Mathematics
Geometry
SimulationBalance Lab
Hang weights on a lever bench, slide the strings of a mobile, and find when blocks, trucks and a crane tip over to explore equilibrium (zero net force and zero net torque) and the stability of structures. The balance point of a mobile turns out to be the internal division point of two masses, on a number line and on a coordinate plane.
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SimulationCushion Billiards
Aim and shoot on a 3D billiard table laid on the coordinate plane so that the ball bounces off a cushion and hits the target ball. Turn on the mirror ball to see B(a, b) reflected in the cushion line beyond the cushion: aiming straight at it gives the bent path to B (x-axis, y-axis, two cushions, and a wall on the line y = x).
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SimulationSlicing a Cone: Conic Sections
Tilt a plane through a glass double cone to get a circle, ellipse, parabola and hyperbola, find the foci with spheres in the cone (Dandelin spheres) to check definitions such as PF₁ + PF₂ = 2a, then connect the curves to their standard equations and to tangent lines found with the discriminant.
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SimulationEllipse Billiards
On a 3D elliptical billiard table, draw the cushion with two pins and a string to find what an ellipse is (PF + PF′ = 2a) and c² = a² − b², then find the tangent line at a point on the cushion from the discriminant D = 0. Shoot and send light to discover that a ball shot from one focus always passes through the other focus and that a parabolic dish gathers light parallel to its axis at the focus.
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