Integrating The Three Stooges into Trigonometry

Robert Davidson and Bob Gardner Department of Mathematics and Statistics East Tennessee State University

Online at: http://www.etsu.edu/math/gardner/stooges/Stooges-Trig.ppt

Mathematical Association of America Elon, NC March 26, 2010

Motivation for the Project

• Stooges are a great attention device – it keeps student’s interest.
• Trig is very applicable – even in the setting of the Three Stooges.
• Watching the Stooges should relieve any form of intellectual anxiety.
• Students learn by doing (measurement, unit conversion, scaling factor, trig).

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The Three Stooges

Moe Curly Larry

The Three Stooges

1. As a group, they were in show business for almost 50 years.
2. Made 190 “shorts” with Columbia Pictures.
3. Had their third short, Men in Black (1934), nominated for an Academy Award.
4. Had 4 different people in the role of “the third Stooge.”
5. Were the first to lampoon Adolph Hitler, in You Nazty Spy (1940).

Are the Three Stooges Still Relevant?

Source: http://www.zogby.com/Soundbites/ReadClips.dbm?ID=13498

Zogby International conducted a poll of 1,213 American adults by telephone in July 2006.

One question asked for the names of the Three Stooges and another asked for the names of the three branches of government.

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Those able to name the Three Stooges: 73%

Those able to name the three branches of government: 42%

A Bird in the Head

The 89^th Columbia Pictures Three Stooges film; this was released in 1946. This short is classic Stooges and has the boys wall-papering a room. We watch from 2:35 to 4:28 (1:53 total).

“…like Moe, Larry was only five-feet-four-inches tall.” (page 10)

Stooges Among Us

edited by Lon & Debra Davis

BearManor Media (2008)

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a

b

c

Students Insert Known Data

= 5’4’’

a = 5’4’’

b

c

Unit Conversion and Conversion Factor

= 64’’

1 foot = 12 inches, so the conversion factor is

12 inches/1 foot = 12’’/1’

So: 5’+4’’ = 5’x12’’/1’+4’’ = 60’’+4’’ = 64’’

= 10.8 cm

a

b

c

Students Make Measurements on Worksheet

= 7.3 cm

= 8.1 cm

Students Set Up a Scaling Factor

7.3 cm = 64.0’’

Scaling factor: 64.0 in / 7.3 cm = 8.77 in/cm

Students must be warned to distinguish between a scaling factor (like on a map) and a conversion factor.

a

b

Students Scale Their Measurements

= 64.0’’

= 71.0’’

c = 94.7’’

Board length = 94.7’’

Now we use the scene where the board falls on Moe’s head to introduce angles and trig functions.

Nice!

Suppose the board hits Moe on the head at a point 6 inches from the end of the board.

A Schematic Diagram

What is the angle, θ, the board makes when it hits Moe on the head?

θ

What are the six trig functions of θ?

θ

Students Use the Pythagorean Theorem

c_m = 94.7’’ – 6’’ = 88.7’’

a_m = 64’’

b_m = 61.4’’

The Pythagorean Theorem

θ

Students Find θ

c_m = 88.7’’

a_m = 64’’

b_m = 61.4’’

Trig Functions and Inverse Trig Functions

θ = 46.2^o

x

y

Introduce Coordinate Axes

From: http://www.collider.com/ dvd/reviews/article.asp/aid/5899/tcid/3

What are the coordinates of the top end of the board when it is standing vertically?

What are the coordinates of the top of Moe’s head?

What are the coordinates of the end of the board when the board hits Moe on the head?

What is the equation of the circle traced out by the end of the board?

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Questions About Coordinates

Convert θ to radians. Use the conversion factor π radians /180^o.

Through what angle did the board travel, from when it was vertical to when it hit Moe? Give your answer in radians.

How far did the end of the board travel from when it was vertical to when it hit Moe?

What area did the board sweep out from when it was vertical to when it hit Moe?

Questions Involving Angles

More Online

Online, you can find a copy of this PowerPoint presentation, the PowerPoint presentation we use in class to introduce the worksheet, the worksheet itself, our solutions to the worksheet, and a summary of student impressions of the in-class experience described today: http://faculty.etsu.edu/gardnerr/stooges-trig/stooges-trig.htm

Questions?

From: http://www.lunkhead.net/

Time and Velocity: The Physical Pendulum Equation

From the short Violent is the Word for Curly. Source: http://www.threestooges.net/episode.php?id=33

The Physical Pendulum Equation relates the mass of the board m, the length of the board L, the gravitational constant g, the moment of inertia I, and angle θ. It is a nonlinear differential equation and hence cannot be solved by conventional methods.

Source: http://www.constitutioncenter.org/CitizenAction/CivicResearchResults/NCCTeens'Poll.shtml

A 1998 survey by the National Constitution Center asked the same questions of American teenagers.

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Those able to name the Three Stooges: 59%

Those able to name the three branches of government: 41%

Sony Pictures released the seventh volume of Three Stooges shorts on November 10, 2009.