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 March 27th, 2019, 07:54 PM #1 Banned Camp   Joined: Mar 2019 From: Mumbai Posts: 66 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 Banned Camp   Joined: Mar 2019 From: Mumbai Posts: 66 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: 2,552 Thanks: 1402 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 Banned Camp   Joined: Mar 2019 From: Mumbai Posts: 66 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: 20,969 Thanks: 2219 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 Banned Camp   Joined: Mar 2019 From: Mumbai Posts: 66 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: 2,270 Thanks: 934 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 Tags decimal right, pythagoras, theorem, triangle Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Antoniomathgini Algebra 8 October 15th, 2017 12:17 PM tanz10 Geometry 3 February 18th, 2015 09:57 AM tanz10 Geometry 1 February 15th, 2015 07:52 AM salma saiid ragab Geometry 2 December 9th, 2014 03:24 PM graviton120 Algebra 3 October 31st, 2008 08:04 PM

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