Pythagorean Triples

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ZMB038

444 posts

ZMB038

#1 h May 19, 2025, 6:04 PM • 3 Y

Y by Exponent11, PikaPika999, RainbowJessa

9Poll:

How many Pythagorean Triples have you memorized?

260 Votes

0

2%

(6)

1

5%

(12)

2-5

23%

(61)

6-10

28%

(73)

11-20

11%

(29)

21-35

3%

(8)

36-50

1%

(3)

51+

8%

(21)

999999999999999(troll)

18%

(47)

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Please put some of the ones you know, and try not to troll/start flame wars! Thank you

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pingpongmerrily

4055 posts

pingpongmerrily

#3 h May 19, 2025, 6:14 PM • 5 Y

Y by Exponent11, BrSpen, PikaPika999, aidan0626, RainbowJessa

3-4-5
5-12-13
7-24-25
9-40-41
11-60-61
20-21-29
8-15-17

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BAM10

190 posts

BAM10

#4 h May 19, 2025, 6:20 PM • 4 Y

Y by Exponent11, BrSpen, PikaPika999, RainbowJessa

3-4-5
5-12-13
7-24-25
8-15-17
9-40-41
11-60-61
12-35-37
13-84-85

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steve4916

117 posts

steve4916

#5 h May 19, 2025, 6:41 PM • 4 Y

Y by Exponent11, BrSpen, PikaPika999, RainbowJessa

3-4-5
5-12-13
7-24-25
9-40-41
11-60-61
6-8-10
9-12-15
12-16-20
15-20-25
8-15-17
12-35-37
20-21-29
33-56-65 (the best one)

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sadas123

1482 posts

sadas123

#6 h May 19, 2025, 6:58 PM • 4 Y

Y by Exponent11, BrSpen, PikaPika999, RainbowJessa

I know infinite ong, 3-4-5 * x,x,x :diablo:

3,4,5 and 6,8, 10 and 9,12, 15 and 15,20,25 and 18,24,30 and.............................

but the main ones:

3-4-5
6-8-10
9-12-15
15-20-25
5-12-13
10-24-26

This post has been edited 1 time. Last edited by sadas123, May 19, 2025, 6:58 PM

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nitride

593 posts

nitride

#7 h May 19, 2025, 7:47 PM • 5 Y

Y by Exponent11, BrSpen, A7456321, PikaPika999, RainbowJessa

you can do some quadratic stuff to name like 50+ triples and even more if ur mental math is good

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ZMB038

444 posts

ZMB038

#8 h May 19, 2025, 7:51 PM • 3 Y

Y by Exponent11, PikaPika999, RainbowJessa

3-4-5
5-12-13
7-24-25
9-40-41
11-60-61
13-84-85
15-112-113
17-144-145
20-21-29
8-15-17
16-63-65
12-35-37
20-99-101
24-143-145
40-399-401
64-1023-1025
69-2580-2581
Is this a lot?

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ZMB038

444 posts

ZMB038

#9 h May 19, 2025, 7:51 PM • 3 Y

Y by Exponent11, PikaPika999, RainbowJessa

sadas123 wrote:

I know infinite ong, 3-4-5 * x,x,x :diablo:

3,4,5 and 6,8, 10 and 9,12, 15 and 15,20,25 and 18,24,30 and.............................

but the main ones:

3-4-5
6-8-10
9-12-15
15-20-25
5-12-13
10-24-26

Not tryna be rude but scaling doesn't count. (3-4-5=6-8-10)

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iwastedmyusername

225 posts

iwastedmyusername

#10 h May 19, 2025, 7:57 PM • 3 Y

Y by Exponent11, PikaPika999, RainbowJessa

technically ive memorized like 40 squares so i can instantly calculate a pythagorean triple in the form {n,n^2-1/2,n^2+1/2}

in reality i've only memorized:
3-4-5
5-12-13
7-24-25
9-40-41
8-15-17
12-35-37
20-21-29
33-56-65

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Soupboy0

635 posts

Soupboy0

#11 h May 19, 2025, 8:37 PM • 3 Y

Y by Exponent11, PikaPika999, RainbowJessa

3-4-5
5-12-13
8-15-17
7-24-25
20-21-29
12-35-37
9-40-41
11-60-61
13-84-85
15-112-113
17-144-145
19-180-181
21-220-221
23-264-265
25-322-323
27-364-365
29-420-421
31-480-481
33-544-545
35-612-613
37-684-685
39-760-761
41-840-841
43-924-925
45-1012-1013

This post has been edited 3 times. Last edited by Soupboy0, May 19, 2025, 8:39 PM

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Andrew2019

2419 posts

Andrew2019

#12 h May 19, 2025, 8:55 PM • 3 Y

Y by Exponent11, PikaPika999, RainbowJessa

3,4,5
5,12,13
8,15,17
7,24,25
9,40,41
12,35,37
11,60,61
20,21,29
20,99,101
15,112,113 (my favorite)
$n, \lfloor\frac{n^2}{2}\rfloor, \lceil\frac{n^2}{2}\rceil$

This post has been edited 2 times. Last edited by Andrew2019, May 19, 2025, 8:58 PM

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ZMB038

444 posts

ZMB038

#13 h May 19, 2025, 9:23 PM • 3 Y

Y by Exponent11, PikaPika999, RainbowJessa

Soupboy0 wrote:

3-4-5
5-12-13
8-15-17
7-24-25
20-21-29
12-35-37
9-40-41
11-60-61
13-84-85
15-112-113
17-144-145
19-180-181
21-220-221
23-264-265
25-322-323
27-364-365
29-420-421
31-480-481
33-544-545
35-612-613
37-684-685
39-760-761
41-840-841
43-924-925
45-1012-1013

dang that's a lot you memorized!

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CJB19

178 posts

CJB19

#14 h May 19, 2025, 9:30 PM • 3 Y

Y by Exponent11, PikaPika999, RainbowJessa

Andrew2019 wrote:

$n, \lfloor\frac{n^2}{2}\rfloor, \lceil\frac{n^2}{2}\rceil$

Yeah I was gonna way that except I describe it as $n, \frac{n^2-1}{2},\frac{n^2+1}{2}$
(Only for odd integers)

This post has been edited 1 time. Last edited by CJB19, May 19, 2025, 9:30 PM

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Capybara7017

682 posts

Capybara7017

#15 h May 19, 2025, 9:40 PM • 3 Y

Y by Exponent11, PikaPika999, RainbowJessa

3,4,5
5,12,13
8,15,17
7,24,25
9,40,41
bro so little

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CJB19

178 posts

CJB19

#16 h May 19, 2025, 9:43 PM • 2 Y

Y by Exponent11, RainbowJessa

for multiples of four I think you can do $n, (\frac{n}{2})^2-1, (\frac{n}{2})^2+1$
Can someone check this?

This post has been edited 1 time. Last edited by CJB19, May 19, 2025, 9:43 PM

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PikaPika999

3729 posts

PikaPika999

#75 h Jul 7, 2025, 8:30 PM

Y by

Ooh so I already put the odd number...

but for even numbers...

1. Take an even number $2n$
2. Divide it by 2 to get $n$
3. Square it to get $n^2$
4. Subtract 1 from it to get $n^2-1$
5. Add 1 to the square to get $n^2+1$

Ta-da! The Pythagorean Triple is $(2n,n^2-1,n^2+1)$

I don't think that the formulas for the even and odd numbers capture every single triple, but idk

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dw22winner

114 posts

dw22winner

#76 h Jul 7, 2025, 8:42 PM • 1 Y

Y by PikaPika999

I know:

3-4-5,
6-12-13,
8-15-17
7-24-25
20-21-29
9-40-41
11-60-61

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PikaPika999

3729 posts

PikaPika999

#77 h Jul 7, 2025, 8:50 PM

Y by

dw22winner wrote:

I know:

3-4-5,
6-12-13,
8-15-17
7-24-25
20-21-29
9-40-41
11-60-61

ooh, 20-21-29 doesn't use the formula

dat kool

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OWOW

259 posts

OWOW

#78 h Jul 7, 2025, 9:02 PM • 1 Y

Y by PikaPika999

quick tip for finding squares. I you have a square, like 5^2, then take the base (5) multiply it by 2 (10), add 1 (11), then add that the original 5^2 (36)

:D

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PikaPika999

3729 posts

PikaPika999

#80 h Jul 7, 2025, 9:08 PM • 1 Y

Y by booking

OWOW wrote:

quick tip for finding squares. I you have a square, like 5^2, then take the base (5) multiply it by 2 (10), add 1 (11), then add that the original 5^2 (36)

:D

Yes, to get from $1^2$ to $2^2,$ you add 3, to get from $2^2$ to $3^2$ you add 5, to get from $3^2$ to $4^2,$ you add 7, and so on.

In summary, to get from $n^2$ to $(n+1)^2,$ you add $n+(n+1)=2n+1$

This post has been edited 1 time. Last edited by PikaPika999, Jul 7, 2025, 9:08 PM

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booking

500 posts

booking

#81 h Jul 7, 2025, 9:10 PM • 1 Y

Y by PikaPika999

Pika, wanna play me on mathdash?
And @above, yeah. That's how I remember all of mine

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PikaPika999

3729 posts

PikaPika999

#82 h Jul 7, 2025, 9:20 PM

Y by

sure

$\text{[math]}$

I'm kinda new to it tho so I prolly won't do that well :oops:

This post has been edited 1 time. Last edited by PikaPika999, Jul 7, 2025, 9:20 PM

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booking

500 posts

booking

#83 h Jul 7, 2025, 9:21 PM • 1 Y

Y by PikaPika999

lets do an amc 8 mini you choose which one

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PikaPika999

3729 posts

PikaPika999

#84 h Jul 7, 2025, 9:22 PM

Y by

booking wrote:

lets do an amc 8 mini you choose which one

idk how to choose one and where to go... :what?:

(also should we continue this conversation in a PM? I'll send it

)

EDIT: oh wait it says u can't accept PMs, oh well

This post has been edited 3 times. Last edited by PikaPika999, Jul 7, 2025, 9:23 PM

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booking

500 posts

booking

#85 h Jul 7, 2025, 9:23 PM • 1 Y

Y by PikaPika999

I'll send you a link
https://mathdash.com/contest/amc-8-mini-3

This post has been edited 1 time. Last edited by booking, Jul 7, 2025, 9:23 PM

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PikaPika999

3729 posts

PikaPika999

#86 h Jul 7, 2025, 9:24 PM

Y by

where 2 go from there?

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booking

500 posts

booking

#87 h Jul 7, 2025, 9:27 PM • 1 Y

Y by PikaPika999

wait uh, i did it already, lets move this to a pm

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PikaPika999

3729 posts

PikaPika999

#88 h Jul 7, 2025, 9:30 PM

Y by

I tried sending PM but it says u aren't accepting new ones...

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booking

500 posts

booking

#89 h Jul 7, 2025, 9:33 PM • 1 Y

Y by PikaPika999

I sent it you see it?

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OWOW

259 posts

OWOW

#90 h Jul 8, 2025, 3:07 AM

Y by

To find cool pythagorean triples, try any odd square (like 17^2=289). Then you can find two consecutive integers that sum to that number: (144 +145=289). The larger one (145) is the hypotenuse, the smaller (144) is the big leg, and guess what the small leg is? 17!!! Pretty nuts right?
Here's some more
9^2=81: (9,40,41)
11^2=121: (11,60,61)
13^2=169: (13,84,85)
15^2=225: (15,112,113)
17^2=289: (17,144,145)
19^2=361: (19,180,181)
21^2=441: (21,220,221)
23^2=529: (23,264,265)

This post has been edited 1 time. Last edited by OWOW, Jul 8, 2025, 3:07 AM

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