The holographic principle emerged from many subtle clues – clues discovered over decades of theoretical exploration of the universe. Over the past several months on Space Time, we’ve seen those close clues, and we’ve built a the...

The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.

Euler's formula, e^{pi i} = -1, is one of the most famous expressions in math, but why on earth is this true? A few perspectives from the field of group theory can make this formula a bit more intuitive.

Euler's formula, e^{pi i} = -1, is one of the most famous expressions in math, but why on earth is this true? A few perspectives from the field of group theory can make this formula a bit more intuitive.

What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.

What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.

The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.

A visual for derivatives which generalizes more nicely to topics beyond calculus. Thinking of a function as a transformation, the derivative measure how much that function locally stretches or squishes a given region.

How do you think about a non-square matrix as a transformation?

A quick explanation of e^(pi i) in terms of motion and differential equations

The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.

A beautiful solution to the Basel Problem (1+1/4+1/9+1/16+...) using Euclidian geometry. Unlike many more common proofs, this one makes it very clear why pi is involved in the answer.

A beautiful solution to the Basel Problem (1+1/4+1/9+1/16+...) using Euclidian geometry. Unlike many more common proofs, this one makes it very clear why pi is involved in the answer.

The answer lies in the weirdness of floating-point numbers and the computer's perception of a number line.

What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.

A quick explanation of e^(pi i) in terms of motion and differential equations

How do you think about a non-square matrix as a transformation?

A visual for derivatives which generalizes more nicely to topics beyond calculus. Thinking of a function as a transformation, the derivative measure how much that function locally stretches or squishes a given region.

How do you think about a non-square matrix as a transformation?

A visual for derivatives which generalizes more nicely to topics beyond calculus.

In this video Paul Andersen explains how equilibrium is achieved in a reversible reaction. When the rate of the forward reaction is equal to the rate of the reverse reaction the system is at equilibrium. Graphical analysis of...

In this video Paul Andersen explains how the reaction quotient is used to determine the progress of a reversible reaction. The reaction quotient (Q) is the ratio of the concentration of products to the concentration of reactants. The...

In this shorts video we will learn how to estimate a square root using a number line. We will first rewrite each integer value on the number line with its equivalent perfect square. We will identify which two perfect squares the...

In this shorts math video we will estimate a cube root. We will create a number line using the provided answer choices. We will add the perfect cube of each value. We will use the perfect cube number line to estimate which integer...