# Naked Science Forum

## On the Lighter Side => New Theories => Topic started by: sim on 11/01/2019 06:32:45

Title: A 1 unit by 1 unit triangle is impossible
Post by: sim on 11/01/2019 06:32:45
If you have none maths  you will have been taught about a triangle that has sides equal to 1 unit long, the diagonal of the triangle is equal to root 2. Root 2 never terminates-it does not stop

but

A 1 unit by 1 unit triangle is impossible- thus maths ends in meaninglessness

a triangle that has sides equal to 1 unit long, the diagonal of the triangle is equal to  root 2 th[is] is a contradiction in terms

the length-property-of the diagonal is root 2 ie non finite but the diagonal is finite a contradiction

Thus root 2  is a non finite number ie it never terminates –thus can never be constructed but the length of the hypotenuse is finite ie terminates
or
But by the mathematics the length of the hypotenuse is finite ie it terminates
Thus we have a contradiction the maths says
3) the hypotenuse is finite ie terminates ie can be constructed
but
4) the length of the hypotenuse is root 2 Ie is non-finite which does not terminate ie can never be constructed
Thus mathematics ends in meaninglessness

This again shows that mathematics/geometry/trigonometry cant be the language of the universe as the objects mathematics creates ie a 1 by 1 root 2 triangle cannot exist in our universe-[as it cant be constructed]
Title: Re: A 1 unit by 1 unit triangle is impossible
Post by: mad aetherist on 11/01/2019 07:12:39
If you have none maths  you will have been taught about a triangle that has sides equal to 1 unit long, the diagonal of the triangle is equal to root 2. Root 2 never terminates-it does not stop
http://gamahucherpress.yellowgum.com/wp-content/uploads/MATHEMATICS.pdfbutA 1 unit by 1 unit triangle is impossible- thus maths ends in meaninglessnessa triangle that has sides equal to 1 unit long, the diagonal of the triangle is equal to  root 2 th[is] is a contradiction in termsthe length-property-of the diagonal is root 2 ie non finite but the diagonal is finite a contradictionThus root 2  is a non finite number ie it never terminates –thus can never be constructed but the length of the hypotenuse is finite ie terminatesrBut by the mathematics the length of the ypotenuse is finite ie it terminatesThus we have a contradiction the maths says3) the hypotenuse is finite ie erminates ie can be constructedbut4) the length of the hypotenuse is root 2 Ie is non-finite which does not terminate ie can never be constructedThus a contradiction in termsThus mathematics ends in meaninglessness This again shows that mathematics/geometry/trigonometry cant be the language of the universe as the objects mathematics creates ie a 1 by 1 root 2 triangle cannot exist in our universe-[as it cant be constructed]
Thats krapp. U are intentionally being silly. U just construct two lines 1 unit long at 90 deg & join the ends. If u want to know the exact length of the diagonal in our decimal system then thats your problem, nobody else wants to know. Why dont u find a non-decimal arithmetic that gives an exact value or a fixed repeating value.

In any case we know that nothing is as it appears. We cant make an exact triangle like that with an exact 90 deg angle because the aetherwind is unlikely to blow equally along all three sides, thusly we will have a different Lorentzian length contraction for each side, therefore u cant actually make such a triangle, or u can but the angle will not be 90 deg, in which case u are correct but for the wrong reason.
Title: Re: A 1 unit by 1 unit triangle is impossible
Post by: Bored chemist on 11/01/2019 09:36:09
Why dont u find a non-decimal arithmetic that gives an exact value or a fixed repeating value.
Because there isn't one.
The sides and diagonal of a square are incommensurate.

However, Sim's point is still obviously nonsense. A square has a diagonal.
Title: Re: A 1 unit by 1 unit triangle is impossible
Post by: evan_au on 11/01/2019 18:38:11
Quote from: sim
the diagonal is root 2 ie non finite
You are confusing several mathematical concepts, here.
- Non-Finite: Means that "whatever number I give you, your number is always bigger". Well, I give you 2, and it's bigger than your number, so your number is finite.
- Non-Terminating Decimal: Means a number that can never be exactly represented in the decimal system. There are a lot of fractions (ie rational numbers) which the Decimal system can't represent in a finite string - basically any fraction where the denominator isn't a product of 2 and 5 (the factors of 10). But that is quite independent from non-finite.
- Irrational Number: Means that the number never terminates, and never repeats. But this is quite independent from non-finite (but it does create a non-terminating Decimal).

Quote
the length of the hypotenuse is root 2 .... ie can never be constructed
There are many irrational numbers that can't be "constructed" (ie produced in a finite number of steps using just a straight-edge and compass, the way the ancient Greeks used to do geometry).

But SQRT(2) is not one of them.

SQRT(2) is the solution of a quadratic equation, and these can be constructed using the traditional tools. Try these easy  steps:
- Draw a straight line. Call this one unit
- Create a right-angle at one end of the unit length. Draw a perpendicular line.
- Mark off a unit length along this perpendicular
- Join the two ends
- You have just created a line of length SQRT(2) exactly*, in a finite number of steps

Examples of numbers that can't be constructed as a straight line include Pi (π) and 21/3

*By exact, the Greeks meant "in principle, if you had a perfectly thin pencil, and a perfectly straight edge, and a perfectly steady hand, and your compass held the radius exactly, and you could line up two points exactly..."