Should trig be fixed? Should tan = - (sin/cos)?
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blamocur
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What is your question? Watching a video takes too long -- do you want to post a summary with a specific question?
Thanks.
Dr.Peterson
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The (terse) answer is, No.
But why do you think it should be? Can you summarize the argument, as you perceive it? And can you see why the current definitions make good sense?
Ultimately, though, definitions are just conventions; we choose to use some word to represent some concept that we find useful. There is no "should"; we just have sufficient reason to do what we do, though other choices are possible, and sometimes equally reasonable.
Thank you for responding.
I Summarise the argument in this paper: https://www.tautime.org/TrigDoneRight
I thoroughly agree with your thoughts on conventions and perhaps on a different day I would be content to leave it at that and move on to some other fascinating aspect of this wonderful life that we are gifted with that happens to peak my interest. On this occasion though, my opinion is that the two positions (for want of a better phrase) are not "equally reasonable", and whilst the magnitude of the difference between them may not be significant enough in some people's opinions, my belief is that is significant and needs to be addressed.
I realise that this is a significant task, but I humbly suggest that we owe it to future generations of Mathematicians and Physicists to conduct a thorough analysis of this potential anomaly and implement a (global) fix - if it is deemed necessary, as I believe it is.
I would like to take this opportunity to thank you, most heartily for your time and consideration in this, is really is appreciated very much.
All the best (from Bonnie Scotland)
Jay
These are wonderful questions, so pertinent. Thank you so much for asking them.
They merit careful consideration and deep analysis and discussion, so I hesitate to try and attempt them here, but I'll kick each off with as simple a response as I can:
Far weightier minds than mine have proposed using radius as the fundamental measure of the circle, so best to start with them:
1) Bob Palais: https://www.math.utah.edu/~palais/pi.pdf
2) Michael Hartl: https://tauday.com/tau-manifesto
3) Bob Palais' page with link to other references: https://www.math.utah.edu/~palais/pi.html
For this one, I'm going with: Yes, abso-blooming-lutely! This really is the main reason to implement "the fix". It will be the reduction in human brain hours that is reaped when teaching maths to new generations simply because Tau makes learning and understanding so much easier, more enjoyable and rewarding.
This is the million dollar question, and is really yet to be seen, but I totally 100% believe that we will turbo boost our "Tau natives" and witnessing their discoveries in the future will be a wondrous sight to behold.
I'll finish with a Carl Sagan quote, simply because he was amazing:
"The brain is like a muscle. When it is in use we feel very good. Understanding is joyous."
Thank you again for you time and consideration
Jay