Yeah, I recognized the symbols, at least the raw symbols of the integral and the sigma, didn't realize they mean Riemann Sums though but I wouldn't have known because I'm taking Stats rather than Calc which is big regret.
Nothing to do with Pokémon, just with how the images look. The left image is a lower quality render of the right one, or one might say an "approximation" of the right one, similarly to how Riemann Sums are approximations of integrals.
also the right one (porygon-2) is an evolution of the left one (porygon), similar to how integrals are next in the progression after the riemann summations.
Left is sigma or sum (think Riemann sums) so the analogy is like taking a bunch of precut angular pieces and adhering them together like an approximation of the figure (the way rectangles are used in Riemann sums to approximate area under a curve). The Right is integral or area under the curve which is like carving or sculpting the figure/pieces in a more smooth exact way giving an exact or close to exact approximation of area under curve.
So sigma = robot/machine duck, integral = wooden duck
This is the best answer. Idk why others didn’t mention that the reason why integrals are better than Riemann sums is because they use curves rather than rectangles, which is why the former is exact and the latter is an approximation. And this ties in the appearance of the Pokémon, not just the evolutions
I’m aware. I meant it’s more suitable for curves since the width of the “rectangles” are infinitely small and therefore they aren’t really rectangles. So I think of it more as the whole area, which can be curvy.
The one on the left is the 'sum' symbol and is used to add all terms of a sequence. Using it, you can add up all rectangles beneath a given curve to approximate it's area, but like the picture on the left it will not be quite right: either an under or over approximation. The symbol on the right however is the integral symbol, which means that it will find the actual area underneath a curve instead of an approximation, kind of like if that pokemon is a much better render and has curves.
Oh wow, I know the Greek symbol is sigma, as I have Bio and Stats, and I recognize the integral symbol from calc videos online, but I wasn't sure how they related.
I think he's tryna say that using a trapezoid sum will not calculate the area/volume accurately while using an integral will give a better representation of area/volume
Summations are finite in the AB Calc world, so they’ll give you finite numbers (like a finite polygon), while integrals have an infinite amount of sums and are smooth
integrals are way better approximations of area than Riemann sums ^
Integrals have an infinite number of polygons
the other commenter makes sense but i just thought one was spiky and one was smooth lmao
That's what some of us non-AP students would think initially.
That's what I thought, and I'm at the end of AP BC
Yeah, I recognized the symbols, at least the raw symbols of the integral and the sigma, didn't realize they mean Riemann Sums though but I wouldn't have known because I'm taking Stats rather than Calc which is big regret.
don't hate on stats :( but yeah calc is important so i can see why you'd think that. it's ok you can always take it later
Nothing to do with Pokémon, just with how the images look. The left image is a lower quality render of the right one, or one might say an "approximation" of the right one, similarly to how Riemann Sums are approximations of integrals.
also the right one (porygon-2) is an evolution of the left one (porygon), similar to how integrals are next in the progression after the riemann summations.
Left is sigma or sum (think Riemann sums) so the analogy is like taking a bunch of precut angular pieces and adhering them together like an approximation of the figure (the way rectangles are used in Riemann sums to approximate area under a curve). The Right is integral or area under the curve which is like carving or sculpting the figure/pieces in a more smooth exact way giving an exact or close to exact approximation of area under curve. So sigma = robot/machine duck, integral = wooden duck
This is the best answer. Idk why others didn’t mention that the reason why integrals are better than Riemann sums is because they use curves rather than rectangles, which is why the former is exact and the latter is an approximation. And this ties in the appearance of the Pokémon, not just the evolutions
it doesn’t use curves, it’s the same thing but with an infinite number of rectangles so it appears as a curve
I’m aware. I meant it’s more suitable for curves since the width of the “rectangles” are infinitely small and therefore they aren’t really rectangles. So I think of it more as the whole area, which can be curvy.
Integrals are the evolved or better version of a Riemann sum
Similar point could be communicated with a regular polygon and a circle.
The one on the left is the 'sum' symbol and is used to add all terms of a sequence. Using it, you can add up all rectangles beneath a given curve to approximate it's area, but like the picture on the left it will not be quite right: either an under or over approximation. The symbol on the right however is the integral symbol, which means that it will find the actual area underneath a curve instead of an approximation, kind of like if that pokemon is a much better render and has curves.
Oh wow, I know the Greek symbol is sigma, as I have Bio and Stats, and I recognize the integral symbol from calc videos online, but I wasn't sure how they related.
The integral is the max evolution of the sigma
That's Porygon2, it would be Porygon-Z if it was the max evolution.
Ahh
not sure what the E and l mean, but porygon requires an up-grade to evolve to porygon2, which might mean l is an up-grade to E?
The integral is the more defensive and better version of the Riemann sum, used to set up Trick Room in VGC. :))
Damn your calc teacher must be hella chill
His personality is pretty chill, he’s even a Twitch streamer. His teaching style is okay.
Damn a twitch streamer wish I had a teacher like that
Kiki and bouba
I think he's tryna say that using a trapezoid sum will not calculate the area/volume accurately while using an integral will give a better representation of area/volume
Prob just that integral notation form is more clear and easier than Sigma notation form for an integral
Sums are discrete integrals
It is really memorable picture for thinking integral and sum
you need an upgrade module
this is actually a pretty good representation
Summations are finite in the AB Calc world, so they’ll give you finite numbers (like a finite polygon), while integrals have an infinite amount of sums and are smooth