Finding Approximate Pythagorean Triples

CSTA Nifty Assignments 2022

Ronald Greenberg

Matthew Fahrenbacher

George Thiruvathukal

Loyola University Chicago

Niles Twp HS District 219

Loyola University Chicago

A Motivation

Diagonal transfer

of motion in a LEGO

robot

(straddle height,

expand wheelbase,

use gearing to change

power/speed.)

A Motivation

You can count

the holes to

see the side

lengths:

7, 11, 13

Haven't heard of a 7-11-13 right triangle?

Let's use the Pythagorean Theorem to check it:

7² + 11² = 49 + 121 = 170 ≠ 169 = 13²

Oops! But, actually, it's close enough that it is easy to construct with a slight deformation of the LEGO pieces.

Programming and Data Analysis

Checking triples with small side lengths to see how close they come to satisfying the Pythagorean Theorem is a good exercise in using nested loops. Then can use a spreadsheet to do things like finding the best triple for a given slope.

Programming is simple enough to do in Scratch as an integration of three units of the Exploring Computer Science high school curriculum (Unit 4: Programming, Unit 5: Computing and Data Analysis, and Unit 6: Robotics).

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Some variations

Generate and/or analyze data using other languages such as Java, JavaScript, VBA macros in Excel, UNIX shell commands, etc.

The next slide provides examples of graphical representations of the data generated using JavaScript.

Absolute error or error for different leg lengths