Calculus Course

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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

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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