Construction
With a compass, sweep an arc sufficient to enclose the desired figure. With radius unchanged, sweep a sufficient arc centred at a point on the first arc to intersect that arc. With the same radius and the centre at that intersection sweep a third arc to intersect the other arcs. The result is a curve of constant width.
Equivalently, given an equilateral triangle T of side length s, take the boundary of the intersection of the disks with radius s centered at the vertices of T.
By the Blaschke–Lebesgue theorem, the Reuleaux triangle has the least area of any curve of given constant width. This area is, where s is the constant width. The existence of Reuleaux polygons shows that diameter measurements alone cannot verify that an object has a circular cross-section.
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 .
Read more about this topic: Reuleaux Triangle
Famous quotes containing the word construction:
“There’s no art
To find the mind’s construction in the face.”
—William Shakespeare (1564–1616)
“There is, I think, no point in the philosophy of progressive education which is sounder than its emphasis upon the importance of the participation of the learner in the formation of the purposes which direct his activities in the learning process, just as there is no defect in traditional education greater than its failure to secure the active cooperation of the pupil in construction of the purposes involved in his studying.”
—John Dewey (1859–1952)
“No real “vital” character in fiction is altogether a conscious construction of the author. On the contrary, it may be a sort of parasitic growth upon the author’s personality, developing by internal necessity as much as by external addition.”
—T.S. (Thomas Stearns)