Super Safi’s Monday Morning Math Mayhem 19 – Polygons, Hypotenuse, and Euclidean algorithms

Morning Mathematical Monsters & Maniacs!

(Today’s post is sponsored by the letter “M”)

Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.

Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.

And what better way to start your week, then by discussing math Monday morning?

With Krusty’s Last Gasp underway, many of you are in the process of unlocking Sideshow Lisa. So this week in Monday Morning Math Mayhem, we honour Lisa by looking at her favourite subject – arithmetic.

In Bart’s Dog Gets an F (Season 02, Episode 16), Lisa is sadder than a sad clown, as she has developed the mumps. Marge takes her to see Dr. Hibbert. During their conversation, Lisa informs Dr. Hibbert that arithmetic is her favourite subject. Dr. Hibbert than reassures her with the following quote.

Dr. Hibbert:  “[Chuckles] Arithmetic.  Now before you know it, you’ll be back among your polygons, your hypotenuse and your Euclidean algorithms.“

Let’s look at these terms used in arithmetic:

Polygons

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit. The segments of a polygonal chain are called its edges (or sides), and the points where two edges meet are the polygon’s vertices (or corners).

Common examples of polygons include triangles, quadrilaterals (like squares and rectangles), pentagons, hexagons, and octagons.

Hypotenuse

Hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. As we discussed earlier when discussing the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the two opposite squares.

In the diagram of the right triangle above, c is the hypotenuse of the triangle, as a and b form a right angle. We can calculate the hypotenuse c using the Pythagorean theorem.

Euclidean algorithms

Euclidean algorithms is an efficient method for computing the greatest common divisor (GCD) of two numbers. The GCD is the largest number that divides both of them without leaving a remainder. The Euclidean algorithm is based on the principle that the GCD of two numbers does not change if the larger number is replaced by its difference with the smaller number. As an example, the GCD of 16 and 12 would be the same as the GCD of 12 and 4 (16-12).

Euclidean algorithms date back to 300 BC, when Greek philosopher and mathematician Euclid described them in his work Elements.

Let’s workout a Euclidean algorithm using Ned Flander’s bank pin number 5316 and Homer and Santa’s Little Helper’s birthday of May 10th, or 510.

So to calculate the GCD of 5316 and 510, we start by calculating how many times 510 can go into 5316 and how much remainder is leftover.

5316 = 10 x 510 + 216

Next we calculate how many times that remainder 216 can go into 510 and how much remainder is leftover.

510 = 2 x 216 + 78

So next we calculate how many times that remainder 78 can go into 216 and how much remainder is leftover.

216 = 2 x 78 + 60

We keep going until the remainder is 0. So this would keep going as follows:

78 = 1 x 60 + 18

60 = 3 x 18 + 6

18 = 3 x 6 + 0

So based on the last calculation that got us to remainder of 0, we can determine the 6 is the GCD of 5316 (Ned’s bank pin) and 510 (Homer and SLH birthday).

Now that we’ve taken a look at Lisa’s favourite subject, hopefully you have a better understanding of these three mathematical concepts.

Were you familiar with any of these concepts? Did you remember Dr. Hibbert’s line in the episode? What was your favourite subject in school? Sound off in the comments below. You know we love hearing from you.