Page 89 - Mathematics Class - X

PROJECT 1

AIM
Sum of the exterior angles of a polygon having n sides will be equal to 360°.

PROCEDURE

We know that, exterior angle + interior adjacent angle = 180° C
So, if the polygon has n sides, then B D
Sum of all exterior angles + Sum of all interior angles = n × 180°

So, Sum of all exterior angles = n × 180° – Sum of all interior angles
Sum of all exterior angles = n × 180° – (n – 2) × 180° A E

= n × 180° – n × 180° + 2 × 180°
= 180°n – 180°n + 360° Z F
= 360°

Therefore, we conclude that sum of all exterior angles of the polygon having n sides = 360°

PROJECT 2

AIM
Ramanujan Number (1729).

DESCRIPTION

Srinivasa Ramanujan was one of the world’s greatest mathematicians. His life story, with its humble and sometimes
difficult beginnings, is as interesting in its own right as his astonishing work was.
1729 is the natural number following 1728 and preceding 1730. 1729 is known as the Ramanujan number after a
famous anecdote of the British mathematician G. H. Hardy.
Once Ramanujan fell ill and he was hospitalised. Hardy decided to visit Ramanujan and took a cab to hospital.
When he got there, he told Ramanujan that the cab’s number, 1729, was “rather a dull one.” Ramanujan said, “No,
it is a very interesting number. It is the smallest number expressible as a sum of two cubes in two different ways.”

That is, 1729 = 1 + 12 = 9 + 10 .
3
3
3
3
The next number in the sequence, the smallest number that can be expressed as the sum of two cubes in three
different ways, is 87,539,319.

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