Home Projects
Math for fixing and building around the house
21 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 EquationsHow many amps does it draw?
Watts divided by volts gives amps. That decides the breaker and the wire.
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.
Linear EquationsHooke’s law: how far does the car sag when you load it?
A spring squeezes in a straight line with the load: twice the weight, twice the sag, until it hits the stops.
Ratios & ProportionsTorque: how hard to pull the wrench, and what an adapter changes
Torque is force times distance. A longer handle takes less push, and an adapter that adds length means you must set the wrench lower.
QuadraticsThe biggest garden from a fixed fence
Same fence, different shapes. A quadratic finds the one with the most room.
TrigonometryHow tall is that tree? Measure its shadow
One shadow and the sun’s angle give you the height, no climbing needed.
Ratios & ProportionsWire resistance: longer and thinner resist more
Resistance grows with length and shrinks with thickness. Pick the wire that keeps it low.
Linear EquationsVoltage drop: what the wire takes before the load gets it
Current times wire resistance is voltage you never get to use.
Systems of EquationsMixing solutions: how much of each?
Two strengths, one target. Two equations tell you exactly how much of each to pour.
Exponents & LogarithmsLoan payments: what a mortgage really costs
One formula sets every car, student, and home loan payment. See where the interest goes.
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.
VectorsSolar panel tilt: how much sunlight it catches
Point one arrow at the sun and one straight out of the panel. Their dot product is the share of full sunlight the panel gets.
Differential Equations & TransformsDoor closer: slam, bounce, or glide
One damping knob turns a slam into a glide. Where two dots (the poles) sit tells you which.
Differential Equations & TransformsWhy the shower goes hot, then cold
You react to water that left the tap seconds ago. Delay plus impatience makes the swing, and one number predicts it.
Calculus (intro)The biggest box from a sheet of cardboard: optimization
Cut a square from each corner and fold up the sides. Too small a cut makes a flat tray, too big a skinny tower. The derivative finds the best cut.