Volume of a pyramid is 1/3 the volume of a prism with the same base and height.

Demonstration of the fact that the volume of a pyramid is one third of the volume of a prism with the same base and height.

STL files of these models to print on a 3D printer:
You can use 5 x 3 mm magnets to make the models snap together.

To make these models snap together, use 5 x 3 mm magnets.

[bassavino]

Thank you! I've drawn a zillion pictures of cube to prism to pyramid, trying to figure this out. So elegant!

[zao]

In ancients China, the three Pyramids the host cuts from a cube were named "hight horse". the word was discribed the corner part of a palace roof, in early time.
In the book written by Liu Hui (a mathematics of Han Dynasty) mentioned this. And Master Liu mentioned two different shapes—— Slope and Half Pyramids. if you cut a cube or a cuboid to half, two slopes are there. A pyramid were made from a slope. If you divid a pyramid into two equal parts, two Trigonal pyramid were made. In Chinese, these three shapes are called —— Qian Du, Yang Ma and Bie Nao as well.
I would mention that these shapes have volume rate: 3 : 2 : 1

That were very interesting, isn't it.

[yordangrigorov]

Great video! You should let us see the shape after you combine 2 of the pyramids, before you add the third pyramid

[normansomera]

Where can I buy those 3 pyramids to form a cube?

[nealcarpenter]

I have looked high and low for the manipulatives (with or w/o magnets) for years! Did you make the 3 pyramids or can they be purchased somewhere?

[domdom]

...but how would 'the ancients' have figured this out without trial and error or without making physical models?

[IdaeChop]

Oh :0

I tried doing this with 4 weirdly shaped pyramid, and 1 regular pyramid which equals a prism, but it lead to me that the weirdly shaped pyramid is actually 1/(3√2) of the size of a prism, instead of 1/3.

[dreamxredits]

We used this in math class today because kids didn’t understand how a pyramid fit into a cube

[Kevangelo]

This is what im a looking for. Not the fucking 6 pyramids with half the height of the cube