The Boy Who Never
Stopped Wondering.
By Rosalia Nolen
Every summer Mr. and Mrs. Agoras would take their son, Pyth on wonderful vacations all over the world. They visited the Pyramids of Egypt, the Great Wall of China, and the Leaning Tower of Pisa in Italy. This summer Pyth’s parents thought Pyth was old enough to start working and pay for his own ticket for their trip to Athens.
Pyth knew there were several dogs in his neighborhood. He used to stop to pet them and the dogs liked him. He asked his neighbors if they wanted to hire him as their dog walker. Pretty soon Pyth had a steady job of walking four dogs everyday after school.
Pyth enjoyed spending time with the dogs and he was making good money. The only problem was that he was getting tired of walking so much.He has to walk 4 blocks west and then 3 blocks north to get to school and then he has to do that commute allover again after school too! Pyth doesn’t mind walking the dogs because he lets them run around the park . Pyth wants to find a way to reduce his walking amount.
One day while he was walking the dogs thru the park he noticed that he could see the school building from one direction and his house in the other direction. Pyth set out to find a shortcut. The next day he followed a path through the park that lead him directly to his school. It seemed shorter but Pyth wondered how much shorter it actually was.
Pyth went home and made a sketch of his neighborhood. “How can I figure out how long the path is?” Pyth thought to himself. “Maybe I should build a model of the neighborhood and I’ll place square blocks where the path is,” Pyth said with excitement and he started building. Pyth used an apple to represent the school and a candle to represent his house. He placed 4 square blocks horizontally to the left of his house and from there placed 3 square blocks vertically to the school building. Finally, he started to place square blocks on a diagonal from the house to school building. Pyth was able to place 5 square blocks on the diagonal that represented the dirt path. Pyth looked at his model and noticed that his blocks just happed to be placed in the form of a right triangle. He labeled the sketch with variables to represent each side of the triangle.
Now that Pyth knew how long the shortcut was, he was much happier. He took the shortcut often especially when he was running late. As he walking one day he thought, “5 square blocks is more direct route than walking 4 square blocks and then 3 square blocks, ” he recalled the saying “the shortest distance between 2 points is a straight line.” “Why is that?” Pyth wondered, “does it have anything to do with the paths forming a right triangle?”
Pyth remembered learning in school that a number squared means to multiply it by itself. “So, if I square 3 - I’ll get 9,” Pyth said proudly, “and if I square 4 - I’ll get 16 and 5 squared is 25!”
When Pyth arrived home he wrote down the numbers he was thinking of:
3x3=9 4x4=16 5x5=25
“Does this mean anything?” he wondered? Pyth arranged the numbers around the right triangle.
The side of the triangle that represents the base is 3 units and the height is 4 units and the longest side, called the hypotenuse, is 5 units long. Pyth made full squares out the lengths of each side. He needed 9 squares for the base and 16 for the height (also known as the legs). He counted 25 pieces and created 2 large squares. Then he realized he needed another 25 squares for the hypotenuse. Pyth thought for a while and then exclaimed, “the sum of the squares of the legs is equal to the square of the hypotenuse!”
“Does this work for all right triangles? What about other kinds of triangles?” These were the kinds of questions that lead Pyth on the path to discovering the Pythagorean triples. He used whole numbers to prove his theory. He started by doubling the lengths of the sides to 6, 8, 10.
62 + 82 must equal 102
36+ 64 = 100.
“It does!!!” he exclaimed. "I've figured it out!
Pyth proved how to find the missing side length of a right triangle. If the two legs a and b are squared and they add up to equal the hypotenuse or c squared then the triangle has a right or 90o angle.
Oh by the way, Pyth earned so much money walking dogs that he even had some spending money when he traveled to Greece with his parents.
Credits
Graphics: pixabay.com, shutterstock.com
Editing: fotoflexer.com
Definitions and graphics: mathsisfun.com
Created for EDLA 615
Rosalia Nolen
