Absolute Involutes

Three Hundred Seventy Second Post: Absolute Involutes

I’ve found that Logarithms can sometimes be confusing. It is supposed to be simple once you know how to work the chart, but there are so many numbers it answers can get jumbled. But I like to look for the creative part of math. There is so much grunt work adding, factoring, and remembering rules, it can be nice to realize what the problem solves. I think of ways to relate logarithms to other things. If you think about it, logarithms are just like logs stacked exponentially.

Seriously though, I find it beneficial to find a relationship between the geometry and the less tangible numbers. In trigonometry for instance, we have a unit circle which is simple once a person is familiarized with it, but may not be clearly pictured when learning it. The key is to think of something circular. In this case a dog tied to a post works. As the dog moves with respect to the pole his chain stays the same length. And what we see is the length and width vary with his position and the dog has just walked a circle. There it is! The unit circle is now given a visual picture. But wait... what if the dog’s chain is wrapped around the pole? So when he runs the opposite directions his chain is lengthened as it unravels. When the dog’s chain is drawn on paper an involute is created. This is a visual representation of how angles change proportionally. And as we know, it is related to length change in a parabola.

Often math is not thought as creative as the arts because math often has rules that are guidelines on how a problem is solved. This is similar in the sciences. However, even a child makes theories. They make them all the time to explain how things work. Sometimes we as people make less of these theories because we have work. But there is no time you ever learn as much as you do while you are young. So just maybe we shouldn’t have stopped our inquisitive nature.

Admittedly, when you’re an adult making theories is a little more complex. The theory must explain the mysteries in a way that answers the known questions. So it’s a little more work but the theories are only limited by the imagination.