THE REULEAUX TRIANGLE –
There are curves of constant width besides circles and spheres. It’s a convex planar shape whose width is the same regardless of the orientation of the curve.
THESE CURVES OF CONSTANT WIDTH CAN DRILL SQUARE HOLES (YES, SQUARE HOLES)
THIS IS WHY PI IS SIGNIFICANT –
This animation shows the act of unrolling a circle’s circumference (or trying to), illustrating the ratio π.
THIS IS HOW TO MAKE PASCAL’S TRIANGLE –
These are used in algebra and probability, where it can be used to find Combinations.
THIS IS A MIURA FOLD –
It’s a method of folding a flat surface into a smaller size. It consists of tessellated parallelograms and is used in the solar panels of satellites.
THIS IS A PARABOLA –
If you kick a soccer ball (or shoot an arrow, fire a missile, or throw a stone), it will arc up into the air and come down again…following the path of a parabola.
THIS IS A RADIAN –
The radian is the standard unit of angular measure, used in many areas of mathematics.
THIS IS A MATRIX TRANSPOSITION –
A matrix is formed by turning all the rows of a given matrix into columns and vice-versa. The transpose of matrix A is written AT.
THIS IS A SIERPINSKI TRIANGLE –
It’s a kind of fractal, a mathematically generated pattern that can be reproducible at any magnification or reduction.
HERE’S HOW YOU CONVERT CARTESIAN (RECTANGULAR) TO POLAR COORDINATES
THIS IS HOW EXTERIOR ANGLES OF POLYGONS WORK –
They add up to 360 degrees.
THIS IS A HYPERBOLOID MADE UP OF STRAIGHT LINES
THIS IS ALSO A HYPERBOLOID OF STRAIGHT LINES
THIS IS HOW WHITE BLOOD CELLS KEEP YOU SAFE –
n the video, a white blood cell chases and engulfs this bacteria — watch until the end.
THIS IS EARTH’S ICE AND VEGETATION CYCLE OVER A YEAR
THERE IS FLAMMABLE MATTER IN SMOKE –
Smoke is not just nothingness, obviously, so it can burn.
THIS IS WHAT IT LOOKS LIKE WHEN YOU SET A FLAMMABLE GAS ON FIRE IN A CONTAINED ENVIRONMENT
THIS IS QUANTUM LEVITATION DUE TO VORTEX PINNING –
A superconductor levitates over a magnetic track.
THIS IS HOW TENSION WORKS IN RELATION TO FALLING OBJECTS –
Watch a slinky fall to the Earth; this is how slinkies always fall.
NOT ALL GASSES HAVE THE SAME DENSITY –
Sulphur hexafluoride is much denser than air.