A blog of Python-related topics and code.
Constructing Reuleaux polygons
Posted by: christian on 21 Jun 2018
A Reuleaux polygon is a curvilinear polygon built up of circular arcs. For an odd number of vertices, it has a constant width, and for this reason many polygonal coins, such as the UK's 50p piece and this Bermudian dollar coin are Reuleaux polygons. This property also means they make serviceable bicycle wheels:
What happens to carbon dioxide dissolved in water?
Posted by: christian on 11 Jun 2018
Carbon dioxide ($\mathrm{CO_2}$) dissolves in water, and some of the dissolved $\mathrm{CO_2}$ forms carbonic acid, $\mathrm{H_2CO_3(aq)}$: $$ \mathrm{CO_2(g)} + \mathrm{H_2O(l)} \rightleftharpoons \mathrm{H_2CO_3(aq)}. $$ This acid can then dissociate to form bicarbonate, $\mathrm{HCO_3^-}$: $$ K_1: \mathrm{H_2CO_3(aq)} \rightleftharpoons \mathrm{HCO_3^-(aq)} + \mathrm{H^+(aq)}, $$ which may further dissociate to carbonate, $\mathrm{CO_3^{2-}}$: $$ K_2: \mathrm{HCO_3^-(aq)} \rightleftharpoons \mathrm{CO_3^{2-}(aq)} + \mathrm{H^+(aq)}. $$
The world's nuclear reactors over time
Posted by: christian on 18 May 2018
The Python program given below generates this stacked area plot of the number of nuclear reactors in different countries over the last six decades or so.
The Duffing Oscillator
Posted by: christian on 15 May 2018
The previous blog post described the motion of a quartic oscillator: a particle moving in the potential $V(x) = \frac{1}{4}x^4 - \frac{1}{2}x^2$. In this case, the motion was always periodic (since the particle's energy is conserved).
A quartic oscillator
Posted by: christian on 10 May 2018
