Calculus Course. ~ X-Ray OriginalRingsSlicesBoards.

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Presentation transcript:

Calculus Course

~

X-Ray OriginalRingsSlicesBoards

Ring By Ring Timelapse 25%100%50%75%

X-Ray

Shape

X-Ray ViewStep-by-step

X-Ray Shape Step-by-step

X-Ray StrategyVisualizationStep-by-Step PatternCalculus Lingo Ring-by-ring Slice-by-slice Board-by-board

X-Ray StrategyVisualizationStep-by-Step LayoutCalculus Lingo Ring-by-ring Slice-by-slice Board-by-board

X-Ray StrategyVisualizationStep-by-Step LayoutCalculus Lingo Ring-by-ring Slice-by-slice Board-by-board

X-Ray StrategyVisualizationStep-by-Step LayoutSingle Step Zoom Ring-by-ring Slice-by-slice Board-by-board r p x dp dx dr 2*pi*r r

X-Ray StrategyVisualizationStep-by-Step LayoutSingle 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 ring Build out a disc Combine discs into a sphere Subtract a smaller sphere to get a “Shell”

CircleRingsSlicesBoards SphereShellsWedgesPlates

Ring-by-ring Timelapse Shell-by-Shell X-Ray Plate-by-plate Timelapse CircumferenceAreaVolumeSurface 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 ×

Did the explanation work? Find a better one No Yes Aha!