Rings Slices Boards Ring By Ring Timelapse 25 100 50 75 XRay Shape XRay View Stepbystep XRay Shape Stepbystep XRay Strategy Visualization StepbyStep Pattern Calculus Lingo ID: 920933
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Slide1
Calculus Course
Slide2~
Slide3X-Ray
Original
Rings
Slices
Boards
Slide4Ring By Ring Timelapse
25%
100%
50%
75%
Slide5Slide6X-Ray
Slide7Slide8Shape
Slide9X-Ray View
Step-by-step
Slide10X-Ray Shape
Step-by-step
Slide11X-Ray
Strategy
Visualization
Step-by-Step Pattern
Calculus Lingo
Ring-by-ring
Slice-by-slice
Board-by-board
Slide12X-Ray
Strategy
Visualization
Step-by-Step Layout
Calculus Lingo
Ring-by-ring
Slice-by-slice
Board-by-board
Slide13X-Ray
Strategy
Visualization
Step-by-Step Layout
Calculus Lingo
Ring-by-ring
Slice-by-slice
Board-by-board
Slide14X-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
Slide15X-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
Slide16Shape Animation Spin
Slide17Slide18Slide19Start with a ring
Build out a disc
Combine discs into a sphere
Subtract a smaller sphere to get a “Shell”
Slide20Slide21Circle
Rings
Slices
Boards
Sphere
Shells
Wedges
Plates
Slide22Ring-by-ring
Timelapse
Shell-by-Shell
X-Ray
Plate-by-plate
Timelapse
Circumference
Area
Volume
S
urface area
?
Slide23Shell-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
Slide24=
+
=
2 ×
Slide25No
Yes
Aha!
Slide26Concept
Math
name
Symbol
Your shape
Function
Shapes can be split apart and put back togetherFundamental Theorem of Calculus
X-Ray a shape(split apart into steps)Derivative
Time-lapse a shape(glue together steps)Integral
Slide27