So doing some random maths for school and thought about root 2 in relation to triangles. If you have a triangle and 2 sides are equal to 1 and the hypotenuse is equal to √2 then how does the hypotenuse end? √2 is an irrational number and the decimal never ends or repeats, but shouldn't it have to end at some point for the line to end in the triangle or does the line keep going on forever? Which wouldn't work when applied to real world geometry.
√2
Eli Cox
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Brayden Price
Sure it does.
Take square.
Cut it on the diagonal
what's the new exposed length?
Henry Cooper
Jaxon Reed
The number represents a real length that would take an infinite amount of time to measure precisely. That doesn't mean the length is infinite.
Jackson Williams
It would be root 2, or 1.41421....
the decimal version of this never ends or repeats though so wouldn't it go on forever theoretically? Or do decimals follow a different set of rules as for what to do with more numbers on the end?
Mason Morgan
Decimals don't properly represent numbers
Dylan Collins
That's just how irrational numbers are
it converges to some value because it just does
Juan Gonzalez
Are you stupid?
Caleb Brooks
The hypotenuse ends because the root of 2 is less than 2. Just because its decimal representation ends doesn't mean the number is infinitely large.
Adam Butler
Your logic is flawed because you are thinking of the sides of the triangle having some thickness. A true line does not have thickness, and as you approach that limit the hypotenuse continues to increase in length but by less and less. Eventually the value converges to sqrt(2), but unlike rational numbers this irrational number takes infinite time to do so.
Zachary Gray
Complex numbers don't exist
regards njwildberger
Cameron Thompson
Are you legitimately retarded? Sqrt(2) < some finite number. Of course the line ends.
Dominic Morales
>[math]\mathbb{Q}[/math]
Nathan Foster
OP think of it like this:
imagine sqrt(2) being its own unit of measurement. That would mean what we consider 3 would be irrational in terms of sqrt(2). Like it being irrational has nothing to do with its geometric plausibility.
Michael Hughes
It seems he is
the relation of H to S (where H is hypotenuse and S is side) cannot be properly represented with a decimal expansion.
It is the decimal expansion that goes on forever, which has nothing to do with the line itself. The line itself is well bounded.
You can also picture it like this, the line's length is 1.41421...
that is, slightly more than 1, very slightly less than 1.5
it is very slightly more than 1.4
quite close to 1.4142 but not quite
And so on
Cooper Jenkins
how many planck lengths in sqrt(2) miles?
Nicholas Murphy
How accurate can you measure real world geometry?
Aaron Nelson
You are talking about a static and PERFECT triangle.
Where in the physical world have you ever seen a circle (perfect), a square (perfect) or a triangle (perfect again)?
Sebastian Miller
...
Nolan Moore
take four lengths of wood.
precision cut them so they are all exactly the same unit length.
place two for the "legs" and the other two for the hypotenuse.
you're welcome.
Colton Long
Jesus!
Look. How do you know the number ends at one third? How do you know the number ends at two?
The fucking number it ends at is SQRT 2. That's the fucking number! Just because you can't write it as a ratio of the lengths of its sides doesn't mean shit!
It is exactly SQRT 2 long!
If you defined it as 2 inches long, then you couldn't write the sides as rationals.