Prodigi
Riemann Surface of Log Eco Canvas
Riemann Surface of Log Eco Canvas
The real exponential function is monotone, and therefore invertible. The complex exponential function, by contrast, is periodic with imaginary period, and therefore fails to be invertible in the same way circular functions in precalculus fail to be invertible. Each non-zero complex number has infinitely many complex logarithms. There is a continuous choice of logarithm on the "slit plane" with the non-positive real axis removed, and other branches are obtained by adding whole multiples of the period. The branches can be assembled into a smooth "helical" surface as shown in the image. Walking around the origin in the domain causes the logarithm to pass from one branch to the next.
Made in the UK from recycled plastic bottles, stretched over a lightweight recycled frame. Packaging is also made from 100% recycled content.