Crinkle Walls
Functions & Equations
Why make walls thicker when you can make them curvy?
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
Check out the site below: "Wiggly walls, also known as “crinkle crankle” walls, is a type of garden wall that is build in a unique snake-like shape. They are quite popular in the UK and often leave visitors wondering why on earth were the walls built in such a distinctive shape. Well, apart from looking rather funky, there’s actually a rather simple explanation – it takes less bricks to make a wavy wall instead of a straight one. If you’re wondering why, that’s because a “crinkle crankle” wall can be built one brick wide without toppling over like a straight wall would."
Guiding Questions
- Crinkle-crankle walls are wavy but only one brick thick. Model the wall as a sine curve.
- How much longer is the wavy wall than a straight wall between the same points? The exact answer uses arc length, a calculus tool beyond both syllabi, but you can approximate it well by adding up short straight segments along the curve.
- Compare the bricks needed for a wavy single-thickness wall and a straight double-thickness wall.
- How do amplitude and wavelength affect both stability and brick count? Find a sensible optimum.