A free standing arch of numbered wooden blocks can be built by laying the blocks on an outline drawn on a horizontal board and then tilting the bound up to a vertical position. The board can then be tilted back down, leaving the arch standing on its base. The curve of the arch is called a catenary.

When a chain is held by its ends, the chain assumes a catenary curve, the same shape as the arch except upside-down.

Neither the chain links nor the block surfaces can withstand shear or sideways forces, they can only withstand forces that are along or parallel to the line of† blocks or the length of† the chain. The chain can withstand tension only and the blocks can withstand compression only.

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The arch is self supporting because itís shaped like a catenary. Every block in the arch is held in place by neighbouring blocks. The blocks donít slide off each other, even at the top, because the forces between the blocks are along the curve of the arch itself. The blocks at the bottom of the arch are more vertical because they have more weight to support from the blocks above. If the free standing arch is touched very gently, it will sway like a chain, but it not will fall down. Catenary arches are specially strong because they redirect the vertical force of gravity into compression forces that press along the curve of the arch.