, but I had a 40% off coupon. The DVD doesn't work on a MAC (sigh). I needed to use 54 pegs for my size foot. It did not work for me! I was unable to make stitches loose enough. After many hours of casting on, ripping out, searching the web for tips, I ended up giving the loom to my sister! Evidently she knows an 80+-year-old woman who makes lots of socks on a loom, and perhaps this woman can give her tips that will allow her to be successful. As for me, I found a wonderful pattern for crocheted socks, and am almost done with my first one. So, I at least get to use the yarn that I bought!

Tuesday, May 6, 2014
In mid-Febrary, 2014, Youngho Cho contacted me from Seoul, Korea. He was in the process of developing www.easydesk.co.kr for an itembank, online testing and publishing system. He came across my TeX Commands Available in MathJax and asked my permission to use it, together with a Korean translation created under his direction, in a commercial setting. In their commercial mode, I will be credited when my material (English and/or a translation) is offered in help mode, and a link will be provided to the original Tex Commands Available in MathJax document. It was also part of the agreement that I could make translation(s) available, linked from my original document, since this will provide a wonderful service to the online mathematics community.
Here is the Korean translation of ‘TeX Commands Available in MathJax’. A Japanese translation may be coming, too!

Monday, May 5, 2014
I updated my monthly stats and website income for April.

Thursday/Friday, May 1/2, 2014
Ray arrived about 2AM Wednesday morning. It is so wonderful to have him here!

My two final IVIG infusions, without steroids, were Thursday and Friday at 8AM at BMC. Unfortunately, at this point in my treatment, my health is regressing, not progressing. I have greatly increased pain in my right leg; the numbness/pins/needles has increased; extreme fatigue/weakness; headache, nausea, back/neck pain. Unable to get any sleep, I ended up taking some percocet both Thursday and Friday nights. Sometimes things get worse before they get better, and perhaps that's what's going on here.

Wednesday, April 30, 2014
Here are a couple cute acronyms/sayings that I've picked up in the hospital: I'm going home today! I'll have my third steroid/IVIG treatment, and will be released from the hospital thereafter. I'll have the remaining two IVIG treatments done as an out-patient (returning to the hospital just for the treatment). I'll be back at my Mom's house when my husband Ray arrives tonight! Hooray!

My right leg is dramatically better: no spasms, no severe pain, very little weakness. I still have minor upper back pain, minor neck pain, minor headache, mild nausea, but not severe enough to require pain meds. When the neurologist ‘tickled’ the bottom of my feet this morning, I felt it for the first time, so I may be recovering some of my peripheral senses. Hooray! Overall, I'm feeling better than I have in two months. This speaks well to a correct diagnosis and treatment.

I'm glad this is my last (third) day of the steroid treatment. The pain at my IV site, during the injection, has gotten worse and worse each day. Today it is quite painful. Usually, the pain disappears a few minutes after they switch to the IVIG.

I like this description of using the pain scale properly. According to this description, I would say that my worst episodes of pain have been between 8 and 9.

Tuesday, April 29, 2014
The abnormality in my CSR (cerebrospinal fluid) from the spinal tap was albuminocytologic dissociation. Here's the definition and I quote: “increased protein in the cerebrospinal fluid without increase in cell count, characteristic of the Guillain-Barré syndrome; it is also associated with spinal block and with intracranial neoplasia, and is seen in the last phases of poliomyelitis.”

Here is some more info on inflammatory demyelinating polyneuropathy from Medscape.

I have cells in my body that are creating ‘bad antibodies’; these ‘bad antibodies’ are breaking down the myelin sheaths on my nerves. This abnormal behavior of my cells could have been caused by exposure to some toxic substances (for example, things that I might have encountered in cleaning the land and filling three 40-cubic-yard dumpsters).

The IVIG is getting rid of the bad antibodies. It is not getting rid of the cells that create the bad antibodies. Steroids, on the other hand, actually kill the cells that are creating the bad antibodies. However, killing the cells compromises your immune system (which is bad), because then the cells are gone and can't do their job in creating the ‘good’ antibodies to fight off other infections.

I am currently on both IVIG and steroids. Here's an analogy—the IVIG is getting rid of the current attackers, and the steroids are getting rid of the intelligence that is sending in new attackers! Since I'm on steroids, it's important that I not expose myself to sickness (get me out of the hospital, right!?). So I ask, please, that if you're sick, don't visit me! Emails, texts, and phone calls are safe!

The doctors hope that this was indeed brought on by (say) toxic exposure, and that, with the toxicity removed, and having ‘cleaned out’ my body of the ‘bad antibodies’, that I will fully recover. He believes that I can recover full ability, including getting rid of the pins-and-needles in both my hands and feet—he doesn't think this has gone on long enough that the damage is permanent. I'm good with this diagnosis!

Here are some possible side effects of IVIG. Today has been a good day for me; I haven't taken any pain medication in over 24 hours as I write this. However, I have had a mild headache, mild upper back and neck pain, mild leg pain, normal numbness (hands/feet/back), some minor chills and some nausea—the headache and nausea are not as normal for me, and are listed as possible IVIG side effects. It's possible that my post-spinal-tap headache is morphing into a post-IVIG-headache! It's also possible that my Motrin-nausea from yesterday is morphing into some IVIG-nausea!

Here are some possible side effects of steroids.

Monday, April 28, 2014
In the continuing saga of my health (i.e., lack of), they think that I may have the very rare CIDP (Chronic Inflammatory Demyelinating Polyneuropathy), which is ‘an acquired immune-mediated inflammatory disorder of the peripheral nervous system’.

I think they may be getting close, because these quotes from the wikipedia article describe my symptoms perfectly:
‘Patients usually present with a history of weakness, numbness, tingling, pain and difficulty in walking.
Some patients may have sudden onset of back pain or neck pain radiating down the extremities, usually diagnosed as radicular pain. These symptoms are usually progressive and may be intermittent.’
Evidently the spinal tap fluid did show abnormalities consistent with this diagnosis. Evidently everything else was normal: MRIs, EKG, chest x-ray, bloodwork.

I am going to stop taking the percocet; I do not want to start dealing with either addiction or building tolerance, on top of my other woes! Today, for the first time, I took a motrin (600 mg); I went from excruciating, level-10, charley-horse cramping pain in my right leg to tolerance in about 20 minutes. It has, however, given me some nausea, whereas I didn't experience any side effects with the percocet.

They are puting me on IVIG (intravenous immunoglobulin). I will have five days of this IVIG treatment. However, they suspect that it will take a few days for this to relieve symptoms. For the first three days, before the IVIG treatment (back-to-back), they are giving me a 1000mg dose of methlyprednisolone, a steroid. This should give more immediate relief of pain, and also remediate some of the possible side effects of the ensuing IVIG.

The steroid, and first dose of IVIG went well! Here is a statement, from Office of Rare Diseases Research, about the long-term outlook for people diagnosed with CIDP. I like the part that I've emphasized, and that's going to be ME!
The course of CIDP varies widely among individuals. Some may have a bout of CIDP followed by spontaneous recovery, while others may have many bouts with partial recovery in between relapses. The disease is a treatable cause of acquired neuropathy and initiation of early treatment to prevent loss of nerve axons is recommended. However, some individuals are left with some residual numbness or weakness.

Saturday, April 26, 2014
Dr. Marina Zaretskaya-Fuchs (a neurologist in Lenox, Massachusetts) came highly recommended by two very close friend/family members. The first test she did—having read my recent medical history—was a neurological conductivity test, which yielded highly abnormal results. She wrote: ‘There is electrical evidence to suggest the presence of acute, not length dependent, asymmetric, mixed motor and sensory, primary demyelinating polyneuropathy.’ Finally, after two months, a test result that showed something wrong—I was ecstatic! She wanted me admitted to the hospital right away, to gather more data on what is causing this compromising of the myelin sheath around my nerves.

Since being admitted, I've had a spinal tap (lumbar puncture), blood drawn, a chest x-ray, an EKG, and just under two hours in the MRI (cervical and thoracic, with and without contrast). I've talked to many doctors and nurses, relating my recent medical history. They are wonderful here at BMC (Berkshire Medical Center) in Pittsfield, Massachusetts. I feel that I'm in very good hands, with a team that is determined to figure out what is causing my symptoms.

The MRI was extremely difficult for me—I was fighting panic attacks throughout. When first pushed in, I made the mistake of keeping my eyes open, and had to be removed immediately, to collect myself. Second time in, I was sure to keep my eyes closed, and I cycled through three strategies for avoiding panic: praying, singing to myself, and envisioning Ray's arms wrapping around me.

Friday, April 25, 2014
I'm now in Massachusetts, and have a neurologist appointment scheduled for tomorrow (Saturday). Hopefully this will shed some light on my health condition.

I'm having a wonderful visit with my Mom. Even at age 55, I gain great comfort from my Mom when I'm in such pain.

I've finished the exposition for Simple Versus Compound Interest. Exercises hopefully coming soon!

Wednesday, April 16, 2014
To all my users: I'm sorry I've produced so little new material on my website for months now. I've been very sick.

I'm headed to Massachusetts for about a month to see my Mom, give my sister a much-deserved break for Mom's care, and see some doctors experienced with late-stage Lyme disease, which I suspect I may have.

I had the Lyme disease AB, total, W/RFX to WBbtest performed in Arizona.
The Lyme AB screen maxed out: >= 1.10 is considered positive, and my result is >5.00.
I was reactive on the 18 kD (IgG) band.
I was reactive on the 41 kD (IgM) band.
I was non-reactive on all other bands.
This resulted in a ‘negative for Lyme disease’ diagnosis.

This page has a good discussion of the bands on the Western blot.

There is considerable controversy and discussion over testing for and treatment of lyme disease: see, e.g., discussions at wikipedia.

In particular, from lymedisease.org (talking about the western blot) I quote (emphasis is mine):
Different laboratories use different methods and criteria, so you can have a positive test result from one lab and a negative test result from another. Lyme disease is known to inhibit the immune system and twenty to thirty percent of patients have falsely negative antibody tests.

I grew up in Massachusetts, and lived there again from 1999 to April 2011, when I moved to Arizona. I was very active outdoors: hiking, gardening, walking. I know I've had tick bites, because I can remember removing ticks. (In particular, in my health log I have documented, 6/1/2008, ‘tick, right butt, Karl removed’). However, I don't ever recall seeing the ‘bulls-eye’.

In November 2009 I was diagnosed with shingles. I mention this only because I've read that a rash caused by lyme disease is sometimes mis-diagnosed as shingles.

Here are my current symptoms (from oldest to most recent):

I am determined to figure out what is going on with me, and start on the road to recovery! If I have lyme disease, then I'm definitely in the ‘late persistent’ (neurologic) stage. I'm determined to get back to serious work on my Precalculus curriculum!

Friday, April 11, 2014
I've written a couple exercises for Diluting a Toxic Liquid.
Even though there are only two cases, there is quite a lot of variability built in.

Thursday, April 10, 2014
This is a very powerful movie about lyme disease: Under Our Skin

Wednesday, April 9, 2014
I've added an optional section to Precalculus,
discussing a real-life problem where the irrational number $\,\text{e}\,$ makes a surprising appearance!
Diluting a Toxic Liquid
I haven't written any exercises yet, but the concept discussion is complete.

Friday, April 4, 2014
My daughter received an honorable mention for Outstanding Interdisciplinary Development by a Graduate/Professional Student (money even!) at the University of Arizona. I'm so proud of all that she does!

We've finished the logo and main page graphic for my web site re-design. They are so beautiful! Now, I'm thinking that, instead of verbiage on the landing page, I'll have a slide show of graphics illustrating key features of my site. I've got Olga working on the first one, over 300 high-quality math lessons.

Tuesday, April 1, 2014
I updated my monthly stats and website income for March.

Wednesday, March 26, 2014
Really beautiful inspirational posters.

I need a greenhouse for wind, harsh sun, and pest protection. They're expensive! I found these DYI plans and youtube video and am tempted to build one myself.

Saturday, March 22, 2014
In my continuing quest for the ‘perfect garden system for me’ I like this Square Foot Gardening.
By the way, my sprouts and composter are doing great, and a bunch of seeds are already up (and a few have already been eaten by critters, so I clearly have to solve that problem). Also, birds have discovered our feeder and waterer, which is great.
My face has almost completely recovered from Bell's Palsy (that was the diagnosis at the Emergency Room on Sunday), but my weakness and upper back pain are still debilitating. So, I'm continuing to try and distract myself with gardening projects.

Tuesday, March 17, 2014
This is a great video showing how to use my Victorio 4-Tray Seed Sprouter.
Also, I've got my first batch going in my new NatureMill Electric Composter!

Saturday, March 15, 2014
This is a really neat DIY Cookie Basket Made from a Paper Plate; pretty, easy, inexpensive.
We just made one, and it came out great!

Tuesday, March 11, 2014
I put about 15 new cases in Solving for a Particular Variable,
after some feedback from my niece, Sarah Morley. Thanks, Sarah!

I've been experiencing debilitating symptoms for the past week and a half.
After extensive research, I think I might have the (very rare) Guillain-Barré syndrome.
The good news is that it usually goes away.
Here are some good articles: To distract myself from my pain, I've been a planting fiend! Cherry tomatoes, potatoes, cantaloupe, beans, peas, wildflowers and bachelor buttons, green peppers, cucumbers, carrots, lettuce, and more! I've constructed two self-made self-watering grow boxes; ended up buying a ‘hot knife’ to help me cut the plastic, which works okay (but is very slow).

We've also hung a bird feeder and a hummingbird feeder, and I hope the birds discover these soon. Here's a neat map that tracks the hummingbird migration.

Wednesday, March 5, 2014
I've been fasting, so have been reading about it. Here are some interesting articles:
Water Fasting for Health
What Science says about Intermittent Fasting
Water Fasting: Is it Safe?
Common Physical Reactions to Fasting

I think I'm going to try this Real Food Menu when I break my fast.

Monday, March 3, 2014
I updated my monthly stats and website income for February.

I'm studying the code for the two templates I purchased, and am coming across some good resources:

Friday, February 28, 2014
I'm so excited!! I've ordered my first illustration from Olga Dabrowska (of a cat on a swing hanging from a branch of a mathematical tree).
This will be my first business with microlancer.com.
I absolute love her work, and I hope this is the beginning of a long fruitful relationship!

Thursday, February 27, 2014
Unfortunately, things didn't work out with Godat Design. They decided that my needs exceeded my budget, so they withdrew their estimate. I am suspicious that I scared them away with too many questions. Sigh. I feel bad about this. I was disappointed, because I believe they would have done a good job for me.

Perhaps it's a bit of a blessing in disguise, because in ‘going back to the drawing board’ I came across envato.com, with their web design templates and freelancers.

I've contacted Olga Dabrowska for a possible mathematical tree.
I've contacted dabaman (Habibur Rahman) to see if he does custom web design, because I really like his Jumper and Pen-and-Paper templates.

So, I spent many hours today going through all thirty pages of freelancers showing off their portfolios. Everything just blurs together after a while. I did single out a few that I liked. How does someone actually find a service that's right for them?

Wednesday, February 26, 2014
I finished the web exercises for A Special Property of the Natural Exponential Function.

The rest of this entry is going to read like a commercial, but I just have to share!
For full disclosure—if you order this product through the link I have here, then you support my work. Thanks!

Since we moved out to the country, I've been plagued by this horrible skunk smell at the end of a nearby storage trailer. For weeks, I kept telling myself ‘it will air out on its own’. After about four weeks and absolutely no lessening of the smell, I decided to take some action.

I started doing web research in getting rid of skunk smells. I tried the spray-with-a-bleach-solution remedy, which did nothing. In the process of researching, I came across this product, ‘Odors Away’. I was extremely skeptical. But I was placing an Amazon order anyways, and it wasn't too expensive, so I decided it wouldn't hurt to try.
Oh my goodness, it works! The skunk smell is completely gone after two applications, two days in a row. I put a few drops on a piece of glass under the end of the trailer yesterday, and that helped, but didn't completely eliminate the odor. This morning, I sprinkled about 6 more drops around the area. In all, I probably used only 10 drops. I am so happy to be rid of that smell!! After about 2 months of living with skunk smell that made me nauseous (I have to go there, since it's by our outside water faucet), there was an unbelievably easy solution.

Here's another use. We're currently living in an RV while we build our eventual home across the street. Those of you with RV experience probably know that the toilets smell. There's really not much you can do, because you're basically on top of where the sewage is stored. I am super clean, and the toilet is clean clean clean, but you flush, and it smells. My husband has very bad chemical sensitivities, so I can't use any ‘traditional’ cleaning or deordorizing products, either. Well, I have now velcroed that tiny bottle to the wall by the toilet with instructions "put one drop in toilet after use". What a difference. Hooray!

‘Odors Away’ does have a citrus-type odor, but it seems to dissipate pretty quickly. Also, you have to work pretty hard to get only one drop (which is all you need) because a typical squeeze produces two or three drops. But, with some practice, you can indeed get only one drop, which will then really give you your money's worth from this tiny bottle!

UPDATE on MARCH 11, 2014:
The skunk smell has returned on various days, and I've had to re-apply some drops.
However, it is dramatically lessened from the initial smell.

I've had to give this to my daughter, since my husband (who has severe chemical sensitivities) is reacting to the citrus-like fragrance.

Changing the subject—I'm determined and inspired to not have any boring bookshelves in our new home!

Finally, this excellent comparison video for flashing-light animal deterrent technology was very influential in helping me to choose two Predator Guard units to protect my Grow Boxes (see prior day's entry) from critters. I've now spent days researching grow boxes, composting and composters, and critter repellents. I think I'm set to go!
Monday, February 24, 2014
I'm so excited about EarthBoxes (and similar self-watering ideas)!
I bought one real one for comparison purposes, and I'm enjoying going through their videos.
I intend to make lots of my own (DIY = Do It Yourself).
Here are a few sites which show a variety of DIY techniques:
Cultivating Conscience
How to build an Earthbox for $20
Container Gardening: Making your own Earthbox
Self-Watering Grow Bag
Global Buckets

This one is fantastic if I can find someone giving away food-grade 55-gallon containers!
How to Build the Ultimate Earth Box, Part I
How to Build the Ultimate Earth Box, Part II
The height saves lots of bending; the large reservoir saves lots of filling time.

Friday, February 21, 2014
I've finished the exposition for A Special Property of the Natural Exponential Function.

Tuesday, February 18, 2014
Ray and I met with Godat Design to explore giving a professional look to my web site (sorely needed).
They showed us this good site explorer and backlink checker.
This is a nice summary of reasons to switch to HTML5.
Here's a graphical summary of where major browsers are in HTML5 support.
I wanted to know if JSXGraph works with HTML5:   it does.
MathJax also works with HTML5.
Here's a good graphic that discusses SEO Friendly Domain Migration (click for bigger version).

This technique worked well to get a list of my pages that are indexed.
A bunch of old ones (that have been removed from my server) are still indexed.

Ah hah. This is why lots of my input tests aren't doing anything.

Monday, February 17, 2014
I've finished the web exercises for Introduction to Instantaneous Rate of Change and Tangent Lines.

I also archived this blog for 2013.

Tuesday, February 11, 2014
I've finished the concept discussion for Introduction to Instantaneous Rate of Change and Tangent Lines.
Web exercises coming soon!

Monday, February 10, 2014
This is a good article on pack rats: How to Get Rid of Pack Rats in Arizona
And another: Pack Rats in Vehicles

Thursday, February 6, 2014
We got our second 40 cubic yard dumpster on Monday, and it's just about full already. Yesterday, two relatives helped remove about 20 old rusty stakes (and broken-down fences) using a technique similar to this: How to Remove Metal Fence Posts or Tree Stakes.
However, we used a thick chain with a hook on the end instead of the C-clamp, and we used a solid steel pipe (about 10 feet long) instead of the two boards. Also, we put wood blocks as close to the stake as possible, between the stake and the far end of pipe, and pushed DOWN instead of pulling up. It worked incredibly well! Some of these stakes I had tried to remove (with banging and digging) for hours.

I like these two videos: three classes of levers and Physics class levers.

I'm also working on the next Precalculus web exercise, Introduction to Instantaneous Rate of Change and Tangent Lines, but don't quite have it to the point of uploading.

Saturday, February 1, 2014
I updated my monthly stats and website income for January.

Tuesday, January 28, 2014
Google has made available a new AdSense Direct campaign, where a publisher (like myself) can contract with a single advertiser. I'd like to get a reputable, professional math advertiser for my site, so I could always count on the quality and appropriateness of the ad that appears. I submitted feedback to Google to see if they are planning a system where publishers can ‘make themselves available’ for an AdSense Direct campaign, and/or find out which advertisers are seeking an AdSense Direct campaign.

Friday, January 24, 2014
I decided to change the style on my homepage.
The design that I viewed as artistic, others viewed as chaotic and unprofessional.

Wednesday, January 22, 2014
I finished the web exercises for Introduction to Average Rate of Change.

Thursday, January 16, 2014
This is a great video for the Speedy Stitcher Sewing Awl that I got for Christmas.

My computer wouldn't turn on yesterday, so I made a trip to the Genius Bar. It is comforting to know that I always have a patient, skilled, professional human being that I can talk to! I needed a new Apple MagSafe 85W Power Adapter, so it was an easy fix (but pretty expensive; just over \$80).

I started the web exercises for Introduction to Average Rate of Change.

Tuesday, January 14, 2014
My daughter posted this on Facebook: an inspiring clip of a young man with progeria sharing his philosophy of life. It is beautiful. Try hard to listen to the entire thing (almost 13 minutes).

We're getting settled in our two tiny trailers in the country, so that we can spend the next year (or so) building our home across the street. It has consumed us for weeks now, which is why I haven't worked on Precalculus lessons. But, I'm finally back to it!

I finished the exposition for the Introduction to Average Rate of Change web exercise.

Thursday, January 2, 2014
My goodness, I haven't had an entry since December 10, 2013. This is definitely a sign of how busy things have been here—we've started serious work on our country land. I now appreciate what 40 cubic yards of junk looks like!

Happy New Year, everyone!

I updated my monthly stats and website income for December, and also for 2013. It's the first time that my stats have declined—this shows the power of search engines. Whatever ‘tweak’ Google made at the end of 2012 hit me really hard. I basically lost two years of progress.

Since I'm making so little income these days, I'm discontinuing my guestbook. People who want to leave me a message can use Facebook instead. I took ‘snapshots’ of all my guestbook entries so I wouldn't lose them, and I've posted them here.

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