Mathematics · 35 visual lessonsGeometry and work
Geometry and work
Change you can see.
Explore limits, derivatives, and accumulation through motion, measurement, and design.
Follow the real situation, derive the mathematics, and test it with interactive graphs and worked practice.
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Geometry and work
Interactive lesson
The top curve can switch in the middle.
Two response curves can cross. A geometric area between them adds contributions on both sides of the crossing.
Explore the idea ↗Interactive lessonStack disks and washers to build volume.
A hollow pipe demonstrates why an annular cross-section uses squared radii. The same slicing idea works when radius changes along the axis.
Explore the idea ↗Interactive lessonA strip parallel to the axis becomes a shell.
A thin vertical strip can rotate into a hollow cylindrical layer. Its volume comes from circumference, height, and radial thickness.
Explore the idea ↗Interactive lessonA varying force requires an area, not one multiplication.
Stretching a spring becomes harder as the displacement grows. Sum the little force–distance contributions.
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