# mnemonic devices tricks - math memorization

Wondering if there are any mnemonic devices for math-related memorization?

Specifically, the first 15 squares.

and

the first 10 cubes.

1 squared = 1
2 squared = 4
3 squared = 9
...
...
14 squared = 196
15 squared = 225

1 cubed = 1
2 cubed = 8
3 cubed = 27
...
...
9 cubed = 729
10 cubed = 1000

For squares, it seems that the difference between 1 and 4 is 3, the between 4 and 9 is 5, the difference between 9 and 16 is 7...  and this pattern follows... 9, 11, 13, 15 etc.

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Commented:
I think:

The difference between 2 successive squares is 2n+1

The difference between 2 successive cubes is 3n^2 + 3n + 1
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Commented:
For example, the difference between 4 squared and 5 squared is 2*4+1=9 (25-16)

The difference between 4 cubed and 5 cubed is 3*16+3*4+1=61 (125-64)
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Commented:
Difference of successive squares = (n+1) * (n+1) - n*n =
n^2 + 2n + 1 - n^2 =
2n+1

Difference of successive cubes = (n+1) * (n+1) * (n+1) - n*n*n =
(n^2 + 2n + 1)(n+1) - n^3 =
(n^3 + 2n^2 + n + n^2 + 2n + 1) - n^3 =
n^3 + 3n^2 + 3n + 1 - n^3 =
3n^2+3n+1
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Commented:
For cubes I remember the last digits by:
1 cubed ends in 1
5 cubed ends in 5
9 cubed ends in 9
and the ones in between are paired so:
2 cubed ends in 8
8 cubed ends in 2
and
3 cubed ends in 7
7 cubed ends in 3
always handy if you are told a cube and want to show off by telling the root.
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Commented:
the differences between cubes goes like 1,7,19,37,...
the differences between the differences goes like 6,12,18,24,...
0
1
1            6
7
8           12
19
27      18
37
64      24
61
125         30
91
216

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Commented:
For squares

(n+1)²  = n²  + 2n + 1

so knowing 5²  = 25 then

6²  = 5²  + 2*5 + 1 = 36

For cubes

This is not quite so simple but you will notice

(n+1)³  = (n-1)³ + 6n² + 2

So knowing 3³ = 27 then

5³ = 3³ + 6*4² + 2 = 125

You would now generate the odd and even cubes separately. This is probably as simple as you will get it
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Commented:
I wasn't clear enough above. It is that if the number ends in 1 then its cube ends in 1, number ends in 2, its cube ends in 8 etc.
Eg:
41^3=68921
92^3=778688
63^3=250047
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Web developerAuthor Commented:
Thank you everyone!
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