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  • MathematicalMagician 3:57 pm on February 13, 2012 Permalink | Reply
    Tags: circle, , Reuleaux, round, shapes, triangle   

    Not Round?! 

    Hi everyone. Have you ever imagined the wheels on a car not being a circle?

    Well it does seem strange. However, there are shapes that are round but not round at the same time! A circle is a shape with one side and a constant width to it. This make it perfect for a smooth ride in a care. There are other shapes that have a consistent diameter all around, for example the Reuleaux Triangle. This is a triangle of constant width, however its edges are pointy. It is made up of of parts of three circles joined together.

    You notice that when a circle is rolled or turned inside a square it fits and keeps touching the sides proving its constant width. The Reuleaux triangle can also be rotated in a square as shown with it touching the sides showing the constant width of the triangle. However, it is still not a really good shape for a wheel because it will not work with a fixed point in the middle but it is still able to roll smoothly if it is rolling without a fixed point of rotation.

    There are also other Reuleaux polygons that consist of shapes with odd number of sides and a constant width. The more sides in a Reuleaux polygon, the rounder it is and the closer it gets to being a circle. A famous example of Reuleaux shapes are the British 20p and 50p coins which are both Reuleaux heptagons (as they have constant width, they will also not get stuck in a vending machine). There are also pencils that are a Reuleaux triangle as it is thought to be more comfortable due to the roundness than the typical hexagonal shape. Due to their constant width, there can also be shapes with a constant width other than a sphere.

    It also answers the riddle of “Other than a circle, what shape can you make a manhole cover so that it cannot fall down through the hole?” The Reuleaux triangle can also be used as a drill bit if it was not fixed and a single point in the middle! 

    Do you know of any objects that are a Reuleaux polygon, or do you have anything else to add on this topic?

    Comment below, share and don’t forget to follow my blog!

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  • MathematicalMagician 2:39 pm on February 13, 2012 Permalink | Reply  

    Funny picture 

     
  • MathematicalMagician 2:27 pm on February 13, 2012 Permalink | Reply  

    Puzzle 

    Johnny, James and Jack paint a fence. Only one person is painting the fence at once. James worked for twice as long as Johnny. Jack worked four hours less than Johnny. In total, they worked for 40 hours. How many more hours did James work than Jack?

    Comment your answers below and don’t forget to subscribe!

     
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