Reuleaux triangle

[jazziza87]

I have a problem in my math that tells me to create a Reuleaux triangle using the five vetices of a regular pentagon. Could someone explain me how to go about doing it. Thanks alot you guys for your help

 

[skeeter]

Reuleaux triangle

 

[pka]

I have a problem in my math that tells me to create a Reuleaux triangle using the five vertices of a regular pentagon.

Surely the problem says Reuleaux polygon on a regular pentagon??
In that case, using the length of a diagonal of the pentagon as a radius draw arcs from each vertex of the opposite side.

 

[jazziza87]

Hey pka, that is what I thought when I looked it up but it tells me clearly to create a Reuleaux triangle using the vertices o a pentagon. Maybe they made a mistake, is it impossible to do that?

 

[pka]

No, it is possible to have a Reuleaux polygon on a regular pentagon.
As you can see I have drawn two of its arcs.

It is impossible to have a Reuleaux triangle on a regular pentagon.
Reuleaux polygons are point sets in the plane with constant width.

 

[TchrWill]

I have a problem in my math that tells me to create a Reuleaux triangle using the five vetices of a regular pentagon. Could someone explain me how to go about doing it. Thanks alot you guys for your help

The Reuleaux triangle is defined as follows.

1--Draw an equilateral triangle with sides equal to "r".
2--With a vertex as center, swing an arc of radius "r" between the other two vertices.
3--Repeat this at the other two vertices and you will have an equilateral triangle with three equal length, equal radius curved legs.
4--This shape has a constant width of "r".

Consequently, a manhole cover of this shape will never fall through the hole it is covering as the width of the hole is always smaller than the cover by the typical overlap.