Math Solutions

Show how the slope of a line is "rise over run" using two points and a slope triangle.

Apply rotation then reflection vs. reflection then rotation. Show that the order changes the result.

Dilate a shape by a scale factor of 2 from the origin. Show how lengths and areas change.

Reflect a shape across the line y = x. Show the original and the reflected image.

Rotate a triangle 90° counterclockwise about the origin. Show the original and the rotated image.

Show how corresponding sides of similar triangles have the same ratio.

Show that a circle's circumference is 2π times its radius by "unrolling" the circle into a straight line.

Show why the area of a triangle is half its base times its height.

Show a visual proof of the Pythagorean theorem with squares built on the sides of a right triangle.

Show how energy oscillates between an inductor and a capacitor in an LC circuit.

Move a magnet in and out of a coil of wire. Show how a changing magnetic flux induces a current.

A positive charge moves through a magnetic field perpendicular to its velocity. Show the force.

Show the circular magnetic field lines around a long straight wire carrying current.

Two charges q₁ = 2 μC and q₂ = 3 μC are 0.5 m apart. Find the force between them.

Show the uniform electric field between two parallel charged plates.

Visualize the electric field of an electric dipole — a positive and negative charge separated by a small distance.

Visualize the electric field around a single positive point charge.

Show under-damped, critically damped, and over-damped solutions for a mass-spring system with friction.

Two SHM oscillators with phase difference π/2. Show their motion side by side and on a single graph.

Drive a damped oscillator at various frequencies. Show that the amplitude peaks sharply at the natural frequency.