Reuleaux triangle

A nontrivial example is the Reuleaux triangle.

The coin is not circular but is an Reuleaux triangle heptagon to aid identification.

This shape is defined and named by analogy to the Reuleaux triangle, a two-dimensional curve of constant width.

The most familiar examples of curves of constant width are the circle and the Reuleaux triangle.

Two well known non-axially-symmetrical rollers are the Reuleaux triangle and the Meissner bodies.

Today, he may be best remembered for the Reuleaux triangle, a curve of constant width that he helped develop as a useful mechanical form.

A Reuleaux triangle is the simplest and best known Reuleaux polygon.

(A Reuleaux triangle or other curve of constant width would also serve this purpose, but round covers are much easier to manufacture.

Triangular (more accurately a Reuleaux triangle)

By the Blaschke-Lebesgue theorem, the Reuleaux triangle has the least area of any curve of given constant width.

The Reuleaux triangle can be generalized to regular polygons with an odd number of sides, yielding a Reuleaux polygon.

The Reuleaux triangle lacks tangent continuity at three points, but constant-width curves can also be constructed without such discontinuities (as shown in the second illustration at right).

Many guitar picks employ the Reuleaux triangle, as its unique shape combines a sharp point to provide strong articulation, with a wide tip to produce a warm timbre.

Many windows in buildings designed by Berlage in Amsterdam's Plan Zuid extension are the shape of the Reuleaux triangle.

A Reuleaux triangle (along with all other curves of constant width) can roll but makes a poor wheel because it does not roll about a fixed center of rotation.

Among all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter is an equidiagonal kite that can be inscribed into a Reuleaux triangle.

The area of Reuleaux triangle is smaller than that of the disk of the same width (i.e. diameter); the area of such a disk is .

Today, the trademarked logo consists of the "General Cable" stylized black text with a green "Reuleaux triangle" on the left, which is a modernized version of the 1927 symbol.

The Harry Watt square drill bit is based on a Reuleaux triangle shape, and is used together with a guide and a special chuck to make a square hole.

You can make a square with a circular drill bit, or in particular, one with a Reuleaux triangle shape, which Ross describes as a sort or Toblerone-Rolo combo.

Valve covers used in the Mission Bay Project of San Francisco to differentiate reclaimed water from potable water are in the shape of a Reuleaux triangle.

For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance.

The school 'mascot' is Blaster the Burro, the athletic teams are called the 'Orediggers', and the 'logo' (designed by architect Jacques Benedict) is a Reuleaux triangle.

Because all diameters are the same, the Reuleaux triangle is one answer to the question "Other than a circle, what shape can a manhole cover be made so that it cannot fall down through the hole?"