Mathematics in a Story

What's Your Angle, Pythagoras? by Julie Ellis is a "math adventure" book about the curious little boy, Pythagoras.  The book starts out with Pythagoras eavesdropping on a conversation between two workmen who are trying to build a temple but are having trouble with their ladder. Pythagoras tries to help everyone but they all doubt him.  "The ladder is too short to reach the roof...not possible, the wall is 12ft tall so I made the ladder 12 ft tall....the ladder only reaches the roof when it is flat against the wall and the no one can climb it! This is as bad as the columns on the porch." (p. 4). Upon hearing this Pythagoras sees that the columns were on crooked bases that made them unable to hold up a roof. When he goes home for dinner he hears his father talking about sailing from Samos (his home) to Rhodes to Crete. Pythagoras asks his father "why don't you just sail straight from here to Crete? It would be a lot faster" (8).  Father responds that it would be too risky to do so with out knowing the exact distance" (9).  When the two go on trip together to Alexandria, Egypt they encounters a man named Nef, a talented builder. Nef introduces Pythagoras to the concept of the "special rope" that he uses to make a special triangle known as the right triangle "because it helps [him] make a nice, square corner that's exactly the right angle for cutting stone" (13).  Pythagoras experiments and makes a triangle with 3 lengths on one side, 4 lengths on another side, and 5 lengths on the longest side (15). Later on, Pythagoras plays around with the red and blue tiles he is supposed to watch over and discovers that the base of the statue is a right triangle and its sides are 3, 4, and 5 tiles long...9 tiles in the red square plus the 16 tiles in the blue square equal 25 tiles. There are exactly 25 tiles in the big red and blue square (19). "the square with 3 tiles on each side had 9 tiles, the one with  4 on each side had 16 tiles, and the one with 5 on each side had 25 tiles.  So in a square, the length of a side times  itself is the number of tiles in the whole square.  I'll call it 'squaring' when I multiply a number by itself. Three times three is three squared. 3^2 + 4^2 = 5^2. (21). Pythagoras links all of this math he has done back to the right triangle. When he returns home he immediately addresses the issues the workmen were having. Then he further connects this to finding the distance between Samos and Crete.  His parents are shocked when he tells them that he figured out the distance from here to Crete. He explains that he discovered a pattern that works for any right triangle (25).  In the middle of his explanation he is interrupted by the workmen who thank him for fixing their ladder. Pythagoras responds by adding his suggestion for the base of columns to the two appreciative workmen. Then father decides that maybe his son is right about his concept and asks him to explain to him the distance from Samos to Crete and so Pythagoras successfully explains it to him. Pythagoras is able to prove all of his doubters wrong.


The major mathematical concepts presented in this story are all about the Pythagorean theorem.  In order to solve the ladder issue for the workmen he decides: "That ladder would be easy to climb if the bottom were about five feet from the wall...Pepros said that the wall is 12 ft high." Therefore, Pythagoras drew out 5^2 + 12^2 = ? --> 25 + 144 = 169 --> 169 = 13 x 13. --> "The ladder needs to be 13 feet long" (24).  In order to solve the distance between Samos and Crete he figures:  "Our island, Samos, forms a right triangle with Rhodes and Crete. If I call the sides of the triangle a, b, and c then I can use my right triangle pattern a^2 + b^2 = c^2 to figure out the distance from here to Crete" (28).  .... a^2 + b^2 = 34, 225... "To find c, the distance between here and Crete, I had to find out what number multiplied by itself equals 34, 225...I already knew 148^2 = 21, 904. That's too small. I tried 200, but 200^2 = 40, 000 thats too big. I tried 180, and 180^2 = 32, 400. That's close! Then, I tried 185 times 185. That's exactly 34, 225. So the distance from our island to Crete is 185 miles" (29).

I believe that What's Your Angle, Pythagoras? is an effective way to teach children a mathematical concept largely due to the storyline which quite simply is that a little boy is doubted by all who surround him in his life, but he does not let that get to him and ultimately he is able to succeed and prove everyone wrong in doubting his ability.  This is so important because math can be a difficult subject and its very easy to get caught up in what your peers are doing and let that impact your ability to learn.  I'll even admit that this story restored my outlook on how to approach the subject of Applied Calculus! :) Additionally, in terms of the specific mathematics, the book does a great job of breaking down a complicated concept into an easily understandable concept for people of all ages.