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 March 27th, 2019, 07:54 PM #1 Member   Joined: Mar 2019 From: Mumbai Posts: 56 Thanks: 3 Pythagoras theorem https://en.m.wikipedia.org/wiki/Pythagorean_theorem Can we apply Pythagoras theorem to decimal points where a,b & c are decimal points sides in a right angled triangle? a^2 + b^2 = c^2 a & b are sides c is Hypothenuse Examples of a,b & c : 3.1,2.3,4.3,5.2,7.3,11.4,13.3 etc Thanks & Regards, Prashant S Akerkar Last edited by prashantak; March 27th, 2019 at 07:58 PM. Reason: Content updates
 March 27th, 2019, 09:09 PM #2 Member   Joined: Mar 2019 From: Mumbai Posts: 56 Thanks: 3 Thanks. Can we have Pythagorean triplets which are decimal point numbers? Thanks & Regards, Prashant S Akerkar
 March 27th, 2019, 09:12 PM #3 Senior Member     Joined: Sep 2015 From: USA Posts: 2,408 Thanks: 1310 scale up a 3,4,5 right triangle until the sides are > 100 (147,196,245) is one example Now divide by 100 (1.47, 1.96, 2.45) is a right triangle with sides that have decimal length.
 March 27th, 2019, 09:22 PM #4 Member   Joined: Mar 2019 From: Mumbai Posts: 56 Thanks: 3 Thanks. So we can have Pythagorean triplets, and the Pythagorean theorem is modified & tested to work with decimal points triplets. Similar to the above decimal points Pythagorean triplets, Can we list all ? Thanks & Regards, Prashant S Akerkar Last edited by prashantak; March 27th, 2019 at 09:39 PM.
 March 28th, 2019, 01:42 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,485 Thanks: 2041 Not quite. By definition, a Pythagorean triplet is a triplet of natural numbers. Corresponding triplets of rationals can be obtained by applying a rational scale factor.
March 28th, 2019, 04:14 AM   #6
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Quote:
 Originally Posted by skipjack Not quite. By definition, a Pythagorean triplet is a triplet of natural numbers. Corresponding triplets of rationals can be obtained by applying a rational scale factor.
Thanks.

We are enhancing Pythagorean theorem.

Can we create a list of Pythagorean triplets of rationals?

Thanks & Regards,
Prashant S Akerkar

March 28th, 2019, 05:39 AM   #7
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Quote:
 Originally Posted by prashantak Can we create a list of Pythagorean triplets of rationals?
Yes we can, and the previous post said how to do it.

 April 13th, 2019, 09:48 AM #8 Member   Joined: Mar 2019 From: Mumbai Posts: 56 Thanks: 3 Thanks. Can we have a Dictionary of Pythagorean triplets of rationals? Thanks & Regards, Prashant S Akerkar
 April 13th, 2019, 04:02 PM #9 Math Team     Joined: May 2013 From: The Astral plane Posts: 2,138 Thanks: 872 Math Focus: Wibbly wobbly timey-wimey stuff. I don't know about a library, but there is a way to generate them (all of them I think.) Given two positive integers m, n such that m > n we can construct: $\displaystyle a^2 + b^2 = c^2$ with $\displaystyle a^2 = (m - n)^2$ $\displaystyle b^2 = 4mn$ $\displaystyle c^2 = (m + n)^2$ The only trick is the value for $\displaystyle b^2$. We have to put in "by hand" m, n such that $\displaystyle b^2$ is actually the square of a number. For example, if we choose m = 4, n = 1 we get $\displaystyle a^2 = (m - n)^2 = (4 - 1)^2 = 3^2$ So a = 3. $\displaystyle b^2 = 4mn = 4(4)(1) = 4^2$ so b = 4, $\displaystyle c^2 = (m + n)^2 = (4 + 1)^2 = 5^2$ so c = 5. Thus we know that 3, 4, 5 is a Pythagorean triple. And, of course, for rational numbers you can use skipjack's comment. For otherwise real numbers you can simply pick a value of a and b can just calculate c. No troubles there. -Dan

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