And sometimes you have more than one variable. Now if you have n variables and n polynomials containing each of those variables and not coplanar with each other, you can solve for each of those variables by adding or subtracting multiples of those equations from each other and/or rearranging and substituting variables for their equivalent equations.
Now we’ll use this principle to write a ray tracer where we combine the equation for a line (that represents a ray traveling through a focal point and a pixel on a grid in front of that focal point) and the equation for a plane or other 3D primitive to find if they intersect and at what point if they do.
Next lecture we’ll have a guest speaker, the ghost of Joseph Fourier in to tell you why jpegs get more jpegy each time you jpeg them.
Any questions? Oh, actually we’ve run out of time and another class needs the room.
I mean that actually sounds like great fun to me, reminds me of when I taught myself matrix algebra to be able to mod bullet penetration and ricochets into GMod yeeeeears ago!
Though I think a good bit of what you are describing is beyond the entry level Algebra text book pictured, lol, Fourier is certainly in the realm of Statistics.
But yes, now its time to either fill in multiple choice dot scantron sheets, or fill out your answers to the final in buggy garbage software that often marks a correct answer is incorrect!
Yeah, I enjoyed this also and have written ray tracers for fun and for grades. And you’re right, this isn’t intro to algebra level stuff, I was just trying to capture the way learning can sometimes be simple and straightforward and then you suddenly hit a wall of unexpected complexity you don’t feel ready for.
Its time for the concept of a ‘variable’!
2 + a = 5
In this example, the variable is indicated by the letter a.
What you want to do is make it so ‘a’ is on one side of the = and a numerical value is on the other side.
One way we can do this is by subtracting 2 from both sides.
Left side: 2 + a - 2 gives us ‘a’
Right side: 5 - 2 gives us 3
Thus we are left with
a = 3
Tada!
/and then somehow, something like half or more of currently living Americans can barely pull off anything more complicated than this./
And sometimes you have more than one variable. Now if you have n variables and n polynomials containing each of those variables and not coplanar with each other, you can solve for each of those variables by adding or subtracting multiples of those equations from each other and/or rearranging and substituting variables for their equivalent equations.
Now we’ll use this principle to write a ray tracer where we combine the equation for a line (that represents a ray traveling through a focal point and a pixel on a grid in front of that focal point) and the equation for a plane or other 3D primitive to find if they intersect and at what point if they do.
Next lecture we’ll have a guest speaker, the ghost of Joseph Fourier in to tell you why jpegs get more jpegy each time you jpeg them.
Any questions? Oh, actually we’ve run out of time and another class needs the room.
I mean that actually sounds like great fun to me, reminds me of when I taught myself matrix algebra to be able to mod bullet penetration and ricochets into GMod yeeeeears ago!
Though I think a good bit of what you are describing is beyond the entry level Algebra text book pictured, lol, Fourier is certainly in the realm of Statistics.
But yes, now its time to either fill in multiple choice dot scantron sheets, or fill out your answers to the final in buggy garbage software that often marks a correct answer is incorrect!
Yeah, I enjoyed this also and have written ray tracers for fun and for grades. And you’re right, this isn’t intro to algebra level stuff, I was just trying to capture the way learning can sometimes be simple and straightforward and then you suddenly hit a wall of unexpected complexity you don’t feel ready for.
And you succeeded at that! Was a good, fun comment to read =)
But first, we need to talk about parallel lines
I think I had that book in high school back in the late 90’s early 2000’s, it goes up to the quadratic equation and maybe logarithms and matrices.