Not really a tip or trick but suggests possible peripheral uses...

I did this as a break from battling to learn basic stuff like viewports and workplanes...

Self-centring Lathe Chucks:

We know or can envisage a-

3-Jaw chuck holds round, hexagonal and polygons of even multiples of 3.

4-jaw chuck holds round, square and multiples of 4.

BUT

4-jaw self-centring chuck also holds concentrically, hexagons. Eh??? 4 jaws moving along the diagonals of an accurate square, gripping a 6-sided bar concentrically?

I did not know this until reading of it in a recent edition of *Model Engineer* magazine, with a remark on its counter-intuitive nature.

SO I analysed it by drawing:

Hexagon, 6inch dia, centred neatly on the grid.

Inner circle, tangential to the sides.

Outer circle, circumscribing.

Square, snapped to grid, enclosing the lot.

- All these concentric.

Diagonals to the square, vertex-snapped.

Colour each component differently to make the cobweb readable.

Dimension the hexagon and circumscribing circle.

Select the inner circle and tweak its diameter, gently, by X & Y in Inspector bar until it passed through the diagonals' crossings of the hexagon's sloping sides.

Sure enough the intersections all lay in a symmetrical, square pattern.

Dimension that new circle.

The mathematician would use the drawing only to guide a lot of trigonometry a bit too tough for me, but allowing for the slight inaccuracy in eye-balling lines on screen, the ratio of about 6.0 : 5.40 probably holds for any size of hexagon. In the workshop, the intersections are the contacts of the chuck's jaws with the sloping flanks of the hexagonal stock, with the top and bottom faces horizontal and the chuck jaws at 45º to that. Having said that, the contact will be edge-to-surface, not surface-to-surface.

Yes, the fact revealed in the magazine surprised me, but while I could simply have played with the real chuck and a bit of bar, or a large nut, to prove it to myself, I was intrigued by the geometry and if nowt else, it was a useful TurboCAD exercise in simply manipulating basic geometrical shapes on a single plane!