June 22nd, 2018, 04:41 PM  #51  
Senior Member Joined: Jul 2015 From: Florida Posts: 154 Thanks: 3 Math Focus: noneuclidean geometry 
Just another update from the other discussion. Quote:
 
June 22nd, 2018, 05:07 PM  #52 
Senior Member Joined: Sep 2015 From: USA Posts: 2,265 Thanks: 1198  
June 23rd, 2018, 01:38 AM  #53 
Senior Member Joined: Jul 2015 From: Florida Posts: 154 Thanks: 3 Math Focus: noneuclidean geometry 
The graph of the function and its inverse. It intercepts the y axis at 0.009657 and the inverse intercepts at 103.550. 0.009657153 * 103.550188399 = 1.000000001 Last edited by steveupson; June 23rd, 2018 at 01:51 AM. 
November 6th, 2018, 07:05 AM  #54 
Senior Member Joined: Jul 2015 From: Florida Posts: 154 Thanks: 3 Math Focus: noneuclidean geometry 
Amazing interactive video tutorial about quaternions: https://eater.net/quaternions It's important to understand that developments in spherical trigonometry halted when vector manipulation became the prevalent technology. The geometry that we're developing has no corollary to quaternions. Octonions probably have a closer relationship to what we are doing because of the use of three complex planes instead of just two. 
November 6th, 2018, 08:14 AM  #55  
Senior Member Joined: Oct 2009 Posts: 706 Thanks: 238  Quote:
Do you mean the reciprocal? Using the terminology inverse is bad here.  
November 6th, 2018, 09:30 AM  #56  
Senior Member Joined: Jul 2015 From: Florida Posts: 154 Thanks: 3 Math Focus: noneuclidean geometry  Quote:
https://en.wikipedia.org/wiki/Lorent...merical_values  
November 6th, 2018, 09:57 AM  #57  
Senior Member Joined: Aug 2012 Posts: 2,136 Thanks: 623  Quote:
In the table below, the lefthand column shows speeds as different fractions of the speed of light (i.e. in units of c). The middle column shows the corresponding Lorentz factor, the final is the reciprocal. Values in bold are exact. My bolding.  
November 6th, 2018, 10:16 AM  #58  
Senior Member Joined: Jul 2015 From: Florida Posts: 154 Thanks: 3 Math Focus: noneuclidean geometry  Quote:
It still isn't clear to me what you are saying. "α (Lorentz factor inverse) as a function of velocity  a circular arc."  
November 6th, 2018, 11:21 AM  #59 
Senior Member Joined: Oct 2009 Posts: 706 Thanks: 238  
November 6th, 2018, 12:26 PM  #60 
Senior Member Joined: Jul 2015 From: Florida Posts: 154 Thanks: 3 Math Focus: noneuclidean geometry 
The reciprocal of a number is its multiplicative inverse. If x is any nonzero number, then x(1/x)=1. I still don't understand the error, but that's why I'm back in school studying algebra. I pretty much suck at this kind of thing. Angels on the head of a pin and such. What's the problem with this? You said it's bad. Why? I really don't know why. Can you explain it? 

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analog, quantum, spacetime, timespace 
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