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

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.

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 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 form the capital letters I, E, F and L. Key learning points: - The capital letters I, E, F, and L all start at the top tramline. - The capital letters I, E, F, and L all go straight down. - The formation of capital...

Pupil outcome: I can form the capital letters A, H, K and T. Key learning points: - The capital letters A, H, K and T all start at the top tramline. - The formation of capital letters A, H, K and T need you to lift your pencil to add the...

Pupil outcome: I can model real-life situations graphically. Key learning points: - Distance-time graphs tell you how far you have travelled over a period of time. - By reading the graph, you can tell if there is mistake with it. - You...

Pupil outcome: I can find the equation of the line from two coordinate pairs as well as from the gradient and one coordinate pair. Key learning points: - The gradient can be found from two points by considering the change in y over the...

Pupil outcome: I can form the capital letters B, D, P, R, I, E, F, L. Key learning points: - A capital letter is the upper case formation of a letter. - The letters B, D, P, R, I, E, F and L all start on the ascender line. - The capital...

Welcome to our complete high school mathematics tutorial series! Whether you’re a student preparing for exams, a teacher seeking additional resources, or a parent helping your child succeed in math, these videos cover a wide range of...

We use a plumb line and hook to find the centre of gravity of an irregularly shaped piece of card. A hole is punched in the card and it is suspended from the hook. A plumb line is used to let us draw the vertical line under the hole on...

In this video, we explore the concept of slope in mathematics, which measures the steepness of a line. Viewers learn how to calculate slope using the rise over run method, where the change in vertical position is divided by the change in...

Mr. Addit explains the term reflection. He also reflects various plane shapes across the line of symmetry and examines the reflected images.

Mr. Addit explains the line of symmetry, and examines a variety of plane shapes to find lines of symmetry.

This video entitled "Noun and Adjectives" discusses the relationship between nouns and adjectives and explains how to diagram a simple sentence.

In this video, I will guide you through an explanation of a stem-and-leaf plot and give you a real world example to help you learn how to construct a stem-and-leaf plot. As a bonus, I will show you how to construct a stem-and-leaf plot...