Optimization Problems in Elementary Geometry.pdf

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Optimization Problems in

Elementary Geometry

Optimization Problems in

Elementary Geometry

A. K. MALLIK

Bengal Engineering and Science

University, Shibpur

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Optimization – Principles of Nature and

Engineering Design

Pierre Louis Moreau de Maupertius

(1698 – 1759)

In 1746, President of Academy of

Sciences in Berlin

“God’s intention to regulate physical

phenomena by a general principle of

highest perfection” – ridiculed by

Voltaire

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Euler , Lagrange and Hamilton –

“Principle of least action”

Calculus of variations – powerful tool

of

Mechanics, optics, electrodynamics

and other branches of physics.

The description of right lines and circles,

upon which geometry is founded, belongs

to mechanics. Geometry does not teach us

to draw these lines, but requires them to be

drawn – Isaac Newton

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Greek geometers – posed and solved

optimization problems in elementary

geometry

Weierstrass – Existence of an optimum

solution

1 is the highest integer!

If x is the highest integer and x > 1, then

x 2 > x . So x cannot be the highest integer.

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Maximum area of a triangle with two

sides of given length a and b .

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