Geometry
Where geometry shows up in real life
7 live exhibits. Each one already works. Change a number and see what happens.
Open as board Play with these together. Solving one grows related exhibits.
GeometryLadder against a wall: how high will it reach?
A ladder, a wall, and the ground make a right triangle. Pythagoras does the rest.
GeometryPizza value: one large or two mediums?
Area grows with the square of the size. That changes which pizza is the deal.
GeometryHow much concrete for a slab?
Length × width × depth, plus a little extra. Get it right and you won’t run short mid-pour.
GeometryHow much paint do I need for a room?
Unfold the walls into one long rectangle. Area, minus doors and windows, sets the gallons.
Ratios & ProportionsWire resistance: longer and thinner resist more
Resistance grows with length and shrinks with thickness. Pick the wire that keeps it low.
Linear EquationsStress and strain: how much does a rod stretch under a load?
Stress is force per area. Divide by the material’s stiffness and you get the stretch, until it yields and stays bent.
Calculus (intro)Distance from a speed graph: area under the curve
Speed times time is distance, one thin rectangle at a time. Add more rectangles and the total closes in on the exact area: the integral.