# 21 GIFs That Explain Mathematical Concepts

Lucas V. Barbosa via Wikimedia Commons

“Let's face it; by and large math is not easy, but that's what makes it so rewarding when you conquer a problem, and reach new heights of understanding.”

Danica McKellar

As we usher in the start of a new school year, it’s time to hit the ground running in your classes! Math can be pretty tough, but since it is the language in which scientists interpret the Universe, there’s really no getting around learning it. Check out these gifs that will help you visualize some tricky aspects of math, so you can dominate your exams this year.

Ellipse:

Via: giphy

Solving Pascal triangles:

Via: Hersfold via Wikimedia Commons

Use FOIL to easily multiply binomials:

Via: mathcaptain

Here’s how you solve logarithms:

Via: imgur

Use this trick so you don’t get mixed up when doing matrix transpositions:

What the Pythagorean Theorem is really trying to show you:

Via: giphy

Exterior angles of polygons will ALWAYS add up to 360 degrees:

If you’re studying trig, you better get pretty comfortable with circles. Check out this visualization that shows what you’re really looking at when you deal with pi:

Via: imgur

If an arc of a circle is the same length as its radius, the resulting angle is one radian:

Visualizing sine (red) on the Y axis and cosine (blue) on the X axis. The relative position of the circle is shown in black:

Via: imgur

This shows the same thing, but a bit more simply:

Via: reddit

Here’s how sine and cosine apply to triangles:

Via: imgur

Cosine is the derivative of sine:

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Via: reddit

Tangent lines:

Flipped on its side, the shape begins to make more sense:

Via: imgur

Converting a function from Cartesian to Polar coordinates:

Drawing a parabola:

Via: giphy

The Riemann sum is the approximate area under a curve:

Via: giphy

Hyperbola:

Via: giphy

Translating that into 3D, you get a hyperboloid. Believe it or not, it’s made with completely straight lines:

Via: tumblr

Seriously. You can even make it do this:

Via: tumblr

BONUS: If you need help remembering the quadratic formula, sing it to the tune of “Pop Goes The Weasel” and you will remember it for the rest of your life. “X equals opposite B, plus or minus the square root of B squared minus 4AC, all over 2A.”

[Hat tip: Distractify, Business Insider and Sheepolution on Imgur