(photo from the cc collection of lambageek, thanks)
I’m not a mathematician, not even by the wildest stretch of imagination. I reckon I have about another 3 years before the kids homework will defeat me. However, I’m a big fan of the history of mathematics and science; Riemann conjecture, Nash equilibrium, Gauss and number theory, Mandelbrot and so on. I’m a sucker for layman books on maths and science history, just don’t ask me to factorise, solving where X is a real number.
One of the great mathematical rivalries was between Newton and Leibniz over who came up with Calculus first. It turns out that they were arguing over second.
A Palimpsest rediscovered showed that Archimedes had a grasp of the principles of calculus 2000 years before either Newton or Leibniz. You can read more about the discovery here.
I wonder how many other inventions and discoveries that we hold so dear are in fact rediscoveries? Palimpsests do make prior art literature reviews rather difficult.
Vendorprisey 
Kepler (demolish) Vs Einstein’s
Areal velocity is constant: r² θ’ =h Kepler’s Law
h = 2π a b/T; b=a√ (1-ε²); a = mean distance value; ε = eccentricity
r² θ’= h = S² w’
Replace r with S = r exp (ỉ wt); h = [r² Exp (2iwt)] w’
w’ = (h/r²) exp [-2(i wt)]
w’= (h/r²) [cosine 2(wt) – ỉ sine 2(wt)] = (h/r²) [1- 2sine² (wt) – ỉ sin 2(wt)]
w’ = w'(x) + ỉ w'(y) ; w'(x) = (h/r²) [ 1- 2sine² (wt)]
w'(x) – (h/r²) = – 2(h/r²)sine²(wt) = – 2(h/r²)(v/c)² v/c=sine wt
(h/ r²)(Perihelion/Periastron)= [2πa.a√ (1-ε²)]/Ta² (1-ε) ²= [2π√ (1-ε²)]/T (1-ε) ²
Δ w’ = [w'(x) – h/r²] = -4π {[√ (1-ε²)]/T (1-ε) ²} (v/c) ² radian per second
Δ w’ = (- 4π /T) {[√ (1-ε²)]/ (1-ε) ²} (v/c) ² radians
Δ w’ = (-720/T) {[√ (1-ε²)]/ (1-ε) ²} (v/c) ² degrees; Multiplication by 180/π
Δ w’ = (-720×36526/T) {[√ (1-ε²)]/(1-ε)²} (v/c)² degrees/100 years
Δ w” = (-720×3600/T) {[√ (1-ε²)]/ (1-ε) ²} (v/c) ² seconds of arc by 3600
Δ w” = (-720x36526x3600/T) {[√ (1-ε²]/(1-ε)²} (v/c)² seconds of arc per century
This Kepler’s Equation solves all the problems Einstein and all physicists could not solve
The circumference of an ellipse: 2πa (1 – ε²/4 + 3/16(ε²)²- –.) ≈ 2πa (1-ε²/4); R =a (1-ε²/4) v=√ [G m M / (m + M) a (1-ε²/4)] ≈ √ [GM/a (1-ε²/4)]; m<<M; Solar system
Advance of Perihelion of mercury.
G=6.673×10^-11; M=2×10^30kg; m=.32×10^24kg
ε = 0.206; T=88days; c = 299792.458 km/sec; a = 58.2km/sec
Calculations yields:
v =48.14km/sec; [√ (1- ε²)] (1-ε) ² = 1.552
Δ w”= (-720x36526x3600/88) x (1.552) (48.14/299792)²=43.0”/century
Conclusions: The 43" seconds of arc of advance of perihelion of Planet Mercury (General relativity) is given by Kepler’s equation better than all of Published papers of Einstein. Kepler’s Equation can solve Einstein’s nemesis DI Her Binary stars motion and all the other dozens of stars motions posted for past 40 years on NASA website SAO/NASA as unsolved by any physics
Anyone dare to prove me wrong?
Hello Joe,
See my first sentence !-)
Thomas
Hi
Very interesting stuff. I love the notion of palimpsets in general, and this one is especially good.
If you like the flavour of this period, have you read Neal Stephenson’s Baroque Cycle, which includes amongst others, both Newton and Liebnitz, and the arguments that they had, interwoven with the masterfully overdone story.
Hamish
Indeed, a fine series!