Math

The leaning tower of blocks

Build the classical harmonic block stack and inspect the centre of mass and support margin at every layer.

Actual application image

Try this

This is a static balance construction for identical blocks. Gold marks show the centre of mass above every support. At 100% extension each support is marginally balanced; above 100% red layers would tip.

Equations used in the module

Equations
Offset of a stack of k blocks = L/(2k)
Maximum overhang = (L/2) Σₖ₌₁ⁿ 1/k = LHn/2
Hn ≈ ln n + γ; overhang is unbounded, but grows slowly
Stability: centre of mass above each contact lies within its support

Related experiments

Back to catalogue

Math

Wallpaper groups

Draw a seed motif and generate all 17 wallpaper groups using lattice translations, rotations, reflections and glide reflections.

Math

Interpolation and Runge's phenomenon

Compare polynomial and cubic-spline interpolation, expose Runge’s phenomenon and measure the effect of Chebyshev nodes.

$Continued fractions — Actual application image$

Math

Continued fractions

Build continued fractions term by term and inspect convergents, denominators and approximation errors for famous constants and custom decimals.