Sep 26, 2014

21 GIFs That Explain Mathematical Concepts

by Lisa Winter
Photo credit: 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:

Via: Wikimedia Commons
What the Pythagorean Theorem is really trying to show you:

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

Via: math.stackexchange
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:

Via: Wikimedia Commons
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:

Via: reddit
Tangent lines:

Via: John Reid  via Wikimedia Commons
Flipped on its side, the shape begins to make more sense:

Via: imgur
Converting a function from Cartesian to Polar coordinates:

Via: Wikimedia Commons
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:
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