Pentagon

A pentagon is a shape with five sides, which is one more than a square needed and one fewer than a hexagon could have spared.^[1]

It is the most widely drawn shape in the world. Every child who has drawn a house, with a square for the walls and a triangle for the roof, has drawn a pentagon and been congratulated on the house. The pentagon has never been credited.

Angles

The interior angles of a regular pentagon add up to 540 degrees, which are shared out equally, 108 to each corner. No corner has ever asked for more, making the pentagon the fairest shape on record.^[2]

Joining each corner to the two corners it is not next to produces a five-pointed star. Geometers describe this as the pentagon showing off, and note that the star still has a small pentagon in the middle, keeping an eye on things.

Classification

Scholars have long disagreed about where the pentagon comes from. The Subtractive school holds that it is a hexagon that lost a side. The Additive school holds that it is a square that was given an extra side as a treat. A conference held in 1922 to settle the matter ran for five days, one per side, and ended with both schools agreeing that it has five sides, which nobody had disputed.^[3]

• Sides: 5.
• Corners: 5, one at the end of each side, by arrangement.
• Houses: 1, if you are under seven.

See also

• Hexagon – a pentagon that kept going
• Square – a pentagon that stopped early
• Octagon – a pentagon that would not stop

References

1. Quint, P. (1922). Five Is Plenty. Corner Books. p. 5.
2. Angle, H. (1987). One Hundred and Eight Each. Obtuse Press.
3. Edge, F. (2004). “Is It a House?” Journal of Shapes Drawn in Crayon, 3(1), 1–5.