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GK- Beauties of Mathematics Print
March 2013

o Mathematics is a language of symbols and numbers.  It is a tool for logical analysis and deduction of phenomenon in the universe.  Richard Feynman (1918-1988), a Physics Nobel prize winner in 1965 said so in a lecture on Physical Law in Cornell University in 1964.  He also said the Gravitational Force equation is simple and beautiful although the equation has far reaching applications and there was not another language that could express the complex relationships so well.  The Gravitational Force is one of the 4 forces governing the entire universe and it is the most significant for large objects.  The other 3 forces are electro-magnetic forces, weak radiation force, and strong nuclear force.

o Plato (BC428-348) was a mathematician and philosopher in Greece.  His house door had this signage “Those who do not understand mathematics: No Entry”. His view was that mathematicians discover and not invent.  Mathematicians did not create new concepts, but explore the common looks of everything outside of the human body.  Ref: The Little Book of Mathematics by Robert Solomon in 2008, translation version page 36

o Charles Snow (1905-1980) English physicist and novelist said there were 2 types of people in the universe.  One understands Mathematics to appraise the beauty of the universe, and one does not know.  Ref: Richard Feynman “The Characters of Physical Law” 1965, translation version page 105.

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Gravitational Attraction Force between Bodies by Isaac Newton (1642-1727)

F = GM1M2 / D 

G: Gravitational Constant (67 x 10-12 Nm2kg2)
M: Mass of object 1 and 2 respectively
D: Distance between the two objects

We can use this equation to find the mass of Moon, Earth or the Sun

Period of Orbit in Universe by Johannes Kepler (1571-1630)

P2 = 4π2D3 / G (M1+M2)

P: Period of Orbit of M1 around M2
D: Major axis distance between M1 and M2

Earth is 365 days roughly for 150M km, Venus is 225 days for 108M km, and the Moon and Sun etc

Circulating and Escape Velocities

Vc = √ GM/D Where M is total mass inside the orbit
Ve = √ 2GM/D

To escape Earth, Ve ≈ 104 m/s
To escape Black Hole, Ve > C (the speed of light)

Relativity by Albert Einstein (1879-1955)

γ = 1 / √ (1 – (V/C)2
Mv = γ M0

V: Velocity of object
C: Velocity of light (300000km/s found by Maxwell -1879)
M: Mass travelling at velocity and at rest respectively