Title : New constants and real representation of new spaces
Elia T .Alabbas
Title : New constants and real representation of new spaces( Part one)
Author : Elia T . Alabbas
Comments 8 Pages, 4 figures.
Tishreen University
Subject-class : Algebraic Geometry
eileaabbas@gmail.com
ABSTRACT
This is a continuation of what the researcher started from previous
research, This research aims to reach an infinite number of Pythagoras
triads, By proportioning the lengths of the right-angled triangle, This will
help to represent really many spaces, The researcher was able to discover
New constants in the right-angled triangle: They are (0.28), (0.96), (1),
These New constants capable of generating an infinite number of
Pythagorean triads,(0.28,0.96,1) It is the source of the Pythagorean triad
( 7,24,25).
Also the researcher was able to discover New constants in the rightangled triangle: They are (1), (2.4), (2.6), These New constants capable of
generating an infinite number of Pythagorean triads,(1,2.4,2.6) It is the
source of the Pythagorean triad ( 5,12,13).
Title : New constants and real representation of new spaces
Elia T .Alabbas
Depending on the Pythagorean theorem" a right angled triangle:the square of the
hypotenuse is equal to the sum of the squares of the other two sides" and
previous research. the researcher works to find New constants in the rightangled triangle.
A2 + B2 = C2
C
A
B
Figure 1
The research paper symbols:
A: The first side length.
B: The second side length
C: Hypotenuse length
IN previous research (Alabbas,2017,6)The researcher was able to
A = (0.6) C
discover constants in the right-angled triangle: They are (0.6), (0.8).
A = (0.6)C
B= (0.8) C
C
B= (0.8) C
Figure 2
Title : New constants and real representation of new spaces
Elia T .Alabbas
A new start:
First:
By proportioning the lengths of the right-angled triangle:
New Observation:
(7,24,25)
A=7
B = 24
C = 25
A / C = 7 / 25 = 0.28
A = (0.28)C
B / C = 24 /25 = 0.96
B = (0,96)C
C / C = 25 /25 =1
From the above, the researcher reaches the new constants:
(0.28) ,(0.96), (1)
[A, B ,C]
[0.28, 0.96, 1]
A2 + B2 = C2
(0.28)2 + (0.96)2 = (1)2
0.0784 + 0.9216= 1
example:
A=?
B=?
C=2
The solution:
A = (0.28)C
A = 0.56
B = (0.96)C
Title : New constants and real representation of new spaces
Elia T .Alabbas
B = 1.92
solution Validation by using the Pythagorean theorem:
A2 + B2 = C2
(0.56)2 + (1.92)2 = (2)2
0.3136 + 3.6864= 4
Pythagorean trilogy
(0.56,1.92,2)
The researcher was able to discover constants in the right-angled
triangle: They are(0.28), (0.96), (1).
[0.28, 0.96, 1]
C
A = (0.28) C
A = (0.28)C
B = (0,96)C
B= (0.96) C
A: The first side length.
Figure 3
B: The second side length
C: Hypotenuse length
[0.28, 0.96, 1] These New constants capable of generating an
infinite number of Pythagorean triads
[0.28, 0.96,1], [0.56,1.92, 2] , [0.84, 2.88, 3] ,[1.12, 3.84, 4] , [1.4, 4.8, 5]
[1.68, 5.76, 6]………………..(1)
IN previous research (Alabbas,2017,) [ 0.6, 0.8, 1] These constants
capable of generating an infinite number of Pythagorean triads
[ 0.6, 0.8, 1] , [1.2, 1.6, 2] , [1.8, 2,4, 3] , [2.4, 3.2, 4] , [3, 4, 5]
[3.6, 4.8,6]…………………(2)
{
From (1) & (2) The Researcher notes [ 0.6, 0.8, 1] ,[0.28, 0.96,1]
}
Title : New constants and real representation of new spaces
Elia T .Alabbas
Hypotenuse length is represented In two different places in space in a
very simple way, Thus enabling the researcher to represent six spaces
in a real way.
Second:
By proportioning the lengths of the right-angled triangle:
New Observation:
(5,12,13)
A=5
B = 12
C = 13
A/A=5/5=1
B / A = 12 / 5 = 2.4
B = (2.4)A
C / A = 13 / 5 = 2.6
C = (2.6)A
From the above, the researcher reaches the new constants:
(1) ,(2.4), (2.6)
[A, B ,C]
[1, 2.4, 2.6]
A2 + B2 = C2
(1)2 + (2.4)2 = (2.6)2
1 + 5.76=6.76
First example:
A=2
B=?
C=?
The solution:
A= 2
B = (2.4)(2)
Title : New constants and real representation of new spaces
Elia T .Alabbas
B = 4.8
C = (2.6)(2)
C = 5.2
solution Validation by using the Pythagorean theorem:
A2 + B2 = C2
(2)2 + (4.8)2 = (5.2)2
4 + 23.04=27.04
Pythagorean trilogy
(2,4.8,5.2)
Second example:
A=3
B=?
C=?
The solution:
A= 2
B = (2.4)(3)
B = 7.2
C = (2.6)(3)
C = 7.8
solution Validation by using the Pythagorean theorem:
A2 + B2 = C2
(3)2 + (7.2)2 = (7.8)2
9 + 51.84=60.84
Pythagorean trilogy
(3,7.2,7.8)
Third example:
A=4
B=?
C=?
The solution:
A= 4
B = (2.4)(4)
B = 9.6
C = (2.6)(4)
C = 10.4
Title : New constants and real representation of new spaces
Elia T .Alabbas
solution Validation by using the Pythagorean theorem:
A2 + B2 = C2
(4)2 + (9.6)2 = (10.4)2
16 + 92.16=108.16
Pythagorean trilogy
(4,9.6,10.4)
Fifth example:
A=5
B=?
C=?
The solution:
A= 5
B = (2.4)(5)
B = 12
C = (2.6)(5)
C = 13
solution Validation by using the Pythagorean theorem:
A2 + B2 = C2
(5)2 + (12)2 = (13)2
25+144=169
Pythagorean trilogy
(5,12,13)
The researcher was able to discover constants in the right-angled
triangle: They are(1), (2.4), (2.6).
[1, 2.4, 2.6]
C = (2.6)A
A
B = (2.4)A
C = (2.6)A
A: The first side length.
B: The second side length
C: Hypotenuse length
B= (2.4) A
Figure 4
Title : New constants and real representation of new spaces
Elia T .Alabbas
[1, 2.4, 2.6] These New constants capable of generating an
infinite number of Pythagorean triads
[1, 2.4,2.6], [2,4.8,5.2] , [3, 7.2, 7.8] , [4, 9.6, 10,4]……………………….
Thus enabling the researcher to represent new spaces in a real way.