Open Access Journal of eISSN: 2641-9335 OAJMTP

Mathematical and Theoretical Physics
Opinion
Volume 1 Issue 6

Topology & astrotheology

Paul TE Cusack
Independent Researcher, Canada
Received: October 02, 2018 | Published: November 30, 2018

Correspondence: Paul TE Cusack, BScE, Dule 23 Park Ave, Saint John, NB E2J 1R2, Canada

Citation: Cusack PTE. Topology & astrotheology. Open Acc J Math Theor Phy. 2018;1(6):239‒240. DOI: 10.15406/oajmtp.2018.01.00041

Abstract

In this brief paper, take a brief look at how Topology might apply to the Astrotheology Math. Much more work in this area remains to be done.

Keywords: topology, Alexander’s Knot, parametric equation, astrotheolgy

Introduction

In this brief paper, we examine the Universal Parametric Equation as an Alexander Know. We see that the there is a topological invariant of “1” which of course, is equal to the Energy and time in Astrotheology (Figure 1).

Figure 1 The universal parametric equation.

The Universal Parametric Equation:

( x,y )=sin( t )+1/3 cos[ 17t+π/3 ],sin[ 17t+π/3 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqadaqaaiaadI hacaGGSaGaamyEaaGaayjkaiaawMcaaiabg2da9iGacohacaGGPbGa aiOBamaabmaabaGaamiDaaGaayjkaiaawMcaaiabgUcaRmaalyaaba GaaGymaaqaaiaaiodaaaGaci4yaiaac+gacaGGZbWaamWaaeaacaaI XaGaaG4naiaadshacqGHRaWkdaWcgaqaaiabec8aWbqaaiaaiodaaa aacaGLBbGaayzxaaGaaGPaVlaacYcacaaMc8Uaci4CaiaacMgacaGG UbWaamWaaeaacaaIXaGaaG4naiaadshacqGHRaWkdaWcgaqaaiabec 8aWbqaaiaaiodaaaaacaGLBbGaayzxaaaaaa@5DFB@

Let t=1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi aadshacqGH9aqpcaaIXaaaaa@3AAE@

= 1.158 2 + ( 7193 ) 2 =1.858 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi abg2da9iaaigdacaGGUaGaaGymaiaaiwdacaaI4aWaaWbaaSqabeaa caaIYaaaaOGaey4kaSYdamaabmaabaWdbiabgkHiTiaaiEdacaaIXa GaaGyoaiaaiodaa8aacaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaa aOWdbiabg2da9iaaigdacaGGUaGaaGioaiaaiwdacaaI4aaaaa@49D1@

=1+sin  59 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi abg2da9iaaigdacqGHRaWkcaWGZbGaamyAaiaad6gacaqGGaGaaGyn aiaaiMdadaahaaWcbeqaaiaaicdaaaaaaa@407C@

Moment. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi abgIKi7kaad2eacaWGVbGaamyBaiaadwgacaWGUbGaamiDaiaac6ca aaa@3FE5@

R= Mom .= 1.858 =1.363 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbGaeyypa0 ZaaOaaaeaacaWGnbGaam4Baiaad2gaaSqabaGccaGGUaGaeyypa0Za aOaaaeaacaaIXaGaaiOlaiaaiIdacaaI1aGaaGioaaWcbeaakiabg2 da9iaaigdacaGGUaGaaG4maiaaiAdacaaIZaaaaa@46C8@

But R=2

So R= Mom /2=68.15=2σ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbGaeyypa0 ZaaOaaaeaacaWGnbGaam4Baiaad2gaaSqabaGccaGGVaGaaGOmaiab g2da9iaaiAdacaaI4aGaaiOlaiaaigdacaaI1aGaeyypa0JaaGOmai abeo8aZbaa@4636@

Alexander’s polynomials

Reef or granny know

x 2 2x+32/x +1/x MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG4bWaaWbaaS qabeaacaaIYaaaaOGaeyOeI0IaaGOmaiaadIhacqGHRaWkcaaIZaGa eyOeI0YaaSGbaeaacaaIYaaabaGaamiEaaaacqGHRaWkdaWcgaqaai aaigdaaeaacaWG4baaaaaa@4375@

Let x=t=1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi aadIhacqGH9aqpcaWG0bGaeyypa0JaaGymaaaa@3CB1@

= 1 2 2(1)+32/1 +1/1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqGH9aqpcaaIXa WaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaaGOmaiaacIcacaaIXaGa aiykaiabgUcaRiaaiodacqGHsisldaWcgaqaaiaaikdaaeaacaaIXa aaaiabgUcaRmaalyaabaGaaGymaaqaaiaaigdaaaaaaa@44CC@

=1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqGH9aqpcaaIXa aaaa@3995@

In fact, all of Alexander’s Knots result in a the same answer =1, including the unknot.

The unknown is a circle. So the universal parametric equation is a knot. 

Euler’s formula for polyhedra

FE+V=2= R 2 = x 2 + y 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbGaeyOeI0 IaamyraiabgUcaRiaadAfacqGH9aqpcaaIYaGaeyypa0JaamOuamaa CaaaleqabaGaaGOmaaaakiabg2da9iaadIhadaahaaWcbeqaaiaaik daaaGccqGHRaWkcaWG5bWaaWbaaSqabeaacaaIYaaaaaaa@4664@

For a circle Face F=2  MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi aadAeacqGH9aqpcaaIYaGaaiiOaaaa@3BA5@ , Edges=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi aadweacaWGKbGaam4zaiaadwgacaWGZbGaeyypa0JaaGimaaaa@3E35@ , Vertices=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi aadAfacaWGLbGaamOCaiaadshacaWGPbGaam4yaiaadwgacaWGZbGa eyypa0JaaGimaaaa@4121@

20+0=2 True! MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi aaikdacqGHsislcaaIWaGaey4kaSIaaGimaiabg2da9iaaikdacaqG GaGaamivaiaadkhacaWG1bGaamyzaiaacgcaaaa@42B1@

R= 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi aadkfacqGH9aqpdaGcaaqaaiaaikdaaSqabaaaaa@3AA8@

This is the 45 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi aaisdacaaI1aWaaWbaaSqabeaacaaIWaaaaaaa@3A58@ Triangle where E=t=1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi aadweacqGH9aqpcaWG0bGaeyypa0JaaGymaaaa@3C7E@

R 2 = x 2 + y 2 = a 2 + b 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaaWbaaS qabeaacaaIYaaaaOGaeyypa0JaamiEamaaCaaaleqabaGaaGOmaaaa kiabgUcaRiaadMhadaahaaWcbeqaaiaaikdaaaGccqGH9aqpcaWGHb WaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaamOyamaaCaaaleqabaGa aGOmaaaaaaa@44F8@  (Pythagoras)

2 + 2 =2 2 =4=| D | MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaGcaaqaaiaaik daaSqabaGccqGHRaWkdaGcaaqaaiaaikdaaSqabaGccqGH9aqpcaaI YaWaaOaaaeaacaaIYaaaleqaaOGaeyypa0JaaGinaiabg2da9maaem aabaGaamiraaGaay5bSlaawIa7aaaa@43D0@

a 2 + b 2 = c 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi aadggadaahaaWcbeqaaKqzadGaaGOmaaaakiabgUcaRiaadkgadaah aaWcbeqaaiaaikdaaaGccqGH9aqpcaWGJbWaaWbaaSqabeaacaaIYa aaaaaa@408E@ 1 2 + 1 2 = c 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbi abgkDiElaaigdadaahaaWcbeqaaKqzadGaaGOmaaaakiabgUcaRiaa igdadaahaaWcbeqaaiaaikdaaaGccqGH9aqpcaWGJbWaaWbaaSqabe aacaaIYaaaaaaa@4294@

c=2=dM/dt MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGJbGaeyypa0 JaaGOmaiabg2da9iaadsgacaWGnbGaai4laiaadsgacaWG0baaaa@3FD4@

Conclusion

We see that once again Occam’s razor applies this time to Topology and astrotheology.1-5

Acknowledgements

None.

Conflict of interest

Author declares that there is no conflicts of interest.

References

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  2. Cusack P. The Universal Parametric Equation. Journal of Generalized Lie Theory and Applications. 2017;11(1).
  3. Mishra VN. Some problems on approximations of functions in banach spaces. Ph.D. Thesis. Uttarakhand: Indian Institute of Technology; 2007.
  4. Mishra LN. On existence and behavior of solutions to some nonlinear integral equations with applications. Ph.D. Thesis. Assam: National Institute of Technology; 2017.
  5. A Study on Fixed Point Theorems for Nonlinear Contractions and its Applications. Ph.D. Thesis. Chhattisgarh: Ravishankar Shukla University; 2014.
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