Reuleaux triangle facts for kids

A Reuleaux triangle is a special shape that looks a bit like a triangle with curved sides. It's made by drawing parts of three circles that overlap. Imagine a triangle, but instead of straight lines, its sides are gently rounded outwards.

This unique shape is interesting because it has a "constant width." This means if you measure it from any side to the opposite side, the distance is always the same! It's like a perfect circle in that way, even though it's not round.

How to Make a Reuleaux Triangle

Making a Reuleaux triangle is quite simple with a compass and a pencil.

• First, draw two dots on a piece of paper. Let's call them Dot A and Dot B.
• Next, place your compass point on Dot A. Open the compass so the pencil tip is on Dot B. Draw a circle.
• Now, move your compass point to Dot B. Keep the compass open to the same width (so the pencil tip is on Dot A). Draw another circle.
• You will see these two circles cross each other at two points. Choose one of these crossing points (either the top or bottom one).
• Place your compass point on this new crossing point. Keep the compass open to the same width (so the pencil tip is on either Dot A or Dot B). Draw your third circle.

The shape formed in the middle, where all three circles overlap, is a Reuleaux triangle!

Reuleaux Polygons and Tetrahedrons

The Reuleaux triangle is part of a bigger family of shapes.

Reuleaux Polygons

A Reuleaux polygon is like a Reuleaux triangle but with more sides. These shapes are made in a similar way using parts of circles. They always have an odd number of sides and also have that special "constant width" property.

Reuleaux Tetrahedrons

A Reuleaux tetrahedron is a 3D version of the Reuleaux triangle. Instead of circles, it's made when four spheres (like balls) cross each other. It looks like a pyramid with a Reuleaux triangle as its base.

Uses of Reuleaux Shapes

Reuleaux shapes are not just for math class; they are used in many real-world things!

• Drilling Square Holes: Special drill bits shaped like Reuleaux triangles can actually drill holes that are almost perfectly square. This is because of their constant width.
• Picks and Rollers: Some guitar picks are shaped like Reuleaux triangles. They are also used in some machines as rollers or cams because of their smooth, constant motion.
• Architecture: You can sometimes see Reuleaux triangle shapes in windows or designs on buildings, like the Church of Our Lady, Bruges in Belgium.
• Maps: Even old maps, like one by Leonardo da Vinci, have used Reuleaux triangle sections to divide up the world.

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  How a Reuleaux triangle is built (the gray shape)

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  Examples of different Reuleaux polygons

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  A Reuleaux tetrahedron made from four spheres

Images for kids

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  A Reuleaux triangle rotating inside a square

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  Comparing a round roller to a Reuleaux triangle roller

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  A Reuleaux triangle part in a film projector

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  A window shaped like a Reuleaux triangle

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  Leonardo da Vinci's world map using Reuleaux-triangle sections

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  Guitar picks shaped like Reuleaux triangles

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  Antennae arranged in a Reuleaux triangle shape

See also

In Spanish: Triángulo de Reuleaux para niños