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Open Access Journal of
eISSN: 2641-9335

Mathematical and Theoretical Physics

Opinion Volume 1 Issue 6

Topology & astrotheology

Paul TE Cusack

Independent Researcher, Canada

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

Received: October 02, 2018 | Published: November 30, 2018

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

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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)+1/3cos[17t+π/3],sin[17t+π/3] MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqadaqaaiaadIhacaGGSaGaamyEaaGaayjkaiaawMcaaiabg2da9iGacohacaGGPbGaaiOBamaabmaabaGaamiDaaGaayjkaiaawMcaaiabgUcaRmaalyaabaGaaGymaaqaaiaaiodaaaGaci4yaiaac+gacaGGZbWaamWaaeaacaaIXaGaaG4naiaadshacqGHRaWkdaWcgaqaaiabec8aWbqaaiaaiodaaaaacaGLBbGaayzxaaGaaGPaVlaacYcacaaMc8Uaci4CaiaacMgacaGGUbWaamWaaeaacaaIXaGaaG4naiaadshacqGHRaWkdaWcgaqaaiabec8aWbqaaiaaiodaaaaacaGLBbGaayzxaaaaaa@5DFB@

Let t=1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiaadshacqGH9aqpcaaIXaaaaa@3AAE@

=1.1582+(7193)2=1.858 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiabg2da9iaaigdacaGGUaGaaGymaiaaiwdacaaI4aWaaWbaaSqabeaacaaIYaaaaOGaey4kaSYdamaabmaabaWdbiabgkHiTiaaiEdacaaIXaGaaGyoaiaaiodaa8aacaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaOWdbiabg2da9iaaigdacaGGUaGaaGioaiaaiwdacaaI4aaaaa@49D1@

=1+sin 590 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiabg2da9iaaigdacqGHRaWkcaWGZbGaamyAaiaad6gacaqGGaGaaGynaiaaiMdadaahaaWcbeqaaiaaicdaaaaaaa@407C@

Moment. MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiabgIKi7kaad2eacaWGVbGaamyBaiaadwgacaWGUbGaamiDaiaac6caaaa@3FE5@

R=Mom.=1.858=1.363 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbGaeyypa0ZaaOaaaeaacaWGnbGaam4Baiaad2gaaSqabaGccaGGUaGaeyypa0ZaaOaaaeaacaaIXaGaaiOlaiaaiIdacaaI1aGaaGioaaWcbeaakiabg2da9iaaigdacaGGUaGaaG4maiaaiAdacaaIZaaaaa@46C8@

But R=2

So R=Mom/2=68.15=2σ MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbGaeyypa0ZaaOaaaeaacaWGnbGaam4Baiaad2gaaSqabaGccaGGVaGaaGOmaiabg2da9iaaiAdacaaI4aGaaiOlaiaaigdacaaI1aGaeyypa0JaaGOmaiabeo8aZbaa@4636@

Alexander’s polynomials

Reef or granny know

x22x+32/x+1/x MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaaGOmaiaadIhacqGHRaWkcaaIZaGaeyOeI0YaaSGbaeaacaaIYaaabaGaamiEaaaacqGHRaWkdaWcgaqaaiaaigdaaeaacaWG4baaaaaa@4375@

Let x=t=1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiaadIhacqGH9aqpcaWG0bGaeyypa0JaaGymaaaa@3CB1@

=122(1)+32/1+1/1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqGH9aqpcaaIXaWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaaGOmaiaacIcacaaIXaGaaiykaiabgUcaRiaaiodacqGHsisldaWcgaqaaiaaikdaaeaacaaIXaaaaiabgUcaRmaalyaabaGaaGymaaqaaiaaigdaaaaaaa@44CC@

=1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqGH9aqpcaaIXaaaaa@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=R2=x2+y2 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbGaeyOeI0IaamyraiabgUcaRiaadAfacqGH9aqpcaaIYaGaeyypa0JaamOuamaaCaaaleqabaGaaGOmaaaakiabg2da9iaadIhadaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaWG5bWaaWbaaSqabeaacaaIYaaaaaaa@4664@

For a circle Face F=2  MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiaadAeacqGH9aqpcaaIYaGaaiiOaaaa@3BA5@ , Edges=0 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiaadweacaWGKbGaam4zaiaadwgacaWGZbGaeyypa0JaaGimaaaa@3E35@ , Vertices=0 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiaadAfacaWGLbGaamOCaiaadshacaWGPbGaam4yaiaadwgacaWGZbGaeyypa0JaaGimaaaa@4121@

20+0=2 True! MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiaaikdacqGHsislcaaIWaGaey4kaSIaaGimaiabg2da9iaaikdacaqGGaGaamivaiaadkhacaWG1bGaamyzaiaacgcaaaa@42B1@

R=2 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiaadkfacqGH9aqpdaGcaaqaaiaaikdaaSqabaaaaa@3AA8@

This is the 450 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiaaisdacaaI1aWaaWbaaSqabeaacaaIWaaaaaaa@3A58@ Triangle where E=t=1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiaadweacqGH9aqpcaWG0bGaeyypa0JaaGymaaaa@3C7E@

R2=x2+y2=a2+b2 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaaWbaaSqabeaacaaIYaaaaOGaeyypa0JaamiEamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaadMhadaahaaWcbeqaaiaaikdaaaGccqGH9aqpcaWGHbWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaamOyamaaCaaaleqabaGaaGOmaaaaaaa@44F8@  (Pythagoras)

2+2=22=4=|D| MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaGcaaqaaiaaikdaaSqabaGccqGHRaWkdaGcaaqaaiaaikdaaSqabaGccqGH9aqpcaaIYaWaaOaaaeaacaaIYaaaleqaaOGaeyypa0JaaGinaiabg2da9maaemaabaGaamiraaGaay5bSlaawIa7aaaa@43D0@

a2+b2=c2 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiaadggadaahaaWcbeqaaKqzadGaaGOmaaaakiabgUcaRiaadkgadaahaaWcbeqaaiaaikdaaaGccqGH9aqpcaWGJbWaaWbaaSqabeaacaaIYaaaaaaa@408E@ 12+12=c2 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiabgkDiElaaigdadaahaaWcbeqaaKqzadGaaGOmaaaakiabgUcaRiaaigdadaahaaWcbeqaaiaaikdaaaGccqGH9aqpcaWGJbWaaWbaaSqabeaacaaIYaaaaaaa@4294@

c=2=dM/dt MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqkY=MjY=Pj0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGJbGaeyypa0JaaGOmaiabg2da9iaadsgacaWGnbGaai4laiaadsgacaWG0baaaa@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

  1. Steward I. In Pursuit of the Unknown. A member of the perseus books group. New York: Basic Books; 2012. 353 p.
  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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