Then this must be two steps too far :)

So what is the conclusion: We know that 4 reference points are needed to ensure that we know the exact location of an object (in 3D). But where and how many places could it be if we only had two or three reference points?

So what is the conclusion: We know that 4 reference points are needed to ensure that we know the exact location of an object (in 3D). But where and how many places could it be if we only had two or three reference points?

For three points, only two possibilities, where one is the opposite of the other, unless the point is exactly on the same plane.

For two... Infinite, unless the point is exactly in the middle of those two points.

For two... Infinite, unless the point is exactly in the middle of those two points.

@EssGeEich I agree, but with two points, I know it is infinite, but the point has to be on the perimeter of some oddly shaped shape, right?

Yes. But as you may agree after some conclusions, there isn't just one kind of infinite.

Reason?

Think of two numbers, as simple as 1 and 2.

Which numbers are between them?

Infinite numbers.

1,

1.00000000000...(insert infinite symbol here)1

1.00000000000...(insert infinite symbol here)2

... and so on.

Reason?

Think of two numbers, as simple as 1 and 2.

Which numbers are between them?

Infinite numbers.

1,

1.00000000000...(insert infinite symbol here)1

1.00000000000...(insert infinite symbol here)2

... and so on.

Isn't the one you are talking about, called an infinitesimal?

EDIT:

There are an infinite number of numbers between 1 and 2, but the numbers are infinitesimal.

There are also an infinite number of points on that perimeter.

The number in both cases is still infinity.

EDIT:

There are an infinite number of numbers between 1 and 2, but the numbers are infinitesimal.

There are also an infinite number of points on that perimeter.

The number in both cases is still infinity.

Last edited on

I get the feeling you're trying to define what it means to have a set of real numbers between two boundaries.

So basically there are an infinite amount of whole numbers and an infinite amount of numbers in between those numbers. Now can we let this die?

> but the point has to be on the perimeter of some oddly shaped shape, right?

a circumference

a circumference

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