Today I was thinking about the differences between algebra and geometry. It is clear that they are both part of mathematics but why? They are considered two different subjects. Or at least that is what we think. When really looking into the basics and the foundation, they are more similar than people or even myself think. I have come to realize that we can't have geometry without algebra and we can't have algebra without geometry.
The obvious one to discuss is that we can't have geometry without algebra. This is seen within every calculation for geometry. For instance, we try to find the angle measurement of a circle by setting an equation equal to alpha and solving for alpha. Or if we know that volume of a cylinder and we can find the height. We do all of this using algebra.
Looking at the other direction is a bit more difficult. How can we relate algebra to geometry. We learn this in the most simple form. We use it when we are looking for a variable, x, and are given a square or a rectangle. We also see it in slopes. Finding the "rise over run" of a simple geometric figure, a line.
There are many difference when comparing algebra to geometry but there are even more similarities. These are just a few examples. Algebra and geometry go hand 'n hand.
It is very interesting to get another person's opinion on this view point. Your examples really show the relationship between both directions. I think of them together and I like the way that you showed algebra and geometry and then geometry and algebra. I also think they are more similar than I thought about before looking into it and reading your blog as well.
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