Maths is a very strange subject which reacts differently at different levels. Sometimes maths is very logical and at other times it doesn’t make sense at all. I would like to give and example of the illogicality of maths when comparing Geometry with Algebra.
You probably have heard of the Pythagorus Theorem which states that in a right angle triangle ( 90degrees ) The square on the hypotenuse ( the side of the triangle opposite the right angle) is equal in area the the sum of the squares on the other two sides.
If the other two sides normally called the opposite and the adjacent have both a length of one unit the sum of the squares will be two square units We would therefore deduce that the square on the hypotenuse is two square units The side of this square becomes root two.
Root two as a number does not exist as there is nothing that multiplied by itself will exactly equal two. In geometry the hypotenuse is a fixed distance but in algebra it is not. The logic of one element of maths defies the logic of another.
If you study maths to a very high level you will find more and more of these conundrums and if you took maths to its limits you might find that the whole subject is full of conundrums. There is possibly an infinite number as maths seems to be a subject of infinity.
Peter Bull (Author of the Get In Touch Series )