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December 21st, 2016, 05:44 AM   #1
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A new way to Pythagorean Theorem numbers

Choos A > 1
Find B by the formula B = 0.5( AA - 1 )
Find C by the formula C = B + 1

the result .... AA + BB = CC

Examples

A1.4 B0.48 C1.48 = (A140 B48 C148) = ( A35 B12 C37 )
A1.8 B1.12 C2.12 = (A180 B112 C212 )=( A45 B28 C53 )
A2 B1.5 C2.5 = (A20 B15 C25 ) = ( A4 B3 C5 )
A2.3 B2.145 3.145 = (A2300 B2145 3145)=(A460 B429 C629)
A3 B4 C5
A4 B7.5 C8.5 = (A40 B75 C85)=(A8 B15 C17 )
A5 B12 C13
A6 B17.5 C18.5 = (A60 B175 C185 )=(A12 B35 C37)
A27 B364 C365
A33 B544 C545
A34 B577.5 C578.5 = (A340 B5775 C5785)=(A68 B1155 C1157)
A31 B480 C481
A73 B2664 C2665

Aetzbar

Last edited by skipjack; December 21st, 2016 at 05:39 PM.
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December 21st, 2016, 08:26 AM   #2
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Yes, that's true but hardly new- it is basic algebra.

With $\displaystyle B= (1/2)(A^2- 1)= A^2/2- 1/2$ and $\displaystyle C= B+ 1= A^2/2+ 1/2$

Then $\displaystyle A^2+ B^2= A^2+ A^4/4- A^2/2+ 1/4= A^4/4+ A^2/2+ 1/4$
and $\displaystyle C^2= A^4/4+ AY^2/2+ 1/4$. It is the adding 1 that converts the "-1/2" to "1/2".

in general (a- b)^2= a^2- 2ab+ b^2. Adding 4ab to that gives a^2+ 2ab+ b^2= (a+ b)^2.
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December 21st, 2016, 10:57 AM   #3
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Certainly this is basic algebra,so the method is correct.

This method does not appear on wikipedia,so it is new.
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December 21st, 2016, 11:46 AM   #4
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You do know that Wikipedia is not a repository of all human knowledge? It's not even reliably accurate.
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December 21st, 2016, 03:36 PM   #5
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i agree with you

wikipedia also does not know, that pi is not fixed.



New Geometry of Circles,
Which has a unique Pi
to each Diameter.


The new geometry, has a new Formula
Pi of D = 3.1416 + root of ( 0.0000003 : D )
D is the Diameter of a circle, above 0.001 mm

The new formula produces the following numbers of pi

D of Circle (mm) Unique Pi

------------------------ 3.164 (pi maximum) 0
0.001-------------------- 3.1589205
0.01---------------------- 3.1470772
0.1----------------------- 3.1433321
1------------------------ 3.1421477
10 ---------------------- 3.1417732
100 --------------------- 3.1416548
1000--------------------- 3.1416173
1000000----------------- 3.1416005
10000000---------------- 3.1416002
1000000000000… 3.1416 (pi minimum)

The Pi revolution
According to the conventional mathematics,
Pi of each D = 3.1416
There for, it is very important number.

According to the new geometry of circles,
There are two important numbers.
Pi minimum = 3.1416
Pi maximum = 3.164

Between pi minimum to pi maximum, there is a unique pi to each D
Pi of D = 3.1416 + root of ( 0.0000003 : D )

Aetzbar
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December 21st, 2016, 05:11 PM   #6
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Diameter of Earth: 12742 km

pi*d = 40030
3.164*d = 40316

40316 - 40030 = 286

So this "new geometry" makes it longer to travel around Mother Earth?
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December 21st, 2016, 06:33 PM   #7
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pi of Earth

is very close to pi minimum (3.1416)
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December 22nd, 2016, 07:54 AM   #8
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The new way to Pythagorean Theorem numbers,

produces Irrational Square.

choose A = 1 + root of 2 (side of irrational square )

B = 0.5( AA - 1 ) = 1 + root of 2 ( side of irrational square )

C = B + 1 = 2 + root of 2 ( diagonal of irrational square )

Aetzbar
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December 22nd, 2016, 09:29 AM   #9
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Dunno; seems to me you're the only one who
understands your "irrational language"....
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December 22nd, 2016, 09:42 AM   #10
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Don't take this question as in any way representing acceptance of your preposterous notion. But, what happens for circles of radius larger than your arbitrary 1000000000000?

If I measure a circle as being 1km in diameter, it's circumference is then 3.1421477 km (you claim).

And if I measure a circle as being 1,000,000 mm in diameter, it's circumference is then 3,141,600.5 mm (you claim).

But these circles are the same circle. And you claim it has two radii that differ by 547.2 m depending only on what units I use to quote my measurement of the diameter. In fact, I could have many different results by using different units.

So your conclusion is that we can never know the actual circumference of a circle. It's a new brand of Uncertainty Principal. Even worse, I could find a polygon with a circumference between the maximum and minimum circumferences of a circle, and we'd never no whether the circle was inscribed or circumscribed or both.

Last edited by v8archie; December 22nd, 2016 at 09:55 AM.
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