Originally posted by royalchickenNo prob! 🙂
Thank you for the vote of confidence in my expository "skills" 😀. Incidentally, extensions of Pythagoras' Theorem work in any number of dimensions. Take, for example, the point (x,y,z) in R^3. Then the distance d from (x,y,z) to (0,0,0) is given by d^2 = x^2 + y^2 + z^2.
That's not what i meant though. You see? I never was a maths-head: It the non-plannar geometry bit i was on about: draw a triangle on a curved surface and you find all the usual rules go to pot. Angles don't add to 180 degrees etc. But yes, in a 3-D carteasian geometry, Pythagoras keeps on going. What a Greek dude!
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Originally posted by ToeOh, yeah. You're absolutely (😛) right. Misread your post 😳. Multiple dimensions are obviously non-planar....I think Pythagoras' theorem could be modified to suit geometires like those you speak of, which would be cool.
No prob! 🙂
That's not what i meant though. You see? I never was a maths-head: It the non-plannar geometry bit i was on about: draw a triangle on a curved surface and you find all the usual rules go to pot. Angles don't add to 180 degrees et ...[text shortened]... carteasian geometry, Pythagoras keeps on going. What a Greek dude!
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Originally posted by royalchickenThat was created on the fly in response to my reaction to this thread and your description of the mathematician as being the "navigator". I was struck that i can't navigate. hence the poem. I never contributed to the poetry sections you did. My poetry tends to be quite bitter and unrelenting. Too personal to put out into the world. But in the spirit of the Forums... a little verse, upon which we converse, a pro pos, when posts are slow.
I quite like that. That is the kind of feeling math is supposed to give...exploration of a strange and austerely beautiful world where traps lurk but the rewards for one's mind are great. Did you write that or am I ignorant?
Originally posted by StarValleyWy😀! I should be a bit wary about posting poetry...one never knows where moderators lurk.
That was created on the fly in response to my reaction to this thread and your description of the mathematician as being the "navigator". I was struck that i can't navigate. hence the poem. I never contributed to the poetry sections you did. My poetry tends to be quite bitter and unrelenting. Too personal to put out into the world. But in the spirit of the Forums... a little verse, upon which we converse, a pro pos, when posts are slow.
You are indeed quite a poet.
Originally posted by royalchickenoddly enough, did you know that the basic three note chord in music obeys Pythagoras relationship? the square of the frequencies of the lower two notes is equal to the square of the upper one. Its a note frequency harmony thing but cool eh? Geometry in music is very intrinsic.
Oh, yeah. You're absolutely (😛) right. Misread your post 😳. Multiple dimensions are obviously non-planar....I think Pythagoras' theorem could be modified to suit geometires like those you speak of, which would be cool.
Originally posted by ToeWow. I suppose it makes sense though. 1 + 49/25 = 64/25 = (8/5)^2.
oddly enough, did you know that the basic three note chord in music obeys Pythagoras relationship? the square of the frequencies of the lower two notes is equal to the square of the upper one. Its a note frequency harmony thing but cool eh? Geometry in music is very intrinsic.
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Hence the "Music Of The Spheres" and Ptolemeus's search for rhythm in the heavens. Ratio is everyting. Which also lead to the discovery of the "Golden Ratio" which turns out to perfectly describe the distrubution of the arc of spiral arms in a spiral galaxy. Go figure. Right answer... just wrong question.
Originally posted by royalchickenthe Music of the Spheres was ratioism based on Pathagorus and his cult following that was the basis of "cosmology" up until the mean old tycho guy actually made measurements and kepler kyped his numbers and ... well. It wasn't pretty, but it sounded good. Everything in the heavens had a ratio. Or so they thought. Did you know that there was whole generations of what we would call "witches" today based on the cult of pathagorus? They made a good living fortelling anything and everything... if you had the right amount of money.😠Some things never change.
I guess. What is this "Music of the Spheres"?
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Originally posted by royalchickenNo, no... quite right... I don't much care for french music. Or most other <self edit> culture... Ribbittt!
Yeah, you're right 😛. But I doubt Mike listens to that sort of thing (purely on the basis of his politics...Mike, if I'm wrong there pay it no mind), so maybe he's talking of something else 😉.
Oh, my. 😳 "Prog"... sorry. don't know what that is...
Originally posted by StarValleyWyHmmm. Mike, thank you for the explanation, spin and all 😉. "Prog" in this context is short for "progressive", and describes bands like ELO, Procul Harum, Yes, Emerson, Lake, and Palmer, etc.
No, no... quite right... I don't much care for french music. Or most other frog culture...
Oh, my. 😳 "Prog"... sorry. don't know what that is...
Originally posted by StarValleyWyI've heard that the pyramids were very 'ratio' based in accordance to cosmology. A similar tale? Or a want-to-believe senario?
the Music of the Spheres was ratioism based on Pathagorus and his cult following that was the basis of "cosmology" up until the mean old tycho guy actually made measurements and kepler kyped his numbers and ... well. It wasn't pretty, but it sounded good. Everything in the heavens had a ratio. Or so they thought. Did you know that there was whole gen ...[text shortened]... ing anything and everything... if you had the right amount of money.😠Some things never change.
Originally posted by StarValleyWyAye, Kepler ran with this idea big time. I think his idea was that the distance between the planets of our solar system (at his time only 6 were known) could be understood by fitting one of the five Platonic solids between each pair of planets. Staggeringly beautiful idea but without a shred of truth in it whatsoever.
the Music of the Spheres was ratioism based on Pathagorus and his cult following that was the basis of "cosmology" up until the mean old tycho guy actually made measurements and kepler kyped his numbers and ... well. It wasn't pretty, but it sounded good. Everything in the heavens had a ratio. Or so they thought. Did you know that there was whole gen ...[text shortened]... ing anything and everything... if you had the right amount of money.😠Some things never change.
T1000