Symbolism: Circle and Square

If you asked someone to pay you a dollar for every squared circle you saw at Temple Square and it's surrounding buildings (conference center, museums, etc.) you'd come away rich! It's everywhere in downtown Salt Lake.

The square is a symbol for the Earth.
(also foundation, balance, stability, direction, basics etc.)

Four corners of the earth
Four cardinal directions (north, south, east, west).
Four major season (winter, spring, summer, fall).
Four prime elements (fire, earth, air, water).

The circle represents Heaven
(also complete, unity, wholeness, infinity, without beginning or end, without sides or corners, the circle is also associated with the number one.)
When you stand on the earth looking up, the shape of the heavens is a circle.

So "squaring the circle" is a representation of Heaven on Earth.

It's a very beautiful concept, taught with a very simple symbol.  (That's the real beauty of symbols). They can teach so much, by showing so little.

I just had the thought that, from up above, temple SQUARE is also a depiction of heaven "the temple" (in the place of the circle) on earth. (square)

Heaven on Earth. It's no wonder it's on many temples.  But what else could it mean? Our homes can and should, most definitely be a heaven on earth.
And our hearts.

Which brings me to another thought:

Jospeh Smith said he was a rough stone rolling.  What could a symbol for that look like?

A square rolling, as the corners are chipped off it becomes an octagon, getting smoother and smoother to finally reveal a circle.

Which is why Christ as our Mediator is sometimes symbolized as an Octogon.  He stands between us and Heaven.
This concept is taught on the steeples of many LDS meeting houses.

A path of progression towards heaven.