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 [email protected] 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.