Name_____________________
THE MATHEMATICS OF THE SIMPSONS
1.
What theorem are the scarecrow and Homer attempting to recite?
2.
Write this theorem in algebraic notation.
3.
Write this theorem in words.
4.
The scarecrow and Homer say, “The sum of the square roots of any two sides of an
isosceles triangle is equal to the square root of the remaining side.” Write this statement
as a mathematical equation.
5.
What are the errors that the scarecrow and Homer make?
6.
Draw a diagram and try to show if the scarecrow’s and Homer’s statement is ever true.
Can you prove it?
7.
What is an approximation of pi? Write as many digits of pi as you can.
8.
What values of pi were used by different civilizations?
9.
What is the formula for volume of a sphere?
10.
Find the volume of the snowman (r = 25, r = 30, r = 35).
11.
What is the formula for volume of a cone?
12.
Based on the diagram, use reasonable estimates for the radius and height of the cone to
find the volume of the cone.
13.
Write Fermat’s Last Theorem.
14.
On a calculator, type in 1782^12 + 1841^12, then press enter. Take the 12th root of this
result (type ^(1/12)). What is the result?
15.
Fermat’s Last Theorem tells us that this isn’t true. Is there another way to prove that
178212 + 184112 ≠ 192212 ?
16.
Does the above argument work to prove that 398712 + 436512 ≠ 447212 ? How else could
this be proven?
17.
Find the derivative of the function y = r3/3
18.
What error did the teacher make?
19.
A Mersenne Prime is a prime number of the form 2n – 1. There are 47 known Mersenne
Primes. The largest known prime number is a Mersenne Prime (243112609 – 1). Use a
calculator to substitute 13 for n.
20.
A Perfect Number is a number that is equal to the sum of its divisors. There are 47
known Perfect Numbers (see above - this is not a coincidence). Examples of Perfect
Numbers are 6 (1+2+3) and 28 (1+2+4+7+14). List all of the divisors of 8128. Is 8128 a
Perfect Number?
21.
A Narcissistic Number is a number that is equal to the sum of the nth powers of its digits.
There are 88 Narcissistic Numbers. For example, 153 = 13 + 53 + 33 and
4150 = 45 + 15 + 55 + 05 . For what power is 8208 a Narcissistic Number?