The foundations of calculus: change and accumulation.
The derivative df/dx = lim (h→0) [f(x+h) − f(x)] / h as the rate of change of f with respect to x, and the definite integral ∫_a^b f(x) dx as the net accumulation of f(x) from a to b.
These power real-world uses like motion analysis in physics, profit optimization in business, and population modeling in biology.
r = a e^(bθ)
Crank once: wooden lattice expands into equiangular spiral with φ = cot⁻¹(b) fixed between radius vector and tangent.
Growth ratio set, all differential geometry, no motors. This same curve powers deployable satellite solar arrays etc.
Harmonious Geometry: The Hirajoshi Wave.
Watch as these gravity-defying spheres trace the hauntingly beautiful paths of the C Hirajoshi scale.
Each ball is tuned to a specific frequency within this traditional Japanese pentatonic scale (C, D, Eb, G, Ab), creating a mesmerizing "Polyrhythmic Pendulum" effect. As the balls oscillate at slightly different speeds, they drift into chaotic patterns before perfectly realigning into a breathtaking visual and auditory climax.
From the sharp, angular bounce to the fluid, sweeping curves of the rainbow trails, this is where physics meets fine art.
Credit: project.jdm
Nothing in space is static.
Solar system moves at 800,000 km/h around the galactic center. The Earth, at 107,000 km/h around the Sun, and the Moon, at 3,700 km/h around the Earth.
Earthset.
The Artemis II crew captured this view of an Earthset on April 6, 2026, as they flew around the Moon. The image is reminiscent of the iconic Earthrise image taken by astronaut Bill Anders 58 years earlier as the Apollo 8 crew flew around the Moon.