## anonymous 4 years ago i need someone to walk me step by step on a Pythagorean theorem i am having trouble with it and just a little bit of extra help

1. anonymous

2. anonymous

Zed

3. anonymous

hey tinkerbell :)

4. anonymous

help

5. anonymous

6. anonymous

ok

7. watchmath

hello satellite :)

8. anonymous

brb zed im going to get a drink

9. anonymous

man that is confusing. pick two numbers, m and n, one even one odd. lets say i pick m = 4, n 1 then take $m^2-n^2=4^2-1^2=15$ also $2mn=2\times 4\times 1=8$ and finally $m^2+n^2=4^2+1^2=17$ those three number, $15,8,17$ will be a pythagorean triple. that is $15^2+8^2=17^2$

10. anonymous

watchmath!! long time no see. i just mentioned you the other day

11. anonymous

saying i missed your interesting questions/puzzles

12. watchmath

yes, you are a legend now here :). Good job!

13. anonymous

legend smegend. when i get to 10,000 medals i am going to have a whiskey and call it a day

14. anonymous

hope to see you more regularly.

15. watchmath

:). I will think some interesting problem for you

16. anonymous

ok im here sorry had to grab a bottle of water i have been sick but im back now

17. anonymous

ok, but right now i am puzzling over how to make truth tables interesting because they are boring me to death. if you have any good puzzles or exercises involving them, let me know.

18. anonymous

@tinkerbell, i wrote out a method for finding triples for you above. the worksheet you sent is rather vague (method on line) etc

19. anonymous

i have been down ill with the flu really bad

20. anonymous

i can walk you through another one if you like

21. anonymous

tinkerbell do you need to use different methods each time?

22. anonymous

It can be proved as the 2 dimensional case of the Parseval equality I think! Functional Analysis is goood. If not, then just remember this: The square on the hypotenuse is equal to the sum of the squares on the other two sides!

23. anonymous

this is the only one i see , a^2+b^2 = c^2.

24. anonymous

maybe it is not clear what you are looking for. not any three numbers a, b and c, but three whole numbers a, b and c with $a^2+b^2=c^2$

25. anonymous

thats what i see

26. anonymous

did you open the link on the worksheet?

27. anonymous

my assignment

28. anonymous
29. anonymous

that confused me

30. anonymous

i see. it looks like your worksheet is asking for 5 different triples. i wrote one above. would you like to do another one?

31. anonymous

can you rewrite it and explain as you go

32. anonymous

ok we can try the first one If a is odd, then b = a2/2 − 1/2 and c = b + 1 If a is even, then b = a2/4 − 1 and c = b + 2 pick an odd number

33. anonymous

7

34. anonymous

ok then to find "b" we compute $b=\frac{7^2}{2}-\frac{1}{2}$ what do you get?

35. anonymous

there any other way we can do this with out fractions

36. anonymous

will 7^2 =49 so it would be 49/2-1/2

37. anonymous

this is a fraction but don't fret $\frac{7^2}{2}-\frac{1}{2}=\frac{49-1}{2}=\frac{48}{2}=24$

38. anonymous

a nice whole number so $a=7,b=24$ and now $c=b+1=24+1=25$ and that is your "triple" $7,24,25$

39. anonymous

and you are supposed to check that $7^2+24^2=25^2$ which you can do with a calculator

40. anonymous

slow down

41. anonymous

let me know if you have any questions about what i wrote

42. anonymous

no i have no questions so far let me type it into the template real qick

43. anonymous

ok that gives me 625

44. anonymous

good so we have one. now we can try another one

45. anonymous

46. anonymous

47. anonymous

ok now we try a different method

48. anonymous

pick two numbers m and n, where one is even and one is odd. make them not too big

49. anonymous

88 and 13

50. anonymous

whoa nice and small!

51. anonymous

you did not say that

52. anonymous

we want to make this easy, not hard. pick small numbers

53. anonymous

11 and 17

54. anonymous

ok i will pick them, one even and the other odd. i pick 5 and 2 now we compute $5^2-2^2=25-4=21$

55. anonymous

then i take $2\times 5\times 2=20$ and finally $5^2+2^2=25+4=29$ and the three numbers $21,20,29$ are also a triple and you can check that $21^2+20^2=29^2$

56. anonymous

ok

57. anonymous

now we have two. do you have to use a different method for each one?

58. anonymous

yes i would like if it is possible

59. anonymous

i will le let you know when im done entering it in the template

60. anonymous

well maybe we can do one more, but if i were you i would use the last method again with two different numbers

61. anonymous

ok hang on im 3^2-8^2=9-64=55

62. anonymous

am i right so far

63. anonymous

you are on the right track, but you should make it $8^2-3^2=64-9=55$ so you don't get negative numbers

64. anonymous

so you picked 8 and 3,and now you have 55 next two numbers will be $2\times 8\times 3$ and $8^2+3^2$

65. anonymous

2x 8x 3=48

66. anonymous

8^2 + 3^2 is to check right

67. anonymous

no that is the third number, the long side

68. anonymous

73

69. anonymous

the three numbers are $55,48,73$ and the check is $55^2+48^2=73^2$

70. anonymous

ok be right with you

71. anonymous

unfortunately i have to run. but you have 3 so far, and it looks like you know what you are doing, so i think you should be in good shape

72. anonymous

i just have to rememer to put the bigger number in front