Notes for a talk introducing highschools to differential calculus.

ESO/L. Calçada Illustration of a white dwarf with a strong magnetic field. In the 1930s, Subrahmanyan Chandrasekhar placed a limit on stars. Using our understanding of relativity and quantum theory, Chandrasekhar demonstrated that white dwarfs could never have a mass greater than 1.44 suns. It didn’t matter how they formed or whether they were mostly hydrogen or carbon. The very laws of physics forbid a greater mass. White dwarfs are the remains of smaller stars such as the Sun. When such a…

G. D. Chakerian [1] discovered the following generalization of the Pythagorean theorem. Take any triangle and attach squares to each side. From each triangle vertex, extend a line perpendicular to the opposite side and extend the line through the square, as shown in the figure below. Then the areas of the rectangles with the same labels are equal. It’s not clear at first why this is a generalization of the Pythagorean theorem, but if we make our triangle closer to a right triangle it’s easier…

What’s a connection between Edgar Allan Poe and Friedrich Wilhelm Bessel? Poe’s story The Pit and the Pendulum describes a pendulum with a semicircular blade being lowered on a cable. This is an interesting variation on the usual harmonic oscillator because the length L of the pendulum is not constant but rather an increasing function of time L(t). Using the small angle approximation sin(θ) ≈ θ, the equation of motion is L θ″ + L′ θ′ + g θ = 0. If we assume the length is increasing at a…