Using Equation Support and Napkin Math in Onenote to solve a real world puzzle

I was thinking about getting a larger laptop with a much larger screen than my current tablet. At first, I naively thought the manufacturers would publish the screen size of their laptops. Naturally they don't - they only publish the diagonal measurement of the screen. Thinking back to high school trigonometry, I first thought I was stuck. To solve a triangle, I need to know at least one side length and two angles, or two sides and one angle, or all three sides. It didn't appear I had enough information to find out how big the screen was. I thought a little bit more and realized that since I knew the ratio of the width and height was either 4:3 or 16:9, I effectively knew all the angles of the triangle, and had the hypotenuse. I still had to perform a little math, and here is what I did. First, I tried using the Windows calculator, and that was taking far too long. I grabbed a scrap piece of paper and a pencil next, but then realized I could do all of this in OneNote after reading this article on slashdot.

Thinking a little bit more about this scenario, I figured this would be a nice end to end scenario for using both the "napkin math" feature in OneNote and our new Equation support in OneNote 2010. I also used Word to help format some of this, so here goes with a new testing scenario.

First, I figured out the height and width of my current 12.1" diagonal tablet monitor.  (I use Live Writer for this blog, and it converts math to images.  Bear with me, please).  Note: this is corrected as of Nov 3, 2009.

So at this point, width is 9.6 and height is 7.25. 7.25*9.6=69.6 square inches (napkin math!) for my 4:3 ratio 12.1" diagonal monitor. Since I did this step in Word to see compare their editing experience to ours, I can't show the napkin math to compute the square root of 52.5, or the computing of 'a' two lines below.

Now repeat for a 16:9 ratio and 17.3" diagonal screen. I'll leave out the redundant steps, and switch to OneNote to enter these equations.

The height and width of the larger screen is 14.9" and 8.4" respectively. The total screen size is 14.9*8.4= 125 square inches. Maybe it is not apparent, but that equation was solved with napkin math.

This is almost twice the size of my current monitor! 125/69.6= 1.85 times larger, to be more precise.

The experience between Word and OneNote was very similar for entering the equations. Having napkin math to quickly solve some of these was very nice in OneNote. Teachers, feel free to use this as a lesson plan :)

Questions, comments, concerns and criticisms always welcome,

John