According to Wickipedia, affine geometry does not have a metric notion of length and angle. I have a series of videos on geometry for quadrature which deal with what I think is affine geometry. ruclips.net/video/RX_ZHDQkyGo/видео.html
Good question! *Absolute* length is when you say I ran 10 kilometers today. *Relative* length is when you say I ran twice as far today compared to yesterday.
@@MathTheBeautiful How would you verify that your reference length is one unit long? Ans: you can't. So what is absolute length? I understand that "1 meter" is a practical definition. But in itself doesn't help in constructing a concept of length. Ask yourself "how long is a line". Ans 1: twice as long as half a line. I.e., a line can be used as a reference length. Call it a meter if you like, but the choice of it's length and name are arbitrary I.e., there are two magnitudes. One is geometric, the other is algebraic. Neither one is absolute.
So I can compare my bag of oranges to your bag of oranges, but I can’t compare my bag of bananas to your bag of oranges.
Precisely!
There are 20 blocks per mile. The US standardizes as 16 E-W blocks or 8 N-S blocks after Chicago.
Thank you for that information!
Would it be possible to upload the whole lecture? Thank you.
Unfortunately, no, due to student privacy considerations.
brilliant :)
Thank you! Glad you enjoyed it!
If we can compare lengths in 1d space without dot product, I wonder if it's possible to compare areas in 2d space similarly
Yes! This is known as bivectors.
Ah man i wish you continued the video :(
See the playlist in the description
According to Wickipedia, affine geometry does not have a metric notion of length and angle. I have a series of videos on geometry for quadrature which deal with what I think is affine geometry.
ruclips.net/video/RX_ZHDQkyGo/видео.html
Yes, agreed. No length defined or needed!
Absolute length? What is that?
Good question! *Absolute* length is when you say I ran 10 kilometers today. *Relative* length is when you say I ran twice as far today compared to yesterday.
@@MathTheBeautiful How would you verify that your reference length is one unit long? Ans: you can't. So what is absolute length?
I understand that "1 meter" is a practical definition. But in itself doesn't help in constructing a concept of length.
Ask yourself "how long is a line". Ans 1: twice as long as half a line. I.e., a line can be used as a reference length. Call it a meter if you like, but the choice of it's length and name are arbitrary I.e., there are two magnitudes. One is geometric, the other is algebraic. Neither one is absolute.