# The Theory of Math Questions

TheTheory of Math Questions

TheTheory of Math Questions

1. Proof of the spherical version of the Sharog-path theorem

TheSharog-path theorem quoted in the story a modified version of theoriginal formula it is represented as:

Weightat speed, v= Rest weight × (1-v2/c2)

Where

v= velocity of the moving body

c= speed of lightness

Thevelocity of a body moving on the surface of a spherical body cannotbe equal the speed of lightness. Consider triangle ABC that isobtained from a spherical body as shown in the diagram below

Asphere has six lunes, and their area is the sum of the individuallunes. The triangle ABC has vertices that are represented by thelunes La,&nbspLb,&nbspLc.

Areaof lune = ¼(2R2(2La+&nbsp2Lb+2Lc)–area of the sphere

=¼(2R2(2La+&nbsp2Lb+2Lc)–4πR2

=R2(La+&nbspLb+Lc)

Multiplyingeither side of the equal sign by 4 gives

=R2(La+&nbspLb+Lc)- πR2

Factoringout R2gives

Areaof lune, A = R2(La+&nbspLb+Lc-π)

La+&nbspLb+Lc=π+1/R2A(This equation gives Sharog-paththeorem)

Where:

La+&nbspLb+Lcarethe three sides of the triangle