# Wild About Math!Making Math fun and accessible

18Nov/0710

## The 7 top free Math homework help sites

This article presents the best resources I know of for free homework help with helpful background information for each. As you read on you'll see that there's something for everyone on this list, everything from help with kindergarden and elementary school Math to help with very advanced mathematics.

My intent when preparing to write this article was to find 10 really good Math homework help forums but, after doing a fair amount of research, I only found 7 that met my standards. Before listing them I'll share my criteria for site selection, and some etiquette tips that will get you or your child better help faster. And, I'll give some cautionary information for kids about being safe on the Net.

17Nov/073

## Math contest problem page created

I've created a new page, Math contest problem links. It lists a number of contest sites. Some of the pages have links to lots of other sites. I'll list more as I discover them.

The impetus for this page is that I like to sometimes find an interesting problem to chew on without having to spend time Googling for Math contest sites. I tried, whenever possible, to link to the page that has problems on it, not the home page for the site. So, hopefully I'll save everyone some searching and clicking.

Filed under: Math contest 3 Comments
17Nov/077

## The amazing volume formula

More Fun With Mathematics by Jerome Meyer is a nice little book of interesting Math explorations. It's out of print but Amazon has a few very inexpensive used copies available. In the book I discovered this very odd volume formula that I've never seen before and couldn't find via Google. The author calls the formula "The Amazing Prismoidal Formula."

The formula states the following for any regular solid:

V = H*(B+4M+T)/6

where:

V = volume
H = height
B = area of the base
M = area of the middle of the solid
T = area of the top of the solid

Take a cube with side = 2 as a simple example:

H = 2
B = 2^2 = 4
M = B = 4
T = M = B = 4

V = H*(B+4M+T)/6 = 2*(4+4*4+4)/6 = 8, which is 2^3.

Use a cone with a base of radius r as another example, ignoring for the moment that it's not a regular solid. We'll get back to that.

H is not fixed. It can be any value.
B = pi*r^2
M = (pi*r^2)/4 since the radius of the circle in the middle is 1/2 of the radius of the base
T = 0

V = H*(B+4M+T)/6 = H*((pi*r^2) + 4*(pi*r^2)/4 + 0 )) /6 = (H*pi*r^2)/3, which is the familiar formula for the volume of a cone.

Meyer claims this formula works for any regular solid. Well, I think of regular solids as the 5 platonic solids. Meyer has illustrations of a cube, cone, cylinder, sphere, and conic frustrum (truncated cone).

I tried his formula on a tetrahedron and it works. I could not get it to work for an octahedron but that might have been an algebra mistake on my part. As the number of sides of the regular polygon increases determining the height and the area of the middle becomes more difficult.

An interesting exploration would be to determine for what solids, regular or not, does this formula work.

Filed under: Algebra, Geometry 7 Comments
16Nov/070

## Chuckle: Completely off topic

Driving in town the other day I saw this great sign on the back of a car:

Wedding Cake Onboard

15Nov/071

This article provides a set of tips for raising your awareness of learning styles as a major factor in how children learn. These tips are adapted from the resources listed at the end of this article.

The tips are based on the Dunn & Dunn Learning Styles Model developed by Professors Rita and Kenneth Dunn to assist the New York State Department of Education in improving the effectiveness of instruction for students not demonstrating sufficient progress. The model is based on 20 elements, divided among five categories (called stimuli in the model), that affect learning. Use of the model has been statistically proven to improve student performance.

The model's five stimuli are environmental, emotional, sociological, physiological, and psychological. A nice illustration of the stimuli and elements is here. A very similar model, the Learning Styles Pyramid Model is illustrated here.

The first half of the tips are not specific to Math and apply to a broad range of learning situations. The second half are Math-specific.

15Nov/070

## Math bloggers: Let’s exchange reviews

If you've got a Math-related blog and would like for me to review your blog in exchange for a review of mine please leave a comment with this message including contact info if your blog doesn't have a way to contact you. I ask that your review be honest, fair, and kind. Tell what you like, what you don't like, and what can be improved. I'll do the same.

There are several dozen (maybe more) active Math blogs out there and I'm sure we'd all like more readers. The more we link to one another the more the Math blog community grows and benefits all of us.

If I get a lot of responses then I'll spread out my reviews over time to avoid saturating this blog with reviews. If I get no responses then I'll just review the blogs I like!

Oh, and if you're not in my Blogroll and want to be, let me know as well and please add me to yours if you find this blog to be of value.

14Nov/071

I have to admit, history has never been one of my strong suits. That's because I don't have a memory for details that are not relevant to my life. However, I realize that some people like, even love, history. And, from my study of Gardner's multiple intelligences I also get that folks with interpersonal intelligence learn things much better if they can relate to the people and events associated with what they're learning.

At a used book sale last weekend I picked up a copy of Agnesi to Zeno by Sanderson Smith and it has very quickly become one of my very favorite books. Why? It contains 108 vignettes from the history of Math in a very visually appealing and very engaging way, with fun explorations.

I'm very sensitive to presentation and layout of material I read. The best stuff I read has lots of white space, attractive layout, illustrations, and a nice flow to the page. This book has it all.

What about the content? Very engaging. Each vignette has a one page description, a set of activities, and suggestions for related reading.

Some examples from the book:

Vignette 83: Counting and computing device. This vignette touches on devices, from fingers, to the abacus, a Greek mechanical computer, the Inca Quipus, Napier's bones, the slide rule, Pascal's adding machine, Babbage's difference engine, and Hollerith's data processing machine. References are provided to other vignettes within the book that also discuss and explore counting and computing devices. Explorations of finger arithmetic (Chisenbop) and use of the abacus are suggested.

Vignette 77: Schools of Mathematical Thought. Three important schools of mathematical thought are introduced, the Intuitionist School, the Logistic School, and the Formalist School. Mathematicians and philosophers are mentioned: Brouwer, Kant, Russell, Whitehead, and Hilbert, and readers are invited to research their lives and contributions. Readers are introduced to paradoxes in mathematical structure and encouraged to explore how the Logistic School dealt with them.

Vignette 78: Grace Chisholm Young: Versatile and Prolific. This is one of quite a number of vignettes that highlight the contributions of women to mathematics. Young, who I have to admit I had never heard of, collaborated with her husband William Young, on more than 200 articles and books. In 1905, she published a geometry book that included many three-dimensional paper-folding activities. From 1914 to 1916, she presented and developed theories and concepts in differential calculus. This is even more impressive given that the establishment did not support women attending university. Despite this obstacle, Young became the first woman in Germany to earn a PhD in mathematics. Impressive!

I highly recommend this book to educators, parents, home schoolers, students, and adults, all of whom might benefit from a historical context to things mathematical.

Filed under: Book Review, History 1 Comment
13Nov/074

## First ever Wild About Math! contest

Hi everybody,

Here's a nice little problem I found in a book, published in 1967. I won't give away the source until the contest is over.

This contest has just one question. The first person to write a comment with the right answer plus a justification of the answer, gets glory on this blog and the admiration of many. Here's the question:

If a millionaire offered you your choice between a barrel filled with half dollars and the same barrel filled with dimes, which would you choose?

Glory and admiration aside this question makes for a nice exploration for children (and adults).

Enjoy!

12Nov/0712

## Need an excuse for not having done your Math homework?

Computer Scientist, Ph.D. Mathematician, and International Math Olympics Gold Medalist Tanya Khovanova has a nice page of unique Math humor.

What caught my attention, in particular, was her list of 10 reasons her kids have given for not doing their Math homework. Even if you don't understand the higher Math behind some of the jokes you should still get a chuckle out of them.

1. I had a constant amount of homework. I tried to derive its purpose, but I got nothing.
2. I assumed that all the homework you assigned me was Abelian, so I thought that I could pass it in and then do it.
3. I could only get arbitrarily close to my textbook, but I could never reach it.
4. I am sure that I put it inside my Klein Bottle last night, but this morning I could not find it.
5. I locked it in my trunk, but a four-dimensional dog got in and ate it.
6. My little sister cut it into a finite number of pieces, and when I put it back together, I got a proof of the Banach-Tarski Paradox.
7. I did part of it; the part I have left to do, is 0.999999999...
8. My homework is a constructive demonstration of Godel's Incompleteness Theorem. That is, it is possible to assign a homework that cannot be completed.
9. I wanted to, but I couldn't find its Godel Number.
10. I completed my homework, but then I beheld it and saw that it lacked character, personality - there was no "me" in it, so I multiplied it by i, and it became imaginary!

Slightly off topic, but also quite funny, is also a list of 7 reasons her kids have given for not having done their Physics homework.