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Husband, father, inline skater, cycling and triathlon athlete and sometimes coach, graduate civil engineer, commercial and residential and commercial Broker Realtor® working in Ellum, Expo Park, Munger, Peak Suburban, PD 98, PD 269, Swiss Avenue, Baylor PD, all of in-town east Dallas, former home building land acquisitions executive, home builder, home designer (chief architect X3 design solutions), LEED Green Associate (GA), NAHB Green Professional (CGP), NAHB Graduate Builder (CGB), Universal Design and Accessability student and Certified Aging in Place Specialist (CAPS), Advanced Historic Home Specialist certified by Preservation Dallas..........EdgyDad is Biff Bailey of Dallas, Texas

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Homer's Conjecture

Is Homer correct? How about the Man in the Stall? Can you prove? Refine what you know about triangles by following this Pathfinder.

Last Update: 2012-07-10 06:38:38

Triangle Pathfinder

Overview:  Research and write a critical analysis paper about the conjectures about Right and Isosceles Triangles made on the animated TV show Homer Simpson.

Essential Question: (10 point, Arial)

Consider the following from a scene from $impsons Episode: $pringfield (Or, How I Learned to Stop Worrying and Love Legalized Gambling) (1F08, 12/16/93):
Description: http://homepage.smc.edu/nestler_andrew/homerpyth.jpg
"[After putting on Henry Kissinger's glasses, found in a men’s room toilet] 

Homer:  The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side. 

Man in stall:  That’s a right triangle, you idiot! 

Homer:  D’oh! "

Source: http://homepage.smc.edu/nestler_andrew/SimpsonsMath.htm 

Instructions

Homer's Conjecture is: "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side."

Man in the Stall's Conjecture is: "Homer's Conjecture refers to a right triangle, not an isosceles triangle."

Now think about those two conjectures.  Analyze them, draw them, research the triangle concepts involved and compose a paper about the two conjectures.  Cover the points below and add whatever else you find relevant.

Tell us in your own words and sketches -- What is Homer saying?  Is Homer right?  Why?  Can you show a proof?  Is he wrong?  Why?  Can you show a proof? 

Sometimes on the internet you may see this referred to as Homer's pythagorean mistake.  Man in the Stall's Conjecture seems to invoke Pythagoras since Pythagoras is famous for his theorem that relates the length of the sides of a right triangle.  Be sure to consider this in your analysis.  Is Man in Stall right? Explain.

Why is it important Homer Simpson and Man in the Stall should know basic triangle properties like the Pythagorean theorem?  Give examples how the Pythagorean Theorem or other triangle properties are used in everyday life.

For this project you will submit a first draft, I will give you some comments and then you will revise and submit a final paper.

Web resources you may find useful are on the following pages.


 

For an introduction to the topic, see:

Watch this clip from the show.

The algebraic formula of the Pythagorean Theorem is drawn in geometric figures in this simple animation

A list of hyperlinked occupations that use the Pyhagorean Theorem directly or indirectly

Search Terms:
To search for websites or webpages, the following search terms should be referred to as they relate to triangle properties:

Websites:

The theorem explained in text and illustrations.  Read as deep as you want.  Link around to catch up on any unfamiliar terms.

Isosceles triangles explained in text and illustrations.  Read as deep as you want.  Link around to catch up on any unfamiliar terms.

A typical short article on a typical “how to” site using right triangle and square properties. You can find bunches of these all over the internet.

Another example of how common the knowledge and use of the Pythagorean Theorem really is.

Read a description for teachers of the theorem and how it applies in to common things

Read a description for teachers of the theorem and how it applies in to common things.  I like this because it’s a very clear presentation of the concept.

YouTube or TeacherTube Videos:

Interactive Problems:

Organization and Associations:

 

TEKS Objective:
111.34(b)(5)(D) identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.
111.34(b)(8)(C) derive, extend, and use the Pythagorean Theorem

This Pathfinder was created by Biff Bailey on February 24, 2012, and may be used under the Creative Commons licensing agreement.

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