Sunday, April 24, 2011

How to create Triple Phytagoras

Something that I like is math but can not be sad if I did not lecture in the majors. Last night when I was given the opportunity to provide math tutoring I find something new to me because previously I had never studied it, namely Triple Pytagoras.



As we know from Theorem Pytagoras expressed in a right triangle apply broad square on the hypotenuse (the side before the right angle of a right triangle) or the hypotenuse equals the total square area on two sides of a right angle clamp elbow.

As for the "Triple Pytagoras" is defined like this in a book I read: if a, b, c natural numbers is the length of the sides of a triangle, with hypotenuse c and satisfy the equation c2 = a2 + b2, then the three numbers a, b, and c is called Triple Pytagoras and the triangle is a right triangle.


So there is a formula
If m > n maka m2 + n2, m2 - n2, 2mn are Triple Pytagoras

From there I got interested, using the formula I use Excel and be a table like this:










m n c a b
2 1 5 3 4
3 1 10 8 6
3 2 13 5 12
4 1 17 15 8
4 2 20 12 16
4 3 25 7 24
5 1 26 24 10
5 2 29 21 20
5 3 34 16 30
5 4 41 9 40
6 1 37 35 12
6 2 40 32 24
6 3 45 27 36
6 4 52 20 48
6 5 61 11 60
7 1 50 48 14
7 2 53 45 28
7 3 58 40 42
7 4 65 33 56
7 5 74 24 70
7 6 85 13 84
8 1 65 63 16
8 2 68 60 32
8 3 73 55 48
8 4 80 48 64
8 5 89 39 80
8 6 100 28 96
8 7 113 15 112
9 1 82 80 18
9 2 85 77 36
9 3 90 72 54
9 4 97 65 72
9 5 106 56 90
9 6 117 45 108
9 7 130 32 126
9 8 145 17 144
10 1 101 99 20
10 2 104 96 40
10 3 109 91 60
10 4 116 84 80
10 5 125 75 100
10 6 136 64 120
10 7 149 51 140
10 8 164 36 160
10 9 181 19 180

from there I was interested in studying some of which I consider similar triangles. With the reference values m and n terkumpullah several triangles the same as below:








2 1
3 1
4 2
6 2
8 4

or








3 2
5 1
6 4
10 2

or








4 1
5 3
8 2
10 6

and so on,
from there I can pull Conclusion I = triple pytagoras triangle will always form a triangle triple pytagoras comparable, with a size twice that of the triple pytagoras triangle at the previous level and the shape of reflection and rotation 900 of the triple pytagoras triangle at the previous level.

After that I met also the uniqueness of the model, where the triangles are "equal" has its own unique formula. Thus formed is also  Conclusion II = if m and n are the authors of a triple pytagoras triangle, while a and b are the authors of a comparable pytagoras triple triangle on it, then
a = m + n,
dan
b = (m2-n2) : a
atau
b = √ a2-4mn 

And there have not finished my curiosity by forming the table below









m n c a b
2 1 5 3 4
3 2 13 5 12
4 1 17 15 8
4 3 25 7 24
5 2 29 21 20
5 4 41 9 40
6 1 37 35 12
6 3 45 27 36
6 5 61 11 60
7 2 53 45 28
7 4 65 33 56
7 6 85 13 84
8 1 65 63 16
8 3 73 55 48
8 5 89 39 80
8 7 113 15 112

From there I can make Conclusion III = To form a triple pytagoras triangle different with elements m and n where m> n then if m odd then n must be even or vice versa Juka m is even then n must be odd. 

Well that's the result of my adventure for 2 hours after knowing what it was Triple Pytagoras. May be useful for you (especially for math teachers to create questions pytagoras not in the form of fractions) ^_^

6 coment:

  1. (Maaf) izin mengamankan PERTAMAX dulu. Boleh, kan?!
    Dulu saya paling sebel kalau pas materi teori phytagoras. Ngitungnya pakai kuadrat-kuadrat terus musti ngerubah juga pakai akar kuadrat.

    ReplyDelete
  2. @Alamendah, bagaimana dengan sekarang? kalau dulu paling sebel? sekarang apakah sebaliknya menggunakan PERTAMANX? eh, pytagoras?

    ReplyDelete
  3. Matematika?
    duh, ampuuuun, dr dulu sewaktu masih berwujud aljabar, ilmu ukur sudut, ilmu ukur ruang dll dsbnya itu, aja bunda gak pernah suka, akhirnya gak pernah ngerti :(

    apalagi sekarang....... hiks......
    yg penting msh ngerti utk hitung2an yg sederhana, misalnya uang belanja utk sebulan heehehe.... ( inilah emak2 )
    salam
    salam

    ReplyDelete
  4. @bunda ah, enjoy aja bunda, matematika juga bisa dibuat rekreasi koq ^_^

    @ usup ^_^

    ReplyDelete
  5. ini ngomongin rumus phytagoras ya ? wah trauma saya kalo ketemu ama yang namanya x, y apalagi ditambah pangkat 2 dll...

    ReplyDelete