[londons_explore]

I don't think this is the case.

A wavy wall with a wave amplitude of X has the same toppling resistance as a straight wall with buttresses on both sides of length x/2.

Assuming this stackoverflow answer is correct[1], the sine wave has (slightly) less bricks.

[1]: https://math.stackexchange.com/a/1500468

[Retric]

A single repetition of the wave is misleading. For N repetitions of the wave you need N + 1 buttresses not 2 N.

Also, while brick is stronger in compression a buttress increases toppling resistance in both directions so you need to consider material properties not just the geometry.

[Dylan16807]

> A wavy wall with a wave amplitude of X has the same toppling resistance as a straight wall with buttresses on both sides of length x/2.

Where did you get that number from, and how does it change as you vary the distance between buttresses?

[londons_explore]

Assuming one pair of butresses (ie to prevent the wall toppling in each direction) per sine wave cycle.

[Dylan16807]

But the math depends so strongly on how often the buttresses are needed, and the length of the buttresses, so you can't assume those things. The goal is a wall of equivalent strength, after all. If equivalent strength needs slightly less distance, or slightly smaller buttresses, the result could be thrown completely off in either direction.