This & That
The field of mathematics is fascinating and complex
By Jack SwiftIím no mathematician but that doesnít stop me from being interested in the magic of numbers and some of the rules that apply to them. I want to make it clear at the outset of this column that Iím not an expert in that very important subject. I just want to convey to my readers some of my fascination of the field, as I understand it.
It is hard for me to conceive of the idea of tending toward zero. Iíll explain. If there were a straight-line distance between two points and you walked half the distance from one point to the other, then half the distance of that half distance, then half the distance of the next half distance continuing on toward the point theoretically you would never actually reach the point. You might come as close as necessary for practical purposes but theoretically you could never reach the point youíre trying to reach. You would always be going half the succeeding distance.
While taking a course in higher equations, I was struck by the fact that some equations have more than one solution. If I remember right, there are as many solutions (roots) as the highest exponent in the equation.
Another concept that fascinates me is huge numbers. I remember reading about the googol several years ago. It is hard to wrap my mind around a number as large as the googol. A googol is the number one followed by 100 zeroes. The Googol was invented by Edward Kasner, an American mathematician. The name googol for a number was invented in 1920 and I read somewhere that Kasnerís 9-year-old son suggested it to him. He also came up with the word googolplex ó one followed by a googol of zeros. Then there are the numbers billion, trillion, quadrillion which are large numbers in their own right. Most of us can visualize what a million is, but a billion is more difficult. A billion is a one followed by nine zeros and a trillian is followed by twelve zeros. Oh well, enough of the large numbers. Itís making my head spin.
Many of us took plain geometry in high school. We remember a few or many of the rules or axioms concerning that subject. Plain geometry is based on a flat surface. With it parallel lines never meet. It interests me that there are at least two other geometries óspherical geometry and I forgot the name of the other one. Iím writing from memory but if I remember right spherical geometry is based on the surface of a globe or any spherical surface. In spherical geometry there are no parallel lines. The other geometry is based on a surface that is hard to describe and I donít remember the name of it. Picture a globe turned inside out and that is pretty much the surface it is based on. Also, there is solid geometry. It deals with three dimensions whereas plain geometry deals with two.
Finally, the concept of zero and infinity has always interested me. The symbol of infinity is like the figure eight laid on its side. While we often think of a zero as being nothing, it is an important part of our number system that is based on 10 ó the decimal system. Another system is the binary system. The binary system is based on the numbers one and zero and is used in computers and other electronic devices we use today.
While I enjoy learning about the simple aspects of mathematics. I wouldnít know much about the solution to a problem that takes an entire blackboard to solve. Mathematicians continue to play an important role in todayís world and I salute them.