# Questions about constants

#### jnicholes

Hello,

Havent been on in awhile. How is everyone? Happy Halloween!

I have a few questions about constants. To explain the question, let me give you an example.

Imagine a regular equilateral pentagon. All the sides are the same length, and all the angles are the same.

Now, let's say that the radius is equal to 1 foot. All the angles are 72 degrees. What I noticed is if these two numbers are constant, and not changing, the other numbers in the pentagon, like the apothem, side length, area were constant also, and not changing.

Here is what I mean. If the radius is 1 constantly, and the angle is 72 constantly, then the apothem would simply be the radius sin(54), or 0.809016994...... Which I might add, is half the Golden ratio constant, 1.618033989...... but that's not the point I am trying to make. The point is that if the angles and the radius do NOT change and are constant, the apothem would be constant also, not changing.

Now the side length would be the radius*2cos(54) or 1.175570505...... Again not changing and constant.

Same with the area, which is what I call Pentagon Pi, 2.377641291. Not changing and constant.

Here are my questions now. First is the definition of a constant. A constant is a part of an equation that never varies or changes, correct?

Second, If you have a number of constants in a geometric shape, (any number), can they set other constants in the shape like I described?

If this is confusing, I will make a video like last time.

Jared

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#### mathman

Forum Staff
A constant is a constant as opposed to a variable.

#### jnicholes

If I'm understanding you correctly, a constant is a fixed number, like pi or e. A variable is not a constant. Am I understanding you correctly?

#### skipjack

Forum Staff
It's often convenient to use a letter to represent a constant value or any value that isn't currently known (whether it may vary or not). In the latter case, the letter may be referred to as a variable simply because its value isn't known, whereas the letter $\pi$ is usually referred to as a constant. It may well be the case that constants are related to each other. For example, $$\displaystyle e^{i\pi} = -1$$.

#### SDK

If I'm understanding you correctly, a constant is a fixed number, like pi or e. A variable is not a constant. Am I understanding you correctly?
This is pretty much it. I would only add that a constant need not be a number. Other "objects" in math can be constants e.g. vectors, matrices, functions, etc.

1 person

#### jnicholes

Thank you all for the input so far. I appreciate it.

@SDK, what you said actually ties into something I believe in. Thanks for saying that!