This is not how I would have thought to prove why the polar formula for dot product doesn't get any more complicated in higher dimensions, while the "sum of the products" formula does, but I also would not have noticed the connection to the law of cosines without this approach, so that's a new insight for me. As an aspiring math teacher, I also really like the effort made to get the students physically involved with pens as vectors and the book as a plane. It demonstrates what I would think is a very simple idea to imagine, but I also know that it's easy to underestimate the value of a literal hands-on representation. There's value in that simple demonstration, that is easy for a math teacher to miss.
Funny thing, I used this + Euclidian Distance to get a really good initial population for genetic algorithm for solving Vehicle Routing Problem, paper will be out soon.
I use this in my statistics class to prove that Pearson's Correlation coefficient, r, is bounded by -1 and 1 as the formula for correlation is sum[(x-mean(x))*(y-mean(y))]/[magnitude(x-mean(x))*magnitude(y-mean(y))] which is cos theta! Theta is the angle between the (x - mean(x)) and (y - mean(y)) vectors.
I love maths alot.i have passion for maths sir.i want to be a professor in maths.That what prompted me to do video on RUclips I will be grateful if you can post me sir or add me to your channel
This is not how I would have thought to prove why the polar formula for dot product doesn't get any more complicated in higher dimensions, while the "sum of the products" formula does, but I also would not have noticed the connection to the law of cosines without this approach, so that's a new insight for me.
As an aspiring math teacher, I also really like the effort made to get the students physically involved with pens as vectors and the book as a plane. It demonstrates what I would think is a very simple idea to imagine, but I also know that it's easy to underestimate the value of a literal hands-on representation. There's value in that simple demonstration, that is easy for a math teacher to miss.
Really wish he was my school teacher
yeah
Funny thing, I used this + Euclidian Distance to get a really good initial population for genetic algorithm for solving Vehicle Routing Problem, paper will be out soon.
Watching this guys 2014 vids on zero index. He been smart for a Wwhiillleee
I use this in my statistics class to prove that Pearson's Correlation coefficient, r, is bounded by -1 and 1 as the formula for correlation is sum[(x-mean(x))*(y-mean(y))]/[magnitude(x-mean(x))*magnitude(y-mean(y))] which is cos theta! Theta is the angle between the (x - mean(x)) and (y - mean(y)) vectors.
He made it so easy
Would this formula work with vectors in 4 spatial dimensions?
Dot product works for all dimensions (as long as the space itself is linear).
I love maths alot.i have passion for maths sir.i want to be a professor in maths.That what prompted me to do video on RUclips I will be grateful if you can post me sir or add me to your channel
0rd