Polygons

Perimeter, perimeter,
Around the edge I roam;
I look into the middle,
Where the area has its home.

Circular Circulation Equals Perimeter Rotation

Perimeter

We measure area with squares:
How many can we glue?
Just multiply the base times height
And area is through.

A-ha! That is One Square Kilometer of Area!

Base Times Height (Do You See Why We Divide By 2 For Triangles?)

For complicated shapes,
Cut into smaller shapes you know,
If lengths aren’t labeled,
Look across at opposite lengths that show.

Not So Scary When You Cut It Up

We measure volume space with cubes:
How much space will there be?
From any corner, look three ways
And multiply what you see.

(That’s base times height times depth
to give dimensionality.)

Volume

To see how triangles really behave when they’re letting all their points hang out, check out the polygon partiers in this video:

Circles

Outside of every circle,
Let’s build a circle fence;
And give that circle fence a name:
It’s called “Circumference”.

Let’s stretch a cord across that fence,
Straight to the other side;
“Diameter” is the fancy name;
Our circle it divides.

This Diameter Is Stretchy and Clever, No?”

With two of our diameter cords,
We try to wrap around,
But two won’t reach;
With D times 3 circumference is found.

One C Unrolls, We Get Three Ds–A Bit More Pi/e Is Left For MEs!(Refresh Your Screen If It Won’t Go: The “One C Equals Three Ds” Show!)

(Of course, the opposite is true:
Divide circumference by 3 to find diameter, too.)

A more exact result you’ll see,
If you use pi (Π) instead of 3.
(That’s 3-point-1-4 and some more,
But it’s close enough with 3-1-4.)

They’ll try to trick you:
They’ll give radius instead of D;
But r times 2 makes D,
And D times 3 will give you C.

(Or 3-point-1-4, pi, to get
A more exact circumference yet.)

r Times 3 Gives Half a C. Yikes! Stick With D Times 3, Like Me!   And Just Keep Quiet About Tau, For Now… (Refresh for Action)

But if you can’t remember “r”
or “radius”, think “ray”:
Two rays of sun join up as one;
And start a brand-new Day.

Good Day!

I’d be remiss to end without including two Pi items well-known in nerd circles (she said, sneeringly, while secretly enjoying the videos as well):

edited 11/13 to shrink some images for phones, to note that ya’ need to click “Redisplay” to reanimate some .gifs by the time you get to ’em, to add a coupla’ more nice .gifs while I was in here, and, last, to toss off another verse which ain’t so hot, but I felt like it anyhow…and lastly last, to add a tau reference (but I draw the [arc?] at eta!).