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okay
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okay Music
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jesus nope not jesus it's just me jesus nope not jesus it's just me what the hell is going on oh yeah um what the hell is going on oh yeah um what the hell is going on oh yeah um yeah i was working on this program and yeah i was working on this program and
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jesus nope not jesus it's just me what the hell is going on oh yeah um
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what the hell is going on oh yeah um
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what the hell is going on oh yeah um yeah i was working on this program and
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yeah i was working on this program and
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yeah i was working on this program and um yeah um yeah um yeah i i think i figured it out i think i got i i think i figured it out i think i got i i think i figured it out i think i got the formula so basically if the formula so basically if
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um yeah
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um yeah i i think i figured it out i think i got
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i i think i figured it out i think i got
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i i think i figured it out i think i got the formula so basically if
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the formula so basically if
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the formula so basically if you merge the projection equation wait you merge the projection equation wait you merge the projection equation wait wait wait wait wait wait wait what are you doing oh right what are you doing oh right what are you doing oh right um okay let let me just show you
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you merge the projection equation wait
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you merge the projection equation wait wait wait
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wait wait
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wait wait what are you doing oh right
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what are you doing oh right
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what are you doing oh right um okay let let me just show you
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um okay let let me just show you um okay let let me just show you let me just finish up real quick let me just finish up real quick let me just finish up real quick Music ready
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um okay let let me just show you let me just finish up real quick
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let me just finish up real quick
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let me just finish up real quick Music
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ready
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ready Music
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wait i i i don't follow this is that wait i i i don't follow this is that it's a donut it's a donut it's a donut it's incredible isn't it it's incredible isn't it it's incredible isn't it so so all this just so so all this just
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wait i i i don't follow this is that it's a donut
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it's a donut
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it's a donut it's incredible isn't it
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it's incredible isn't it
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it's incredible isn't it so so all this just
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so so all this just
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so so all this just to render a donut on your terminal
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what the thanks for watching what the thanks for watching the idea and code were originally from the idea and code were originally from the idea and code were originally from the amazing andy sloan the amazing andy sloan the amazing andy sloan where he was able to code this whole where he was able to code this whole
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what the thanks for watching the idea and code were originally from
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the idea and code were originally from
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the idea and code were originally from the amazing andy sloan
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the amazing andy sloan
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the amazing andy sloan where he was able to code this whole
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where he was able to code this whole
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where he was able to code this whole program and see program and see program and see and made the code itself look like a and made the code itself look like a and made the code itself look like a donut donut donut he has an article explaining how the he has an article explaining how the
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program and see
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program and see and made the code itself look like a
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and made the code itself look like a
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and made the code itself look like a donut
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donut
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donut he has an article explaining how the
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he has an article explaining how the
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he has an article explaining how the code works which i'll link code works which i'll link code works which i'll link in the description so why is math in the description so why is math in the description so why is math important for programming important for programming important for programming well it's because even if 99
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code works which i'll link
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code works which i'll link in the description so why is math
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in the description so why is math
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in the description so why is math important for programming
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important for programming
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important for programming well it's because even if 99
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well it's because even if 99 well it's because even if 99 of the time you won't need it there's a of the time you won't need it there's a of the time you won't need it there's a one percent chance that you might one percent chance that you might
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well it's because even if 99 of the time you won't need it there's a
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of the time you won't need it there's a
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of the time you won't need it there's a one percent chance that you might
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one percent chance that you might
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one percent chance that you might and it's in those moments that separate and it's in those moments that separate and it's in those moments that separate out a great programmer out a great programmer out a great programmer from average ones and if you do know from average ones and if you do know
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and it's in those moments that separate
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and it's in those moments that separate out a great programmer
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out a great programmer
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out a great programmer from average ones and if you do know
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from average ones and if you do know
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from average ones and if you do know your math your math your math you'll know how to modify this donut to you'll know how to modify this donut to you'll know how to modify this donut to increase the size increase the size increase the size change the rotation or even make a cube
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your math
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your math you'll know how to modify this donut to
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you'll know how to modify this donut to
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you'll know how to modify this donut to increase the size
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increase the size
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increase the size change the rotation or even make a cube
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change the rotation or even make a cube change the rotation or even make a cube instead instead instead also if you want to do computer graphics also if you want to do computer graphics also if you want to do computer graphics machine learning or cryptography machine learning or cryptography
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change the rotation or even make a cube instead
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instead
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instead also if you want to do computer graphics
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also if you want to do computer graphics
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also if you want to do computer graphics machine learning or cryptography
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machine learning or cryptography
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machine learning or cryptography you're gonna need math so might as well you're gonna need math so might as well you're gonna need math so might as well get good at it get good at it get good at it as you did for programming anyway back as you did for programming anyway back
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you're gonna need math so might as well
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you're gonna need math so might as well get good at it
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get good at it
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get good at it as you did for programming anyway back
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as you did for programming anyway back
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as you did for programming anyway back to the donut to the donut to the donut how do we write this program well first how do we write this program well first how do we write this program well first you have to create you have to create you have to create a donut which is essentially a solid of
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to the donut
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to the donut how do we write this program well first
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how do we write this program well first
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how do we write this program well first you have to create
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you have to create
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you have to create a donut which is essentially a solid of
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a donut which is essentially a solid of a donut which is essentially a solid of revolution revolution revolution where we have a circle that rotates where we have a circle that rotates where we have a circle that rotates around the y-axis around the y-axis around the y-axis which will make a donut aka a tourist
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a donut which is essentially a solid of revolution
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revolution
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revolution where we have a circle that rotates
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where we have a circle that rotates
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where we have a circle that rotates around the y-axis
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around the y-axis
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around the y-axis which will make a donut aka a tourist
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which will make a donut aka a tourist which will make a donut aka a tourist this is the formula to create the circle this is the formula to create the circle this is the formula to create the circle centered at r2 centered at r2 centered at r2 with radius r1 and this with radius r1 and this
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which will make a donut aka a tourist this is the formula to create the circle
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this is the formula to create the circle
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this is the formula to create the circle centered at r2
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centered at r2
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centered at r2 with radius r1 and this
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with radius r1 and this
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with radius r1 and this is the rotation matrix to rotate this is the rotation matrix to rotate this is the rotation matrix to rotate this circle circle circle around the y axis so when we combine around the y axis so when we combine around the y axis so when we combine them them
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is the rotation matrix to rotate this
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is the rotation matrix to rotate this circle
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circle
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circle around the y axis so when we combine
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around the y axis so when we combine
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around the y axis so when we combine them
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them
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them we get the coordinates of every point on we get the coordinates of every point on we get the coordinates of every point on your donut your donut your donut now that we have a donut shut up i know now that we have a donut shut up i know
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we get the coordinates of every point on
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we get the coordinates of every point on your donut
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your donut
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your donut now that we have a donut shut up i know
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now that we have a donut shut up i know
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now that we have a donut shut up i know this is a bagel this is a bagel this is a bagel now that we have a donut we want to now that we have a donut we want to now that we have a donut we want to rotate it around the x rotate it around the x
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this is a bagel
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this is a bagel now that we have a donut we want to
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now that we have a donut we want to
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now that we have a donut we want to rotate it around the x
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rotate it around the x
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rotate it around the x and z axis so it looks cool all flying and z axis so it looks cool all flying and z axis so it looks cool all flying and stuff and stuff and stuff we can do that by multiplying our donut we can do that by multiplying our donut
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and z axis so it looks cool all flying
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and z axis so it looks cool all flying and stuff
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and stuff
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and stuff we can do that by multiplying our donut
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we can do that by multiplying our donut
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we can do that by multiplying our donut coordinates with coordinates with coordinates with these two rotation matrices these two rotation matrices these two rotation matrices now we have to map this 3d flying donut now we have to map this 3d flying donut
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coordinates with
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coordinates with these two rotation matrices
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these two rotation matrices
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these two rotation matrices now we have to map this 3d flying donut
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now we have to map this 3d flying donut
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now we have to map this 3d flying donut onto a 2d screen which will become our onto a 2d screen which will become our onto a 2d screen which will become our terminal terminal terminal so each character on the terminal will so each character on the terminal will so each character on the terminal will be a pixel
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onto a 2d screen which will become our
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onto a 2d screen which will become our terminal
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terminal
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terminal so each character on the terminal will
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so each character on the terminal will
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so each character on the terminal will be a pixel
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be a pixel be a pixel on the screen to figure out how to shade on the screen to figure out how to shade on the screen to figure out how to shade our donut our donut our donut we calculate the dot product of the we calculate the dot product of the
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be a pixel on the screen to figure out how to shade
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on the screen to figure out how to shade
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on the screen to figure out how to shade our donut
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our donut
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our donut we calculate the dot product of the
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we calculate the dot product of the
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we calculate the dot product of the surface normal surface normal surface normal and the direction of the light so as you and the direction of the light so as you and the direction of the light so as you can see can see can see when the normal points this way it's way
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surface normal
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surface normal and the direction of the light so as you
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and the direction of the light so as you
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and the direction of the light so as you can see
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can see
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can see when the normal points this way it's way
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when the normal points this way it's way when the normal points this way it's way brighter brighter brighter and when it points that way it's way and when it points that way it's way and when it points that way it's way darker darker darker so the dot product will tell us how
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when the normal points this way it's way brighter
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brighter
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brighter and when it points that way it's way
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and when it points that way it's way
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and when it points that way it's way darker
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darker
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darker so the dot product will tell us how
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so the dot product will tell us how so the dot product will tell us how light or dark it is light or dark it is light or dark it is we take the result of the dot product we take the result of the dot product we take the result of the dot product and map it
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so the dot product will tell us how light or dark it is
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light or dark it is
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light or dark it is we take the result of the dot product
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we take the result of the dot product
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we take the result of the dot product and map it
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and map it and map it into these characters from darkest to into these characters from darkest to into these characters from darkest to brightest brightest brightest and lastly we draw that on our terminal and lastly we draw that on our terminal and lastly we draw that on our terminal and voila and voila
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and map it into these characters from darkest to
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into these characters from darkest to
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into these characters from darkest to brightest
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brightest
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brightest and lastly we draw that on our terminal
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and lastly we draw that on our terminal
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and lastly we draw that on our terminal and voila
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and voila
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and voila if you like the way i teach you can if you like the way i teach you can if you like the way i teach you can check out my new course on data check out my new course on data check out my new course on data structures and algorithms structures and algorithms
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if you like the way i teach you can
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if you like the way i teach you can check out my new course on data
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check out my new course on data
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check out my new course on data structures and algorithms
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structures and algorithms
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structures and algorithms where i use easy to understand where i use easy to understand where i use easy to understand animations to explain these concepts animations to explain these concepts animations to explain these concepts the first 100 people to sign up for joma the first 100 people to sign up for joma
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where i use easy to understand
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where i use easy to understand animations to explain these concepts
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animations to explain these concepts
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animations to explain these concepts the first 100 people to sign up for joma
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the first 100 people to sign up for joma
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the first 100 people to sign up for joma class will get class will get class will get 15 percent off joma class
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class will get
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class will get 15 percent off joma class
