Civil & Construction
The math behind building things that stand up
9 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.
Linear EquationsRoof pitch and ramp slope: rise over run
Slope is one number that decides whether a roof sheds water or a ramp is safe to roll up.
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.
TrigonometryHow tall is that tree? Measure its shadow
One shadow and the sun’s angle give you the height, no climbing needed.
Linear EquationsHome heat loss: where does the heat go?
Heat leaks through each surface in proportion to area and temperature difference, divided by R. Windows and drafts punch far above their size.
Ratios & ProportionsInsulation payback: how long until it pays for itself?
Heat saved goes as 1/R_before − 1/R_after, so the first few inches pay back fastest.
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.
VectorsHanging a hammock: why the 30° rule works
Your weight and the two strap pulls are arrows that must add to zero. Hang it tight and flat, and each strap pulls with several times your weight.