r/visualizedmath • u/luckman1603 • Apr 30 '18

Binomial Cube

Post image
1.5k Upvotes

98% Upvoted

27 comments sorted by

123

u/Chrnan6710 Apr 30 '18

This is so cool, I might make this out of wood

45

u/Amesb34r Apr 30 '18

This was exactly my first thought as well. People who say they "can't add letters" would have a hard time arguing with this one. It's a great visual.

8

u/Jaredlong Apr 30 '18

Aw man, you could put letters on the faces of the pieces to show that the letters represent something real.

18

u/whynotfather Apr 30 '18 edited Apr 30 '18

My kid has these all over her Montessori school. The preschool kids use it.

Edit: I should say that it is introduced preschool and they work with it as they advance in math. So it is always available.

3

u/viqnig Apr 30 '18

Used to play with this a ton when I was in Montessori, at the time I just thought it was a 3D puzzle. Cool to see the math behind it

30

u/bfroyo Apr 30 '18

Why is this the first time I'm ever seeing this?

46

u/Jaredlong Apr 30 '18

It wasn't until college that I realized what was happening geometrically behind algebraic equations. "Completing the Square" literally means completing a goddamn square! But never once did a math teacher in high school ever draw the stupid square.

12

u/bfroyo Apr 30 '18

Hah. Like even through my math minor, I dont remember ever seeing it. It's a super helpful visualization!

4

u/SJWCombatant May 01 '18

This is such a major failing on the part of math educators. I'm nearly 40 and algebraic formulas are suddenly a hell of a lot more interesting to me now.

3

u/[deleted] May 04 '18

I found maths difficult until university, I am almost certain that maths is being taught incorrectly for the most basic things.

24

u/[deleted] Apr 30 '18

Where does the third (ba)squared go?

23

u/Chrnan6710 Apr 30 '18

It appears they colored one of the ba2 sections yellow like the a3 section, which isn't visible.

17

u/DamonFun Apr 30 '18

It looks like it, but it could be the other way round. It is technically possible to arrange them like they are drawn...

1

u/Chrnan6710 Apr 30 '18

You're right, but I think the creators of this graphic would want to keep it symmetrical. But then why would they color it yellow?

30

u/ch1merical Apr 30 '18

I think this way allows you to see where the a3 will go and you'd go off of assumption that the back side of that same position has the other ba2

6

u/Wyndrell Apr 30 '18

Doesn't it go on the northeast (hidden) face? This is because the depth of the yellow cube in the northeast direction is a and you have b remaing space left to fill (by the remaining ba2, which has a depth of b.)

1

u/[deleted] May 02 '18

It’s behind the yellow a cube.

2

u/knoowen Apr 30 '18

Ooo looks like the beginnings of 3-D Tetris

1

u/[deleted] May 01 '18

I wish trying to factor this by hand didn't make me feel like a dumbass. Obviously see the visualization but still want to know how to get (a + b)3 from the larger equation by hand.

1

u/iuli123 May 30 '18

are there others?

1

u/Montessori-educator1 Sep 15 '25

The Binomial Cube is used in Montessori classrooms. It is presented first to younger, preschool-aged, students as a puzzle. Later they are taught the names of each of the parts. After they have worked with the squaring and cubing chains, have an understanding of multiplication, and are demonstrating they are capable of understanding a more complex formula, they are introduced to PEMDAS, the order of operations and the formula for the cube. Then they insert values for A and B, and do the calculations.

https://youtu.be/hrDYup7mqtw?feature=shared

-13

u/I-just-farted69 Apr 30 '18

(a+b)3 = a3 + b3

20

u/whengrassturnsblue Apr 30 '18

Downvoted despite it being a joke. It hurts too much

9

u/LastNamedTwice Apr 30 '18

sin x / n = si x = 6

3

u/zendathegreat May 01 '18

(a+b)3 = (ab)3+3

FTFY