Pythagorean Theorem (derive final numbers based on A=1021-829, B=1021-461)

G

Glistener

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Hi
I’m trying to solve a puzzle based on the Pythagorean Theorem. I understand the Pythagoras Theory and how it can be proved but I am trying to derive final numbers based on the following, written as shown:

A = 1021 - 829
B = 1021 - 461

I have identified the numbers as prime numbers that form parts of various Pythagorean Prime Triples. But I don’t know the significance of the larger, bold numbers or have any other ideas of what to do next so please can you give me a pointer as to the principles I need to follow to derive A and B

Many thanks
 
Yes, 192, 560 and 592 are pythagorean triples.

Where did 1021and 461 come from ???????

Given 1021 and 461 it is easy to figured out where 1021 and 829 come from.
829 is the number you subtract from 1021 to get 192 and
1021 is the number that when you subtract 461 gives you 560!
 
Glistener said:
Hi
I’m trying to solve a puzzle based on the Pythagorean Theorem. I understand the Pythagoras Theory and how it can be proved but I am trying to derive final numbers based on the following, written as shown:

A = 1021 - 829
B = 1021 - 461

I have identified the numbers as prime numbers that form parts of various Pythagorean Prime Triples. But I don’t know the significance of the larger, bold numbers or have any other ideas of what to do next so please can you give me a pointer as to the principles I need to follow to derive A and B

Many thanks
Click to expand...
Please state the puzzle, as given to you, so that we know at least as much as you do about it! Don't make it even more puzzling to the poor people who are trying to help you.

Without some information about the goal, we can't possibly know what to do next!
 
Thank you. I wasn’t trying to be obtuse. I didn’t want to spoil the puzzle for anyone else trying to solve it who has better understanding of geometry than I do.

The puzzle is a geocaching puzzle and is set out below. A and C are likely to be 2 digit numbers and B and C, 3 digit numbers.



Puzzle



Most of us will know Pythagoras' theorem about the lengths of the sides of a right-angled triangle:the sum of the squares of the shorter sides is equal to the square of the longest side.

a2 + b2 = c2

But how many of us could prove it?



Below is one of the simplest proofs. The triangles in the left-hand square have been re-arranged to give the right-hand square. Can you see how this proves Pythagoras's Theorem?

There are hundreds of way to prove the theorem. One was devised by Leonardo da Vinci, and there's even one by Garfield.


The cache, a magnetically attached bison can be found at a fitting location:

N 51° A.B

W 000° C.D

Where,

A = 1021 - 829

B = 1021 - 461

C = 937 - 241

D = 157 - 157
 
And, because of known information about the location, A is likely to be 31 (or 30 or 32) and C may be 06 (or 05).
 
Glistener said:
The puzzle is a geocaching puzzle and is set out below. A and C are likely to be 2 digit numbers and B and C, 3 digit numbers.
Click to expand...
Glistener said:
The cache, a magnetically attached bison can be found at a fitting location:

N 51° A.B

W 000° C.D

Where,

A = 1021 - 829

B = 1021 - 461

C = 937 - 241

D = 157 - 157
Click to expand...
The picture is just a fun way to "prove" the Pythagorean Theorem, namely that in a right triangle, [imath]a^2+b^2=c^2[/imath]. Since there is no actual triangle mentioned, most likely it just suggests, as you inferred, that the numbers somehow involve Pythagorean triples, which are sets of three whole numbers that fit the equation (and therefore could form right triangles).

The puzzle is to figure out what in the world that has to do with A, B, C, and D.

As Steven pointed out,
Steven G said:
Yes, [A = 1021 - 829 =] 192, [B = 1021 - 461 =] 560 and [A^2+B^2 =] 592 are [a] pythagorean triple[s].

Where did 1021and 461 come from ???????

Given 1021 and 461 it is easy to figured out where 1021 and 829 come from.
829 is the number you subtract from 1021 to get 192 and
1021 is the number that when you subtract 461 gives you 560!
Click to expand...
So it would appear that A = 192, and B = 560, taking the first two equations literally. But then what number is 592, and are we to take C = 937 - 241 = 696 literally too? And D = 0? And where does 592 fit in?

All I'm doing is saying what I see; I haven't figured it out yet. It's not just a math problem.

(I'd wondered if this was a geocache puzzle; I geocache a little, but don't often do the puzzles.)
 
I have discovered the following sets of Pythagorean triples but still didn’t see any way of making a link

660 779 1021
215 629 937
540 629 829
261 380 461
120 209 241
85 132 157

There is a related web page but again, I have tried various “calculations“ to determine absolute measurements but have failed!
I feel bad about asking for help so am not looking for the answer, but rather the steps I need to follow to get there as the maths is clearly beyond me.
 
I don't think that you will find a link.
Of course, you can multiply each number in the triple by any number you like.
3 4 5
6 8 10
32 38 35...
 
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