Is the pythagorian theorem true for X^2 +Y^2 = 1?

Question

If x, y are smaller than 1 can we still write the pythagorian theorem?
Seems like the root square of any number smaller than one never ends. and therefore the sum of the square of two numbers never reaches one. Looks like an approximation to me.

Answer 1

Well, I'll try to clear up some things you appear to be confused about:

The decimal expansion of an irrational number never ends, but it's still a number.

Also, squaring an irrational number may give you a rational number. One poster's suggestion of sqrt(2)/2 is a good example.

Even adding two irrational numbers can give you a rational number. For example, if x = sqrt(2) and y = 1 - sqrt(2), both x and y are irrational, but x + y = 1.

Bottom line, the Pythagorean Theorem still works fine.

Answer 2

If either 'x' or ' y ' is a-zero, Pythagorean theorem is true for
x^2 + y^2 =1 (and not for both 'x' and ' y ' values that are both 'less than a-one' and 'greater than a-zero')!

A radius 'r' has ' x ' and ' y ' co-ordinate relation...

r ^2 - x^2 = y^2

9^2 = 81--> 41...40 split and 41^2 - 40^2 = 9^2

7^2 = 49 -->25...24 split and 25^2 - 24^2 = 7^2

5^2 = 25 -->13...12 split and 13^2- 12^2 = 5^2

3^2 = 9 --> 5... 4 split and 5^2- 4^2 = 3^2

1^2= 1 --> 1... 0 split and 1^2- 0^2 = 1^2

Said relation has been used in ancient Indian mathematics , which incidentally is Pythagorean theorem!

Answer 3

Yes. As long as the distances are positive, the Pythagorian theorum still applies.

The square root of 1/3 is the square root of 1/3. It is an exact number. Trying to write it out makes it an approximation.

If the triangle is three atoms wide by four atoms high, you can still use the pythagorian theorum. You'll have to adjust your units, though.

(3 atoms)^2 + (4 atoms)^2 = (5 atoms)^2 is a lot easier to write than the inch or millimeter equivilant.

Answer 4

Is definetely not an approxiamtion. Your expresion is a circle, center in (0,0) and radio of 1. Any pair of numbers that fall in the circumference will satisfy the equation.

Part of what you saying is true, the square root of a number less the 1 is always less than the number. But you are adding two of these smaller number and by adding you can get the 1 you need.

Answer 5

It is true for any numbers, irrespective of size. The numbers need not be rational. However, the formula x^2 + y^2 = 1 is the formula for a circle, centered at (0, 0) and with radius 1.

Answer 6

For a triangle inscribed within a circle, the above eqn is the Pythagorian theorem

Answer 7

"root square of any number smaller than one never ends" is *incorrect*, for one thing.

sqrt (0.25) = 0.5 Is one example.

Secondly, the units for a triangle's measurement is arbitrary.

If you accept that a triangle with side 3 inches, 4 inches, and 5 inches is Pythagorean, then considering that very *same* perfect triangle in units of miles will have you dealing with lengths far less than 1.

Answer 8

Yes, if the hypotenuse is 1 then this formula is correct.

Here is a sample right triangle that fits this formula:

a = 1 / (sqr(2))

b = 1 / (sqr(2))

c = 1

Answer 9

certainly it is still true. the pythagoran theorem is nothing more than the equation for a circle. in the present case you have stated the equation for a circle with radius = 1 and center at 0,0.

Answer 10

If the hypotenuse is 1 then this is still true.
For the isosceles triangle x = y = sqrt(1/2) this works.