John Heuver

The number two has a companion called three , and from there they carry wildly on with the claim that there is no end . Does this wild affair make sense ?

A number can get so large that it might take a lifetime to pronounce ; just think of the amount of paper it might take to write down . Applied to collections of material things , monetary or otherwise , a larger count is usually more valued , while sometimes an increase may not be welcome .

Then there is this strange bird called zero . Why did mankind invent it or name it ? Early civilizations kept records as marks on a stick or knots on a string . So what is zero ?! A “ nothing ” that is supposed to make sense ? Or something that lives on the margin and fills space ? It was used by the Mesopotamians as a placeholder .

If we add zero to a fixed number , nothing changes . Multiplying a number by one has a similar result . In algebra , we have variables that have the equivalent of a zero and a one , named neutral element and unity , respectively .

The necessity to measure length and volume lies at the origin of geometry . Early geometry developed in Asia and moved west . The most familiar figures in geometry are the point , line , and plane . The point exists in dimension zero , the line in dimension one . The plane is in dimension two , and the space where we live is in dimension three .

If , in our imagination , there was a creature living

in dimensions lower than our own , it would have no room in dimension zero , and in dimension one , it could only move back and forth . In a plane , it could travel left and right in dimension two but could not jump . The creature would be flat because height would not exist .

In higher dimensions than the one in which we live , dimension four leaves a lot to the imagination . In present day mathematics , however , the count of dimensions carries on . A calculation of the volume of a sphere with radius of one approaches a maximum volume somewhere between dimensions seven and eight , and from there it goes down , approaching zero against our expectation , as the dimension increases .

Another matter arises when we travel from one place to another . Over a short distance , a straight line seems obvious . However , on a long flight this does not work as the surface of the earth is curved , and we must follow a path along a great circle . Imagine the earth sliced through the centre so the two airports lie along the same circle ; we travel along the shortest arc . We arrive at this result using slightly different geometry than our familiar , linear one .

There are many things to ponder .

John Heuver taught math in his younger years and has come to reflect on what this was about .

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