Why is 1x1=1, 2x2=4, but 3x3=6, 4x4=16, and 5x5=25?

Question

Is the current number system used the most optimal for the human race?

Answer 1

Most optimal? Not remotely. We'd be much better off if we'd all learned a twelve-based "duodecimal" (or "dozenal") counting system instead of our ten-based "decimal" one. Instead of having ten digits, 0123456789, we'd use twelve digits, like 0123456789AB, or 0123456789χε, or something similar.

Each digit-place in our notation would represent a number of twelves or powers of twelve, instead of tens or powers of ten. The number written "23" would stand for two twelves and three ones -- the number we write as "27." And we'd write "100" for the number we currently write as "144."

It sounds odd at first, but that's just because you've used powers of ten your whole life. The multiplication tables would be easier to learn, there'd be fewer digits in most numbers, more fractional numbers would have terminating decimal expansions instead of repeating ones, and we could still count on our fingers (by using the three segments of each of the four fingers, and the thumb-tip of the same hand moving from segment to segment).

For more info, see the links below. Hope they inspire some interesting thinking! :-D

Answer 2

1x1 means one 1 counted up.
2x2 means two 2's counted up.
3x3 does not = 6
3x3 means three 3's counted up (which = 9).

These multiplication patterns you present are called squares because you can interpret the 'x' operator as making a square in these cases.

2x3 means 2 colums of 3 dots each (which is a rectangle).
3x3 means 3 colums of 3 dots each (which is a special kind of rectangle called a square).

As for your second question. its hard to know if its the most optimal, but it works fairly well. When we need other number systems, we tend to create them. the base 2 number system (called binary) is used greatly in electrical and computer engineering (especially computer engineering and computer science), but so is octal and hexidecimal.

I guess my answer is that the base 10 system we use is good enough for most work, but we can create any number system we need when it isn't optimal for specific tasks.

Answer 3

1x1=1 2x2=4 3x3=9 not 6 4x4=16 5x5=25.
this number system can be verified by the chain reaction of fission of uranium. a system is optimal if it can be physically dipicted. which is possible so its a optimal number system.

Answer 4

3 x 3 =9

Answer 5

3 x 3 would be 9

Answer 6

Because:

1=1
2+2=4
3+3+3=9 (not 6)
4+4+4+4=16
5+5+5+5+5=25

It's been working for centuries. Don't fix it if it isn't broken.

Answer 7

Because:

1=1
2+2=4
3+3+3=9 (not 6)
4+4+4+4=16
5+5+5+5+5=25

It's been working for centuries. Don't fix it if it isn't broken.

Answer 8

Becos almost everybody has ten fingers, making it easy counting for smaller numbers, e.g. counting money, finding how much you save after a discount.
That's why 10 is the base and that makes 3x3=9, 4x4=16, 5x5=25...

(or at least i think dat's the ans.)

Answer 9

If we used a different number system, we'd still be doing the same calculations, only with different symbols for our numbers. We'd still come up with the same concept, only have different ways of writing down that concept.

3 x 3 = 9 -> think about that for a second. 3 is a symbol representing a concept. Multiplication is another concept. 9 is another. What does it mean that the concept of three times itself is 9? This one breaks down into counting objects. No matter what symbol we use to represent the concept of three, or that of nine, we will always get that three multiplied by three is nine in some symbolic way. Using different number systems will not help you understand multiplication.

Answer 10

The base 10 system is just umm Useful? And it would be too large of a transition to go to something else I think...

3x3 is 9

Answer 11

Because the number system is created a long time ago. You can ask those ancient people this question. and 3x3 does not equal 6 so correct that.