Iowa Caucus Statistics in Albuquerque Journal

I am always looking for good examples of statistics or geometry to use in class with an eye for misrepresentations of the math that might lead people to make incorrect assumptions. Tuesday's paper (Feb. 2, 2016) offered coverage of the results of the Iowa caucus and also provided an excellent opportunity for us to explore how the results were displayed to the readers of the Journal. Indeed, election year media coverage seems to always provide good material for me to use in class.

This is not meant to be a partisan blog; both sides of the aisle are guilty of misrepresenting the truth.  News media, however, does tend to be particularly biased in their reporting.  HOWEVER, if the readership is savvy and informed, the presentation of "facts" backfires. People tend to get irritated when they think they are not being told the truth.

So the above image appeared on the Front Page (FRONT page, mind you) of our own Albuquerque Journal. Based on the image, you'd think that Rafael "Ted" Cruz had won the primary in Iowa by a landslide -- after all, look at the size of his circle compared to those of  DonaldTrump and Marco Rubio.  I'm glad they printed the percentage of votes right there so I don't have to look them up.  Let's do some math.

I pulled the image into Geometer's Sketchpad and measured the radii of the three circles representing the votes for each of these three republican candidates.

We can then find the approximate areas of the three circles.  Cruz: 87.9 square cm; Trump: 17.5 square cm; Rubio: 16.6 square cm.  Senator Cruz appears to be cruising, with his image covering an area just over 5 times that of Trump's image and nearly 5 and 1/3 times that of Rubio's image.

But reality?   Look at the percentages of the votes received.

First of all, notice that 28%, 24% and 23% do not add up to 100%.  We are missing 25%.  How did that 25% vote (likely for other candidates)?  We don't know from this front page image. Also notice that 28%, 24% and 23% are not that far apart. Furthermore, Cruz did not win a simple majority (that is, more than 50% of the vote.) Numerically, this does not particularly look like a landslide.

Of the 75% of the votes represented by these three circles, Cruz earned 37% of those votes.  Trump and Rubio earned 32% and 31%, respectively (notice my 37, 32, and 31 sum to 100% of the 75 percentage points). Cruz earned nowhere near 5 times the votes of Trump.   No landslide here, either.

So the newspaper was interested in having people believe, on some level (perhaps even unconsciously), that Cruz won by a wide margin.  Might that bias affect what the readers think or or what they might perceive their peers in Iowa think?  We can debate that until the cows come home.  But this visual image seems to misrepresent the success of Cruz: it was actually a pretty close election.

Your blog can take one of several routes.

1. Find something else that's mathematically misrepresented in the media.  Anything.  And explain why the data is misrepresented.  You'll need to show an image and complete an interpretation of what's incorrect and perhaps how the information should have been represented.

2.  Explain my geometry.  How did I construct the exact center of each circle?  (I did NOT just guess!)  Then how did I find the area of the circles?  Why did I use ratios of area and not ratios of radii?  How might the numbers have turned out it I had compared radii? Find those values and interpret.   Is the ratio of the radii the same as the ratio of the areas?

Why Mathematicians find math thrilling.

Why mathematicians find math thrilling. 

great article/ted talk.

Algebra II/Trigonometry: Applications of Parabolas/Quadratics: Due Monday, November 16, 2015

Many of you have seen or played with the whispering discs on the east side of the science building.  How many of you know how they work?  Their unique parabolic shape helps to focus sound.  The following 4 min video discusses how a parabola directs sound.  Please watch this lovely illustration and explanation.

While we've studied quadratics a lot, we never seem to do enough applications.  In this blog, you will search the internet for applications.   Find at least one. If you discuss one, discuss in detail and well. If you discuss two, then you can write less about each.  Here are some hints:

So your job is to not just say, hey, it's a projectile path.... or hey, a parabola is the shape of those whispering things... your job is to explain why this is a parabola.  Find something about the FOCUS, or the LATUS RECTUM or the DIRECTRIX.  Explain something NEW about the parabola. Below is a hint. Ask Purple Math or Khan Academy to help you out with this.  I found HOT MATH to be the simplest explanation. 

Beware of catenary arches posing as parabolic arches. When you google "parabola" you'll find images of catenary arches. Be sure you are familiar with what those arches are before you write about them in your blog.  OR..... Write a blog about catenary arches.  What are they?  How are they formed?  They are kind of cool.  

Also beware of semicurcular Roman Arches.  These are not parabolic either.  In short, be careful about your choices. While you can use a parabolic model to fit catenary and semicircular shapes, this blog asks you to be more accurate mathematically and theoretically.  There's some bad information out there on line! 

Someone who understands the difference between catenary arches in architecture and parabolic arches in architecture is Ivars Peterson in his blog, The Math Tourist.  

Algebra II/Trig. NYT: The Importance of Recreational Math

You've heard me say, "Math used to be cool," or "It used to be cool to study math."  Some people still believe that doing math is cool -- some people don't recognize that some of the cool stuff they are doing is, indeed, math. And, well, you know, math is still cool.  Sometimes, perhaps we just make it into a process that we've come to call "math," but it's not really math.

Read this article from the New York Times.

Follow one (or more) of the links in the article, or simply google "Vihart."

Here are a couple links to Vihart pieces you might find entertaining:

Hexaflexagons. 

Elephants. 

I hope this is fun for you; please keep asking yourself the "Why?" or "How?" questions so you can delve a little more deeply into your blog.  Find something fun or interesting and write about it.  Let is be recreational!

Everyone: Symmetry, Palindromes and the year 2015. Due April 15.

Symmetry is a topic we look at in many areas of mathematics.  We've seen even functions, odd functions, and relations symmetric to the x axis. Because of the elegance, simplicity and beauty of symmetry, we are drawn to symmetric objects and ideas.  

 Palindromes represent a kind of symmetry; they read the same way forwards as backwards.  When written in binary form, 2015 is a palindrome: 11111011111. Even better, when factored completely, 2015 can be written as a palindromic number: 13*5*31. This won't happen again for another 30 years.

Some other non-numeric palindromes: 

race car;  

A man, a plan, a canal, Panama; 

Madam, I'm Adam.

And my all-time favorite:

Go hang a salami I'm a lasagna hog. 

Your task for this (hopefully) fun blog, is to find TWO new palindromes that are interesting. One MUST be a numeric palindrome with some interesting characteristic that is not just the symmetry, the other can be any kind (a word or a phrase or a number with an interesting characteristic).  Feel free to search the internet, but credit your sources.  Feel free to make up your own.  Explain the symmetry, say why it's interesting to you.  Describe the characteristics of your palindromic number.  

3-D Polar Graphing. Q4 Blog 1 Due March 20, 2015

You saw the basics of two dimensional polar graphing.  Che asked if there was a way to graph in 3-d in polar form.  There's a couple ways that you'll consider in Calc 3 in college, and there's a way you can think about it now.  Some of you actually use this all the time.

First, in Calc 3, you'll be using integrals to find cylindrical coordinates or spherical coordinates.  Cool stuff that you can see down the road.  Have a look at the links.

But here's an idea for you that's a commonly used and known form of three dimensional polar graphing. 

So look at this interesting form of three-dimensional graphing that we all have some familiarity with. After you look at it and consider it, then look at the task below (The following questions/ideas won't make sense if you haven't yet followed the link above headed "three dimensional polar graphing")

Your task in this blog:

1. Find the three-dimensional polar coordinates of some places that you've either visited or would like to visit.  Find the coordinates of "home."

2. There are some lines called "meridians" -- or some lines that have some important significance.  What are these and how are they used?  Have you ever crossed any?  What happened (if anything....)

3.  Your choice.  Find something interesting relating to this idea (and math) that you'd like to read and write about.  Have fun.

Jobs that Didn't Exist 10 years ago and GOOGLE.

So, one of the ideas I  keep bringing up in class is that the jobs that will be available to you -- jobs you'll hopefully love, find inspiring, lucrative, satisfying, and a big part of your life -- don't currently exist.  Indeed, many of the jobs held by young Americans NOW didn't exist when they were in high school or even college. Some examples: analyst of marketing data (did people purchase from your company using an iphone, computer, or store for example?); marijuana packager in Colorado; APP developer; sustainability director.)

So how do you prepare for these jobs that don't exist?  How did other folks who now hold these brand-new job opportunities develop the skills they use in their current jobs?  Great questions.  I'm convinced you just need to develop good, clear thinking skills, organizational strategies, and good habits of mind.  You can start working on those now; they are universal skills.

So, for this cycle's blog, there's two options.

The first: think about these "new" jobs that include math skills. Look around, or GOOGLE something to see if you can find a job that definitely did not exist 5 or 10 years ago. Please don't repeat those ideas shared already in class -- come up with your own NEW idea.  Describe that job, the skills necessary, and hypothesize how folks developed those skills to be able to do those jobs.

The second: read this powerpoint written by some of those great brilliant and creative geniuses from GOOGLE itself.  Find some cool, novel way they used math in their GOOGLE product.  There's lots of links provided in the presentation. You might not know what linear algebra is, but feel free to surf to learn something about different areas of math, such as linear algebra.  Find something appealing to you -- surely you can find something that rocks your boat in this presentation.  (How about that phrase, "rocks your boat" ?  It's a combo of "Rocks your world," and "Floats your boat."  Somehow, it seems to work better for me than both of the two more traditional phrases.)

Be sure your blog on this topic is substantive.  Write more than one 4 sentence paragraph. Develop an idea.  Be thoughtful and meaningful. You'll begin to lose points on your blog grade if you're  too brief or flippant or write too much fluff.  Make this fun and interesting for yourself and choose something that you think is cool and that you can expand upon. There are lots of options.