Grade 10

Math Inquiry: The Math and Appeal Behind Animations


(Not all animations of pictures entering are supported on PowerPoint Online)

 

I started this inquiry with the question: How does Math affect Animations? But then as I was working, my project slowly changed into the appeal of an animation (Mostly 2D Animations). So from there, I worked my project around the 12 Principles of Animation by Frank Thomas and Ollie Johnston. From there, I was able to pinpoint math concepts within three of the 12 principles.

 

My curiosity continued during this project which made me think:
Why do we find human like components appealing?
and
Is it possible to create something appealing without doing math?

With this, I think that I can go further and start finding out what other things we as humans find appealing. I found other presentation that people made about Phi and found that interesting. I was able to see how a number like Phi is used in so many ways to make something seem ‘pretty’. I will also be able to look into abstract art and see if there are any math concepts to be found within the work of art.

Desmos Art

 This is the Santa Face I made on Desmos!

I stared by doing as many circles as I could (Head, nose, eyes) because then later on, it would be easier to put things over them. To change where I wanted the circles, I added or subtracted value from x and y which moved the circle around.  For Santa’s smile, I used a parabola (x²=y) and changed the y intercept and made it so y<-1 so it would stop the parabola from going into infinity. Then I started making a line across his head to start his hat. I made the hat with straight lines, restricted where the lines went, filled in the shape (using > or< instead of =) then restricted where the shape would finish filling. I added a little pompom on the top of his head and some points to make it look like a few stitches. The last part was his beard and I used two parabolas, one for the top and one for the bottom to fill up to the top. I had both a black and a orange one to try making a brown colour since Desmos doesn’t have a white fill.

That’s how this Santa was made!

 

Algebra Tiles Review Math 10H 2017

Factoring two Binomials

When expanding two binomials, you create a chart so that the binomials are on the outside, and you multiply them inwards to get your answer on the inside. In this model, it shows:

(x+2)(x-2)= x²-4

As the red sides are negative and the positive sides are green, blue and yellow. You can see that there are an equal amount of positive and negative x’s in the result. Because of that, the x’s cancel each other out because your adding 2x, then subtracting 2x, which leaves you with 0.

Simplifying a Trinomial

 In this trinomial, x²-x²+3x-3x (or 0), it can be simplified back into the binomial/trinomial it originated from. When you start, I find it easier to try to figure out one side first. If we start with the left side, you can tell that it has to be 2x because you need and x to get a x². To coninue we can assume that the left side is (x-x). On the top side we can use the x²s to figure out the first x. We can guess that it’s -x because a double negative is a positive and a positive and a negative is a negative.

We can then look and see that since on the far right side, they are all single x’s. With that we know that they are 1’s/ Since our first x is positive, we can see that it’s 2-1. So in the end, we simplified it to (x-x)(-x+2-1).

Surface Area of a Sphere

Partner: Micole

In this activity, we had cut an orange in half (the top and bottom, not symmetrically), we used to those halves to trace circles on a piece of paper. With those circles, we started peeling the two halves and filled the circles with the orange peel so that you could only see orange. In the end, we filled exactly 4 circles with orange peel and found that the surface area of a sphere is 4πr².