\(c^2 = a^2 + b^2 \)
This goal of this series is to share information on a topic that is a passion of mine: mathematics. There are so many different topics in math to learn and fascinate about. My goal is to create a series of puzzles that share these math topics, and some of their history, while also allowing you to use those skills to solve for the necessary coordinates. The goal is to provide puzzles that aren’t too difficult but can also offer a challenge.
The Pythagorean theorem has fascinated people for nearly 4,000 years; there are now more than 300 different proofs. This theorem, known and used by many, states that the sum of the squares on the legs of a right triangle is equal to the square of the hypotenuse. We have all come to know \(c^2 = a^2 + b^2 \) .
This theorem is most associated with its namesake, Pythagoras, the Greek mathematician and philosopher. It is much older than him, though. Babylonian tablets from almost 4,000 years ago indicate the theorem with accurate calculations. Some proofs have come from famous people such as Leonardo da Vinci and even the United States’ 20th president, James Garfield.
There are special integers, known as Pythagorean triples. These are sets of positive integers that fit the rule of \(c^2 = a^2 + b^2 \) , such as 3, 4, & 5.
\(3^2 + 4^2 = 5^2 \)
\(9 + 16 = 25\)
Many of these triples are actually multiples of previous triples! There are infinite possibilities.
To find the required coordinates, solve the problems below. Be sure to check your calculations!
xx yy.zzz
xx = 
yy = 
zzz =
ab° cd.(eee-2)
a = 
b = 
c = 
d=
eee=
Please replace cache exactly as you find it for the next cacher to experience.
Congratulations to 3omahakids & TheBeave! on the FTF!