In this blog just i would like to post any technical stuff which caught my attention...
Friday, June 16, 2006
Euler & Polyhedra
Leonhard Euler noticed that if you add the number of faces and vertices of most solids, and then subtracted the number of edges you would get 2. Faces are the 2-Dimensional figures on the solid figures. For example a cube has 6 square faces, 8 vertices (Vertices are where the edges meet, the corners) and 12 edges. The result is, 6+8-12=2.
The helical angle is similar to a right angled triangle wrapped around a cylinder,where the height of the triangle is the interflute distance.The base of the triangle is the circumference and the hypotenuse is the flute itself.
The relationship between helical angle and pitch is
tan (alpha) = pitch/circumference
i.e, tan(alpha) = I/C
When a vane or blade is kept in place of helical path,with flow along the axial direction, the vane angle is to be calculated as,
Squaring the circle is the problem proposed by ancient geometers of using a finite compass and straightedge construction to make a square with the same area as a given circle. In 1882, the problem was proved to be impossible. The term quadrature of the circle is synonymous.