Waste less time on Facebook — follow Brilliant.
×

Variation on Pythagorean Theorem

I already know about the Pythagorean Theorem, where \(a^2 + b^2 = c^2\). Now I'm wondering if there can be a solution where \(\frac {1}{a^2} + \frac {1} {b^2} = \frac {1}{c^2}\). Is this possible?

Note: If this question has already been asked, please show me a link where this question was asked so I can look at that.

If this is impossible tell me how it is impossible to get a solution (or solutions) for this equation.

If this is possible tell me how it is possible to get a solution (or solutions) for this equation.

Note by Ananth Jayadev
1 year, 11 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

We can put it into the form of

\[a^2+b^2 = (\frac{ab}{c})^2\]

of which one answer is \(c = \frac{ab}{\sqrt{a^2+b^2}}\). Some answer of (a, b, c) for natural number \(x\) is

\[(a, b, c) = (15x, 20x, 12x), (175x, 600x, 168x)\]

Kay Xspre - 1 year, 10 months ago

Log in to reply

汶良 林 - 1 year, 10 months ago

Log in to reply

for example:

x = 3, y = 4, z = 5

a = 20, b = 15, c = 40

汶良 林 - 1 year, 10 months ago

Log in to reply

\(a = 20, b =15, c= 12 \)

Pi Han Goh - 1 year, 11 months ago

Log in to reply

Thank you very much!

Ananth Jayadev - 1 year, 11 months ago

Log in to reply

Cool!

Kamalpreet Singh - 1 year, 10 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...