Assignment 3

Assignment-3
Course- History of Science
Assigned on- Jan 28, 2009
Submitted on- 4-2-09
Submitted by- Amit Sharma

Question- How did Thales measure the height of a pyramid by using a pole of known height? No modern trigonometry to be used in the response.
Answer- To measure the height of pyramid, Thales had made use of the knowledge of the proportionate shadows casted by the Sun at a definite time for all the bodies on the Earth, and that, the height of every object, their shadow and the hypotenuse always make a right angled triangle. So, to find out the height of pyramid, Thales used the measurement of the height of pole, the length shadow of stick, length of shadow of pyramid and the breadth of the base of pyramid.

                                                                                                         X
                                             A


                             C B Z O Y P
  Suppose, the height of stick is AB = 2 m, the length of shadow of stick is BC = 3m, the height of pyramid is XY and the YZ side is 300m, which represents the distance of the tip of the shadow of pyramid from the centre point of the base of pyramid ie. YO + OZ (say 200m +100m). Since, the right angled triangles ABC and XYZ have all the angles equal, their sides are proportional to each other, hence we can use the equation as-
                          AB = XY
                          BC YZ
 Now putting the values of AB (height of stick), BC (length of shadow of stick) and YZ (distance of the tip of the shadow of pyramid from the centre of the base of pyramid).
So, 2m = XY
                  3m 300m

or, XY = 2m x 300m = 200m
. 3m
Thus, the height of pyramid is calculated to be 200meters.

                                                                              

Oh! After saving the comments, i realised that the odt file format in which i had typed my comments could not be copied safely to this site. The line figures and the equation part has got distorted. If someone wants to look at its original, then please ask me for a hard copy.

Thales might have used the idea of similar triangles.He might have kept a stick of known length(l) vertically on the ground on a straight line to sun and pyramid (obviously not in the shadow of the pyramid).he might have measured the length of the shadow(s1) and also the length of the shadow of the pyramid(s2).if P is length of pyramid, then s1/s2=l/p. and hence he could calculate the height of the pyramid.

I think thales measured the height of pyramid by similar triangle method.
This problem of the height of pyramid can be solved by similar triangle method .
According to this ,place a stick of known height(say L) and measure the height of image(of stick and pyramid)say it is M and B respectively .then from similar triangle method L\M=A\B, where A is the height of pyramid.