Pascal's Triangle Recreated in Minecraft

We recreate Pascal's Triangle in Minecraft by making a Galton board and recording how many times a villager lands on each block.

You can see all of my previous Math and Minecraft episodes here:

Make sure to subscribe for more Math and Minecraft episodes. Please share this video with any Minecraft and Math lover in your life :)

#minecraft, #education, #makemathfun

[bjh]

Ah, Pascal’s triangle makes sense now!

[skaryzgik]

You made it look like a christmas tree, and then played that nutcracker song. ^_^

[purwantiarif]

Pascal's triangle can be constructed in the following way.
The leftmost and rightmost entry of each row is 1.
Every other entry is the sum of the two numbers over it.

One thing to note:
The sum of the entries in the zeroth row is 1, the sum of the entries in the first row is equal to 2, and in general, the sum of the entries in the ith row is 2 to the ith power.

Another less obvious fact is that each entry counts the number of lattice paths from the top to that entry. Let's say for example...

This number here is four (4), because there are four paths from the top to this entry.

[GiacomoAakbr]

omg you're so good with redstone mechanisms! keep it up, love these videos!

[thedoublehelix]

Wow I didn't expect to learn new math in this video

[MarkusDarkess]

Oh wow. The Pascal rows work and add up like the 90-45-45 triangles I talked about.

[Munakchree]

This is a very cool idea. I'm wondering about the way of recreating the numbers though.
If in the fourth row for example there is one way to land on the outer boxes and three ways to land on the inner boxes, makes 1+3+3+1 in total, so 1/8 of the villagers shoul land on each outer block and 3/8 of the villagers should land on the inner blocks.
You could just let a number of villagers (f.e. 1000) go through the triangle and then compare the outcome to those partials (1000/8=125, so 125/375/375/125).
It's basicaly the same thing you did but i think for students the concept might be easier to grasp that way than with the multiplication you presented.

I will definitely use this for my classes though, thank's for the idea!

[ZenoRogue]

If you used some mechanism which sends each villager alternately to left and right, you would get the exact result (no idea how to do it in Minecraft).

[briann]

Any world download for all of these, its amazing.

[arfareandaneswara]

Pascal's triangle can be constructed in the following way. The leftmost and rightmost entry of each row is 1. Every other entry is the sum of the two numbers over it. One thing to note: The sum of the entries in the zeroth row is 1, the sum of the entries in the first row is equal to 2, and in general, the sum of the entries in the ith row is 2 to the ith power. Another less obvious fact is that each entry counts the number of lattice paths from the top to that entry. Let's say for example... This number here is four (4), because there are four paths from the top to this entry.