Umm, yes, sorry, got waylaid doing a new book. Here's what lies behind a trick I would perform for Year 9 (9th grade) kids. It was basically a stage act that is based on a very small amount of memorisation and a lot of trickery. Suppose I tell you I can supply the cube roots of every integer cube between 1 million and 8 million.
I give you a
calculator, inviting you to enter a 3-digit number, less than 200, and read off
the result after multiplying the number by itself twice. You might choose to enter the
value 173, which would give you the value 5,177,717 for 173 x 173 x 173. When
you read this out from the calculator, I would immediately tell you that the
number you entered first was 173.
This does not
involve memorising all the cubes up to 2003. That would also be
possible, but it is unnecessary. You only need to memorise the cubes up to 20,
because adding three zeroes will give you the cubes of all of the multiples of
10 up to 200. You can extend this further if you wish, but for this discussion,
that is enough. My lower limit of 1 million means I can concentrate on 3-digit
numbers, but again, the trick can be extended. I start with a table of cubes,
where I only need an approximate value.
Here are the ten
values I need to know:
|
number |
100 |
110 |
120 |
130 |
140 |
150 |
160 |
170 |
180 |
190 |
200 |
|
cubed
(millions) |
1 |
1.3 |
1.7 |
2.1 |
2.7 |
3.3 |
4 |
4.9 |
5.8 |
6.8 |
8 |
There is a curious feature about the last digit of a perfect
cube and how it relates to the cube root, the number we began with:
|
number ends in |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
cube ends in |
0 |
1 |
8 |
7 |
4 |
5 |
6 |
3 |
2 |
9 |
I thought I had invented this method, but I found out in 2019 that somebody called Wallace Lee beat me to it. Mathematics is like that!
To search this blog, use this link and then use the search box
Another way: use the index!
