Mathematics causes some people to cringe when the subject is broached. People for some reason have a fear of numbers and calculations, and I have to admit that when I was a student in school, math could be really difficult at times. It's amazing that many of us have this loathing for calculations, yet without mathematics almost every advance and every breakthrough would be impossible. Numbers are at the core of everything in life, in our world and in the universe. If God exists, then He must be a mathematician, because everything around us is built by the numbers.
I know that for the first several years of school we learn basic operations: addition, subtraction, multiplication and division; and fractions, decimals and all their related calculations. At some point, we move onto algebra and spend a few years chasing "X." The whole goal of algebra is to locate the value of that mystery letter in its various equations and problems. We learn about slopes and intercepts, trains racing across the country toward each other and interest, among other things.
I never understood how algebra stands out as an enigma until eight years of mathematics are under your belt, and when you finally sit in an algebra class, you realizes the calculations and problem solving for X is something that we have done for years, starting when we solved our first equations in grade school. There is no mystery about algebra when we replace the little boxes and question marks of grade school with the X's and Y's of junior high. In other words, 1+3=? is as much an algebraic equation as 1+3=x. Yet we don't call it algebra until high school, which still baffles me.
People will tell me they can't do algebra even today, and yet if I ask them how much a pizza is if I can purchase two for $24, they will tell you they are $12 each. When you ask them how they figured it out, they will tell you they divided 24 by 2. If I asked you, though, to solve this problem: 2x=24, then it would be one of those algebra problems, yet the answer is still 12. Even though we don't call it "X", we still find it probably several times a week. But we don't think about it as algebra.
The next branch of mathematics most of us are exposed to following algebra is geometry.
Geometry is a fascinating subject that really teaches logical and critical thinking as we build a set of theorems based on some simple postulates. Euclid was one of the most famous geometers to ever exist. He is considered to be the "Father of Geometry." Euclidean geometry is a small set of axioms from which we derive several propositions and theorems. While Euclid did not necessarily derive the axioms he used, he was the first person to build them together into a framework that created a system from which one could develop theorems in comprehensive, logical manner.
Those basic axioms include the idea that a line can be drawn between two points, connecting them. A line can be extended from a finite line that continues being straight. A circle can be described from two points that represent the center and a point on the radius of the circle that makes all points around the center equally distant from it. A fourth axiom is that all right angles are equal to each other. Finally, the last postulate is that two lines that cross a third line and create angles that are less than 90 degrees will eventually meet at a point on the line with the smaller angles.
From those basic tenets, all of the rules that describe physical forms and angles and their relationships can be derived. When we examine the body of work that Euclid produced in his "Elements" from five small rules, it is truly amazing. When we say the shortest distance between two points is a straight line, that comes from Euclidean geometry. In a flat world, this is a true statement, but when we try to describe this classical geometry in a three dimensional world, the statement Is no longer accurate as our lines are no longer straight. Lines drawn along the surface of a three dimensional globe are actually arcs, so in three dimensional geometry that arc is shorter than a straight line would be.
What is the purpose of all of this deriving and solving? Well, while most of us do not grow up to be geometers, believe it or not this branch of mathematics is probably critical in helping us develop as analytical people. The ability to synthesize information from given ideas is paramount to advancing technology, science, philosophy and almost every area of life. Geometry teaches problem solving, puzzle solving and inductive and deductive reasoning which has a myriad of applications.
After geometry comes trigonometry the study of triangles. One might ask what importance is the study of triangles. I can remember spending what seemed like months studying sines and cosines and tangents and logarithms and the concept of triangular calculations seemed foreign to me. To be honest, I never really did understand the practical purpose of trig while we were learning it.
It was only years later that I started to comprehend the value of this branch of mathematics.
Triangles help us find heights of flagpoles, distances across streams and highways. More importantly we use this in music theory, astronomy and geography. In fact, trigonometry is essential in making the GPS devices in our cars and cell phones work. The idea of finding your position by triangulating it is a necessity in this modern world and it's all trigonometry.
This is just a brief survey of these branches of mathematics and while we all despised them at one time or another the knowledge they impart on all of us continue to help us all through life in all aspects of the world. Without math, we would still be living in caves.
Until next time…