calculus course. ~ x-ray originalringsslicesboards
TRANSCRIPT
Calculus Course
~
X-Ray
Original Rings Slices Boards
Ring By Ring Timelapse
25% 100%50% 75%
X-Ray
Shape
X-Ray View Step-by-step
X-Ray Shape Step-by-step
X-Ray Strategy Visualization Step-by-Step Pattern Calculus Lingo
Ring-by-ring
Slice-by-slice
Board-by-board
X-Ray Strategy Visualization Step-by-Step Layout Calculus Lingo
Ring-by-ring
Slice-by-slice
Board-by-board
X-Ray Strategy Visualization Step-by-Step Layout Calculus Lingo
Ring-by-ring
Slice-by-slice
Board-by-board
X-Ray Strategy Visualization Step-by-Step Layout Single Step Zoom
Ring-by-ring
Slice-by-slice
Board-by-board
r
p
x
dp
dx
dr
2*pi*r
r
X-Ray Strategy Visualization Step-by-Step Layout Single Step Zoom
Ring-by-ring
Slice-by-slice
Board-by-board
r
p
x
dp
dx
dr
2*pi*r
r
Shape Animation Spin
Single Ring
Multiple Rings (Area)
Spin Area (Volume)
Dissect Volume (Surface
Area)
Start with a ringBuild out a discCombine discs into a sphereSubtract a smaller sphere to get a “Shell”
Circle Rings Slices Boards
Sphere Shells Wedges Plates
Ring-by-ringTimelapse
Shell-by-ShellX-Ray
Plate-by-plateTimelapse
Circumference Area Volume Surface area
?
Shell-by-Shell X-Ray…
Take a Ring Ring-by-ring timelapse… to a circle
Plate-by-plate timelapse… to a sphere
Take a sphere to surface area
= + = 2 ×
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Concept Math name Symbol
Your shape Function
Shapes can be split apart and put back together
Fundamental Theorem of Calculus
X-Ray a shape(split apart into steps)
Derivative
Time-lapse a shape(glue together steps)
Integral