May 9th, 2018, 04:29 PM  #41 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,331 Thanks: 2457 Math Focus: Mainly analysis and algebra  A word to the wise. It's better to post actual mathematics if you want to stimulate discussion. Pictures with no mathematical content are unlike to excite interest. Also, without the mathematics behind them, they are more or less meaningless. 
May 9th, 2018, 07:43 PM  #42  
Senior Member Joined: Jul 2015 From: Florida Posts: 150 Thanks: 3 Math Focus: noneuclidean geometry 
Or, it looks like the opposite, where a square wave is gradually filtered by tuning a circuit in order to produce a sine wave. In reality, this is the function that is discussed in the proof, and is based on the small circle tridentity. Take out your globe (I don't know why I think that you would have one) and place a wire loop on it so that the loop touches up against the pole. Now look at the intersections that are made between the wire and the lines of longitude. Now change the diameter of the loop and do this again. Under careful scrutiny you will see that, as the wire loop gets smaller and smaller, it loses all of its spherical excess and becomes a flat circle, with the corresponding sine function. When the loop expands to become a great circle (lying on a line of longitude), it no longer has that sinusoidal relationship with the lines of the globe. If you were to try and revolve around the wire, you would go from perpendicular to the longitude to parallel with it, in one tiny move. This is the way that space is structured, and this is what is captured in the equation. Another quote from another member of another forum: Quote:
 
May 9th, 2018, 07:48 PM  #43  
Senior Member Joined: Jul 2015 From: Florida Posts: 150 Thanks: 3 Math Focus: noneuclidean geometry  Quote:
https://www.steveupson.xyz/wpconten...identities.pdf  
May 9th, 2018, 08:14 PM  #44 
Senior Member Joined: Jul 2015 From: Florida Posts: 150 Thanks: 3 Math Focus: noneuclidean geometry 
The identities which require three dimensions will be called tridentities in order to distinguish them from all of the other mathematical identities which can be expressed in other forms than exclusively in Euclidean 3space. An example of a known tridentity is (Chapter XVII (Chapter XIV) – Arcs Drawn to Fixed Points on the Surface of a Sphere (Todhunter)): $\displaystyle \cos^2TA+ \cos^2TB+ \cos^2TC = 1$ (page 133 of this edition: https://www.gutenberg.org/files/19770/19770pdf.pdf >>>> Solving the spherical isosceles triangle Δabc gives simultaneous equations $\displaystyle \cot\alpha = \cos\upsilon\tan\frac{\phi}{2 } $ $\displaystyle \sin\frac{\lambda}{2 } = \sin\frac{\phi}{2 }\sin{\upsilon} $ which describe a family of functions. If we hold $\displaystyle \upsilon$ constant, the function for each member of the family α = ƒ(λ) is: $\displaystyle \alpha={\cot}^{1 }(\cos\upsilon\tan{\sin}^{1}(\frac{\sin\frac{\lambda}{ 2}}{ \sin\upsilon})) $ It is a smooth function that approaches a sine curve when $\displaystyle \upsilon$ → 0, and that approaches a hyperbola when $\displaystyle \upsilon$ → π/2. The simultaneous equations can be rewritten in the form of: $\displaystyle \sin{\upsilon}= \frac{\sin\frac{\lambda}{2}}{\cos\frac{\phi}{2}} $ $\displaystyle \cos{\upsilon}= \frac{\cot\alpha}{\cot\frac{\phi}{2}} $ and since, $\displaystyle \sin^2 \upsilon+\cos^2\upsilon=1$ then this gives the tridentity: $\displaystyle (\cos\frac{\phi}{2}\,\sin\frac{\lambda}{2})^2 +(\cot\frac{\phi}{2}\,\cos\alpha)^2=1 $ Last edited by steveupson; May 9th, 2018 at 08:17 PM. 
May 9th, 2018, 08:26 PM  #45 
Senior Member Joined: Sep 2015 From: USA Posts: 2,011 Thanks: 1044 
What kind of response are you looking for here? Are we supposed to do more than look at your proof and produce oohs and ahhs? 
May 10th, 2018, 03:13 AM  #46  
Senior Member Joined: Jul 2015 From: Florida Posts: 150 Thanks: 3 Math Focus: noneuclidean geometry 
I was hoping for a response that isn't about me. I'd rather discuss the math. But sure, you may have missed all that because, you know, English. timespace, a quantum analog to spacetime timespace, a quantum analog to spacetime timespace, a quantum analog to spacetime timespace, a quantum analog to spacetime timespace, a quantum analog to spacetime From the OP: Quote:
 
May 10th, 2018, 08:17 AM  #47 
Senior Member Joined: Sep 2015 From: USA Posts: 2,011 Thanks: 1044 
So you're unsure how to go about proving your theory but have an 18 page proof that you want us to review, for free. Well good luck with that. I'm sure there are lots of people with nothing better to do than look at your rehash of spherical trig. 
May 16th, 2018, 06:51 PM  #48  
Senior Member Joined: Jul 2015 From: Florida Posts: 150 Thanks: 3 Math Focus: noneuclidean geometry 
It has become apparent that there is a very common misunderstanding of the math behind the tridentities. The tridentities that are the foundation of this geometry are mathematical expressions of characteristics of Euclidean space. These characteristics of space are completely disregarded by current models and current geometries. In the small circle tridentity, we aren’t mapping a 2D circle to the 2D surface of a sphere, we’re mapping a circle in space to space itself. Here’s another update from the other conversation. We are still trying to recruit help, just in case anyone here enjoys math or physics or science in general. Quote:
 
May 17th, 2018, 03:31 AM  #49 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,600 Thanks: 546 Math Focus: Yet to find out.  
May 17th, 2018, 04:14 AM  #50  
Senior Member Joined: Oct 2009 Posts: 430 Thanks: 144  Quote:
"A must read for old and young" "The debuting author has completed a work that will soon be the gold standard."  

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