Geometry Questions (1)

Answer two questions, one of which must be question 4.

  1. (a) In Book 2 of Euclid's elements he dealt with geometrical algebra. His proposition 4 was "If a straight line can be cut at random, the square on the whole is equal to the squares on the segments and twice the rectangle contained by the segments

    Use a diagram to illustrate that this is the same as

    (a + b) = a + 2ab + b

    (b)Describe Pythagoras' Theorem with Euclid's proof (use non technical language to describe how the proof works)

  2. Discuss Euclid's Books V VI XI XII and explain congruency similarity and conics (briefly!)

    (Mathematics in Western Culture)

  3. Find 2 more methods of proving Pythagoras' theorem (there are approximately 257!!)

  4. If the Greek scholar were required to construct a line x having the property expressed by

    ax - x = b

    Where a and b are line segments with a>2b, he would draw line AB = a and bisect it at C. Then at C he would erect a perpendicular CP equal in length to b. With P as centre and radius a/2 he would draw a circle cutting AB at D.

    Then on AB he would construct rectangle ABMK of whidth BM = BD and complete the square BDHM. This square is the area x having the property specified in the quadratic equation. Try this construction (choose values of a and b)

    Why does this construction work?

Origins of Geometry

The Golden Age of Greek Mathematics

History of Mathematics Module

Links to other History of Mathematics sites

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