The same fence, different area

Once upon a time, there was a king named Euclid who was very fond of mathematics so he built identical castles with beautiful gardens with fencing in the shape of a triangle, square, pentagon, hexagon, octagon and circle. He wanted to have a lot of children who would each have their own castle once they grow up. At the same time, he said to the architects that the fence of each castle had to be the same length.

He married the beautiful Hypatia, with whom he had (amazingly) six children who were called Dopey, Grumpy, Sleepy, Bashful, Sneezy and Smiley.

When the time came for them to learn to rule, the King gathered them and told them that he had decided that everyone would get their own castle to manage it. He also added that the one that chose best would inherit the throne.

Dopey chose the castle with the fence in the shape of a red triangle, Grumpy took the yellow square, Sleepy took the blue pentagon, Bashful took the purple hexagon, Sneezy chose the sky-blue octagon castle and Smiley chose the castle with the  fence in the shape of a green circle.

Help the king to choose his heir.

7 povrsina kruga i mnogouglaYou can talk with your students about what it means to have the fences with the same length (same perimeter for regular polygons and circle). What is the best decision for the heirs (to choose the biggest figure with the biggest area).  Who will inherit the smallest castle?

What is the lie in this story? Snow White and the Seven Dwarfs. Who is missing?

Prepared by Danilo Borovnica based on task.

About DaNe

Math teacher and IT expert with nearly 30 years of experience with interest in math, astronomy, life long learning, dance, music.
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