Sum of n^3 [with 3D printing]

 

 
To understand the formula,
Linking a formula to a visualized image or physical object is
Very helpful.
 
For this aim, we developed 3D model.
 
Step 01. Tinkercad modeling [Code block]

1^2 (for 1^3)

 
 

1*1 (for 2^3)

 
 

2*2 (for 2^3)

 
 

3*3 (for 3^3)

 
 

4*4 (for 4^3)

 
 

4*2 (for 4^3)

 
 

5*5 (for 5^3)

 
 
 
Step 02. [Enjoy visualization with images]
 
Load all pieces into the workspace.
Now all the pieces stay together in Tinkercad's 3D design workplane.
The images upper shows cube blocks of length 1, 2, 3, 4, and 5.
 

 
On the lower part of the workplane, cubes were arranged flat  square foam.
If we observe the lower part of this square, it is easy to find the sum of N (n=1, 2, 3, 4, 5). 
Gray + Red + Green + Orange + Yellow
parts represent all together the Sum of N
 

Side of a square

 
 
All cubes of different lengths will be added together.
 
Sum of cube blocks with length of 1, 2, 3, 4, 5,
is the same with an area of a square flatten arranged of all those cube blocks. 
So we get following formula.
 

Area of a square

 
 
 
 

Step 03. [Enjoy physical manipulation]
 
We printed those pieces. 
let's play cube blocks. 
and connect your feeling of the formula to the understanding about the formula. 
and remember it. 
 

n^3 들의 합

 
and be truthful happy.