Christmas and Maths

Being the nerd that I am, there are just tons of things that we can relate numbers to in holidays. Christmas is coming up and there are a plethora of number related fun that we can have like the probability of obtaining a certain present, estimating the price of a present (taking into account the Christmas "sales" that were present at the time), or the usual estimation of the speed of Santa based on the weight of presents using statistics of popular "wished for" gifts of the year along with average reindeer speed, wind resistance, entry/exit house time, etc.

There is quite a list of things you can do this holiday season, but one that I stumbled upon was this one:

12. Unwrapping Gifts (and Math)

Well, I doubt that anyone will be in the mood, but here goes!

1. Determine the probability that Dad gets a tie.
2. Estimate and time how long it takes to unwrap all the presents.
3. Compare and contrast this with how long it took to wrap them.
4. Chart the number of gifts received versus those given.
5. Estimate and weigh the bags of recycled wrapping paper.
6. Explore nets with the extra boxes, and measure them using cubits.
7. Sort your gifts into Venn diagrams and make a pie chart to illustrate your findings.
8. Line up all the Christmas chocolates into arrays; sort, group and put them into sets.
9. Use the leftover ribbon to explore topology and create a gigantic mobius strip.
10. Try to build a rhombicosidodecahedron out of the recycled wrapping paper or just take a short break from math.

They have more Christmas maths you can do here: http://homeschooling.gomilpitas.com/articles/121106.htm

Fun stuffs!

Theory: Asymptotes and Negative Space

Recently, I've been working with some graphs and the many different types of lines that we can have fun with like hyperboles and parabolas. But among these I start to think about Asymptotes. I think it's a pretty interesting word that has very little use in everyday conversation (unless you are into analytical geometry or something). What is an Asymptote? In a nutshell: An Asymptote is a line on a graph that the graph will never intersect as it approaches infinity. Asymptotes are the DO NOT CROSS lines of graphs with curves.

Image of an Asymptote from Wikipedia

After thinking about it for a little bit, I came to think that an Asymptote is the Negative Space of a graph. Negative Space in a nutshell (from a Graphic Design perspective): The space where content is not usually located around the content. Breathing room, if you will. Negative Space is one of those things that I am interested in as it allows me to view graphic images in black and white creating something I could easily translate into a graph.

Taiwan recycling logo displaying use of Negative Space

While Asymptotes generally deal with graphs that contain curves and you can't guarantee that all your designs will have some crazy curves or parabolas, I imagine that for those designs that do use curves, knowledge of Asymptotes could improve the synergy of your design between the content and it's Negative Space. How? I'm not sure yet, it's just a theory, an idea that came into my mind out of nowhere. But I think that it's worth at least putting out there for a few minutes of thought.

Turkey Day in Numbers

It's Thanksgiving so here is an interesting list of the numbers of turkey day. Source: http://www.infoplease.com/spot/tgcensus01.html

242 million 
The number of turkeys expected to be raised in the United States in 2010. That's down 2 percent from the number raised during 2009. The turkeys produced in 2009 together weighed 7.1 billion pounds and were valued at $3.6 billion.

Weighing in With a Menu of Culinary Delights

47 million 
The preliminary estimate of turkeys Minnesota expected to raise in 2010. The Gopher State was tops in turkey production, followed by North Carolina (31.0 million), Arkansas (28.0 million), Missouri (17.5 million), Indiana (16.0 million), and Virginia (15.5 million). These six states together would probably account for about two-thirds of U.S. turkeys produced in 2010.

735 million pounds 
The forecast for U.S. cranberry production in 2010. Wisconsin is expected to lead all states in the production of cranberries, with 435 million pounds, followed by Massachusetts (195 million). New Jersey, Oregon, and Washington are also expected to have substantial production, ranging from 14 million to 53 million pounds.

1.9 billion pounds 
The total weight of sweet potatoes — another popular Thanksgiving side dish — produced by major sweet potato producing states in 2009. North Carolina (940 million pounds) produced more sweet potatoes than any other state. It was followed by California (592 million pounds) and Louisiana (162 million pounds).

931 million pounds 
Total production of pumpkins produced in the major pumpkin-producing states in 2009. Illinois led the country by producing 429 million pounds of the vined orange gourd. Pumpkin patches in California and Ohio also provided lots of pumpkins: Each state produced at least 100 million pounds. The value of all pumpkins produced by major pumpkin-producing states was $103 million.

If you prefer cherry pie, you will be pleased to learn that the nation's forecasted tart cherry production for 2010 totals 195 million pounds, albeit 46 percent below 2009's forecasted total. Of this 2010 total, the overwhelming majority (140 million) will be produced in Michigan.

2.2 billion bushels 
The total volume of wheat — the essential ingredient of bread, rolls, and pie crust — produced in the United States in 2010. North Dakota and Kansas accounted for 33 percent of the nation's wheat production.

736,680 tons 
The 2010 contracted production of snap (green) beans in major snap (green) bean-producing states. Of this total, Wisconsin led all states (326,900 tons). Many Americans consider green bean casserole a traditional Thanksgiving dish.

$7.3 million 
The value of U.S. imports of live turkeys from January through July of 2010 — 99.1 percent from Canada. When it comes to sweet potatoes, the Dominican Republic was the source of 62.1 percent ($3.4 million) of total imports ($5.5 million). The United States ran a $3.9 million trade deficit in live turkeys during the period but had a surplus of $31.5 million in sweet potatoes.

13.8 pounds 
The quantity of turkey consumed by the typical American in 2007, with a hearty helping devoured at Thanksgiving time. Per capita sweet potato consumption was 5.2 pounds.

The Turkey Industry

$3.6 billion 
The value of turkeys shipped in 2002. Arkansas led the way in turkey shipments, with $581.5 million, followed by Virginia ($544.2 million) and North Carolina ($453 million). In 2002, poultry businesses whose primary product was turkey totaled 35 establishments, employing about 17,000 people.

$4.1 billion 
Forecast 2010 receipts to farmers from turkey sales. This exceeds the total receipts from sales of products such as barley, oats, sorghum (combined) and peanuts.

The Price is Right

$1.33 
Retail cost per pound of a frozen whole turkey in December 2008.

Where to Feast

3 
Number of places in the United States named after the holiday's traditional main course. Turkey, Texas, was the most populous in 2009, with 445 residents, followed by Turkey Creek, La. (362), and Turkey, N.C. (272). There are also nine townships around the country named Turkey, three in Kansas.

5 
Number of places and townships in the United States that are named Cranberry or some spelling variation of the red, acidic berry (e.g., Cranbury, N.J.), a popular side dish at Thanksgiving. Cranberry township (Butler County), Pa., was the most populous of these places in 2009, with 27,560 residents. Cranberry township (Venango County), Pa., was next (6,774).

28 
Number of places in the United States named Plymouth, as in Plymouth Rock, the landing site of the first Pilgrims. Plymouth, Minn., is the most populous, with 72,849 residents in 2009; Plymouth, Mass., had 56,842. There is just one township in the United States named "Pilgrim." Located in Dade County, Mo., its population was 126 in 2009. And then there is Mayflower, Ark., whose population was 2,257 in 2009.

117 million 
Number of households across the nation–all potential gathering places for people to celebrate the holiday.

Read more: Thanksgiving: Census Facts — Infoplease.com http://www.infoplease.com/spot/tgcensus01.html#ixzz16LlLkEXe


And just for my amusement and your curiosity (you numerologists, you), the sigma value of all the bold numbers is 8!

Textbook Rage

With all my ramblings about how some math and science content is really boring looking, I decided to look for some answers. I came across an article in The Faster Times that contained an interview with a textbook "professional." While the article is a bit lengthy, there was one section that really caught my attention:

KM: Doesn’t creating a textbook require specialized knowledge? Do you mean that anyone can do it, like learning to operate the espresso machine at Starbucks?

TP: Interestingly, you would think that highly skilled educators, historians, etc. would be required, but given the detailed format provided by adoption committees, making a textbook is like filling out a complex form. You need professionals, but you don’t need good writers, much less educators. That has been taken out of the hands of the publishers (and to their minds, good riddance). When textbook adoption committees tell you EXACTLY what you want, what you need is a task force that can fill out the form. That still takes skill, but not creative skill. Except to the degree that if you really did do it just as they asked, the result would be embarrassing.

To put it at its most drastic, these books are intended as crib sheets so students can pass standardized tests. The better their scores on these tests, the higher the rating of the schools they attend. The higher the school rates, the higher the real estate values go in the community that pays the taxes for the schools. Everyone wins when the students score high. The icing on the cake? The same publishers that make the textbooks do the testing! Now REALLY everyone wins. Except nothing is more tedious or conducive to high drop out rates than the tedium of cramming for tests, and the inevitability of failure for students who don’t do well on them. In Edison schools, kids who don’t perform well are actually excluded from taking the tests, to raise the average. These kids are classed as learning-disordered. This is the heart of the matter: Education that becomes all about testing becomes a factory. The best and the brightest, generally, will not do well in this environment. The more standardized this system becomes the more of these bright students will be carved out of the process, or lose their marbles.

Now I've highlighted the important parts in bold as most of you are accustomed to in educational textbooks. So if a professor wants to put some content into a math or science textbook, all they would have to do is fill out a form? Then a machine processes it and spits out a mediocre looking book but at least it has all your information in it right? But how well will your information get to your intended audience if it has no design to appeal to them? Sure your book may have 700+ pages but having a designer go through and applying at least the minimal amount of negative space, tracking, leading, etc. can make your book at least 700 times better! (Assuming 1 better page adds to the better whole of the book)

Math, they don't like it. FIX IT!

So I'm reading news again: http://www.nytimes.com/2010/11/07/education/edlife/07books-t.html?_r=1&ref=mathematics

This is an article, by Kenneth Chang, in the New York Times about how Math is "hard". While most of the article supports the beginning statement of "MATH is not an easy subject." there is some information about what some people are doing to fix that. What caught me about this article though, is some of the statements such as the following:

"Mathematics is, in itself, an exercise in the abstract — twiddling funny squiggles on paper, really, which is fairly pointless except to mathematicians. It’s when math is applied to the universe that the mental game becomes something useful. Budgets can be balanced, bridges designed and laws of physics deduced. So good math education is in society’s best interest."


I'm sure this is not the only place where you can find something that says "Math is pointless." But the wording of it made me think...well this can apply to various studies because when you think about it, everything is kind of pointless unless it applies to something we are familiar with.  For example, I'm going to reword it:


"Graphic Design is, in itself, an exercise in the use of type and imagery - changing font size, crafting or manipulating imagery and communicating information visually is all pointless except to designers. It's when design is applied to things such as advertising or marketing that the creative process becomes something useful. More products can be sold, messages get visual interpretations in an image-based culture, and a little bit of information can have a huge impact. So good design is in society's best interest."


Now, I didn't do that to be mean, but just to prove a point. For the most part, I side with the article when it says that things should change about the way we teach mathematics. While I am not a huge fan of the books exampled within the article because of how silly they seem to me because they were not exactly written for a person like me, I applaud them for reaching out to various audiences and doing its intended job with some success.


The reason why I like to rant about articles like this is because I too believe that math can be taught better yet my methods would involve bringing the power of information transferring that is Graphic Design. People like and are influenced by good design whether they realize it or not. But based on some discussions I've had with some math folk, they are on the same boat of not knowing lickity-split about what Graphic Design is and that's fine. But if they did and are able to harness the power of it, those Algebra II books would definitely be a lot easier to read.

Cure for Phobia?

There have been quite a few articles about how researchers have found a way to improve math skills in humans by sparking an area of the brain. I read the article first here: http://www.digitaljournal.com/article/299922

So I suppose in the future there would be no excuse for "not understanding" something about math. If this were to really enhance mathematical skill though, imagine the combinations for various professions! Aside from Math and Graphic Design, which I already know is more useful than many think, we could have Super Math Journalists or Super Math Judges! (Boy it was difficult to think of professions that didn't seem to use math that much.) But of course the main target of this research were those who have "degenerated" in their math skills or have a mental disability such as dyscalculia.

Eventually, with more studies like this, the world will come to at least respect mathematics and the capabilities of it rather than fear it, as has been the case for centuries.

Curious PDFs

While doing some math work, I was rummaging through some Google links and came across a particular PDF document. I was looking up some information about regression analysis and this particular document caught my eye. Why? Because it looked different than all the other stereotypical documents about math that you could find. (Things like TIMES NEW ROMAN and total disregard of negative space, tracking, leading, etc.)

The document can be found here: http://www.math.tamu.edu/~maggie.mcgrath/Math142/math142regressionexamples.pdf

Now I'm not pointing out any superiorities it has over standard math documents, because it has obvious design flaws. But it at least tries! The font is easily not recognized as the standard textbook Times New Roman (which IS a nice font, but through overuse it kind of loses a lot of it's classy flare.) and they attempt some forms of hierarchy with their headings. The font here looks similar to a Century type of font, but unclear of what it really is.

Compare that document to this one, also about regression but different content somewhat: http://www.ltrr.arizona.edu/~dmeko/notes_11.pdf

I've opened it up in Acrobat and confirmed it's use of Times New Roman. Also, the paragraphs feel squished together, another similarity to a stereotypical document, which when combined with the functions and equations written has a very high probability of leading a reader to the conclusion of: Blah blah blah.

I bring this up because I currently possess a mathematics textbook that, compared to the previous textbook, is so difficult to read because of poor design choices. And it was even published later than the previous textbook! (2009) That just makes things even worse. Some would argue that the important stuff is the content and the learning. But take it from a Graphic Designer that people will learn a lot better when they pay more attention to your "content" because it looks better.

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