How to visualize quaternions, a 4d number system, in our 3d world

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.

How to visualize quaternions, a 4d number system, in our 3d world

How to think about this 4d number system in our 3d space.

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.

In this math video lesson, students analyze a graph with six plotted points and determine which point could be removed so the relation becomes a function. The exemplar solution models how to apply the vertical line test, showing that...

In this video we are going to focus on mistakes that students make when they need to solve a system of equation by graphing the system.

When graphing piecewise functions there are some great tips that I want you to follow. This video will explain all.

In this video we are going to explore three tips that you can follow to better understand graphing logarithms.

Let's be honest. The real controversy around the issue of guns is, what might we do about it? It's the potential firearms policy changes that make people squirrelly. But guns have been regulated in the United States, we can see what...

Howcast - This humble, homespun guitar is all you need to make sweet music.

Howcast - Learn how to read a person just by looking at their hand using the ancient art of palmistry.

Design your own clothes by making sewing patterns, but pay attention to the details.

Sharpen your pencil, grab some sketch paper, and learn how to draw the girlish charms of the female species.

Pupil outcome: I can form the capital letters B, D, P and R. Key learning points: - The capital letters B, D, P and R all start at the top tramline. - The capital letters B, D, P and R all go straight down and back up and around. - The...

Pupil outcome: I can form the capital letters M, N, W and V. Key learning points: - The capital letters M, N, W and V all have the same starting point and go down and back up. - These capital letters are formed by one continuous movement...

Pupil outcome: I can form the capital letters J, U, X, Y and Z. Key learning points: - The capital letters J, U, X, Y and Z start on the ascender line. - The capital letters J, U, X, Y and Z all have either one or two vertical or...

Pupil outcome: I can correctly form the numerals 6-10. Key learning points: - A numeral is a digit that represents a number. - The numerals 6, 7, 8 and 9 are made using one continuous movement and without lifting your pencil. - The...

Pupil outcome: I can form the capital letters A, H, K, T and S. Key learning points: - All of the letters start on the ascender line except for the letter S which starts just below the ascender line. - Letters A, H, K and T all have...

Pupil outcome: I can describe the shapes made when rectangles are cut on the diagonal. Key learning points: - An angle can be exactly a right angle. - An angle can be less than or greater than a right angle. - When you cut a square using...

Pupil outcome: I can explain why the angles in a quadrilateral sum to 360° and use this to find missing angles. Key learning points: - A quadrilateral is a shape with four sides and four vertices. - Interior angles in a quadrilateral are...

Pupil outcome: I can recall understanding and identification of right angles. Key learning points: - A right angle is a square corner. - A right angle is a quarter turn. - There are right angles in buildings and the environment.

Pupil outcome: You can decompose or split shapes into rectangles in different ways. Key learning points: - Different ways of decomposing the shape will give the same answer. - The area stays the same however you split the shape. -...

Pupil outcome: I can solve problems involving missing coordinates Key learning points: - Coordinate grids are not always presented with grid lines, and the axes are not always fully-labelled. - When this is the case, it is essential to...