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> The Spencer Triangle Method: c = x + y
P JayS
post Apr 24, 2013, 07:28 PM
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This method of mine solves for a right triangle using the information gathered from only one side of the triangle or a simple line with a value attached to it without the use of any other sides or angles.

When placing a value on the line it is then determined at what point the hypotenuse should be separated into 2 individual pieces.

The results of my methods can be double checked by using Pythagoras method of solving triangles.

It is recognized that the line of this triangle will serve as the hypotenuse of the new triangle labelled "c".

c = x + y therefore becomes c^2 = cx + cy.

Side a of the triangle is simply the square root of cx and likewise side b of the triangle is also just the square root of cy.

For example: we can take the right triangle with the sides of 3, 4, 5 and calculate c = x + y

5x = a^2
5x = 3^2
x = 9 / 5
x = 1.8

5y = b^2
5y = 4^2
y = 16 / 5
y = 3.2

c = x + y
5 = 1.8 + 3.2

c^2 = cx + cy
5^2 = (5*1.8) + (5*3.2)
25 = 9 + 16
25 = 25

Therefore knowing what the difference is with a hypotenuse results in a new right triangle every time.

Another random example: 23 = 11.627 + 11.373

c^2 = cx + cy
sqrt cx = sqrt (23 * 11.627)
side a = sqrt 267.421 = 16.35301195

sqrt cy = sqrt (23 * 11.373)
side b = sqrt 261.579 = 16.17340409

Now double checking with Pythagoras theorem: c^2 = a^2 + b^2

23^2 = (16.35301195)^2 + (16.17340409)^2
529 = 267.421 + 261.579
529 = 529

Noting that the triangle with a hypotenuse of c = 23 and side a = 16.35301195 and side b = 16.17340409 forms a right triangle and the Spencer Triangle Method: c = x + y is sound.
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P JayS
post Apr 25, 2013, 12:28 PM
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If I simply drew a picture of a triangle and marked the base x = 2.3 and y = 2.7 you would have no way of telling what the 3 sides of the triangle was using Pythagoras theorem which requires two sides.

But using my method of c = x + y you can easily find that the three sides of the right triangle associated with the hypotenuse or the longest side.

c = x + y
5 = 2.3 + 2.7

c^2 = cx + cy
side a = sqrt 11.5
side b = sqrt 13.5
side c = 5

checking with Pythagoras theorem:

c^2 = a^2 + b^2
25 = 11.5 + 13.5
25 = 25
a = sqrt 11.5
b = sqrt 13.5
c = 5

P.j.S .
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P JayS
post Apr 25, 2013, 02:02 PM
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Using the c = 1.8 + 3.2 to find that side a = 3 then we can find the height of the smaller triangle still using
c = x + y methods. See? ...

( a * b ) / c = height 3,4,5 triangle
(3 * 4) / 5 = 2.4
a^2 - h^2 = a*x1
9 - 5.76 = 3.24
a^2 - a*y1 = a*x1

h^2 = a*y1 = 5.76
5.76 / a = y1
y1 = 1.92

a^2 - a*y1 = a*x1
9 - 5.76 = a*x1 = 3.24
x1 = 1.08

c = x + y = 1.8 + 3.2 = 5
a = x1 + y1 = 1.08 + 1.92 = 3

(h * x) / 3 = height "h1" of the smaller triangle a, h, x
(2.4 * 1.8) / 3 = h1 = 1.44

Please note that Pythagoras Theorem was not used to find the heights of the two particular triangles.

P.j.S .
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P JayS
post Apr 25, 2013, 03:21 PM
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I started a discussion about this matter at physicsforums.com with the user name Crazy Horse 11 but one of the mentors of the site banned me forever as a crackpot.

I am very grateful to brainmeta.com for allowing me to develop my math in a discussion with the world watching. Anyone is free to join in and participate at any given time. Thus as the discussion endures to the end I can fully see where I am right and where the original work needs to be corrected.

I thank you fully BrainMeta.com.

As for a discussion: These current words of advice from an admired poet on this site. "Let it Happen".
http://brainmeta.com/forum/index.php?showtopic=24688

With deep Regards to the Reasonableness of this Internet Site,
Peter Jeffrey Spencer.
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