Brush Notes: 7 hours to cut a single line.

Is that title too clickbaity? I can't decide. Forgive me if you know all of this already but I go kicked out of almost every maths lesson at school so this is all new to my pea-sized brain.

Anyway, I just spent hours head butting the desk. The table at the NGV that I'm broadly copying had legs splayed at 1.5 degrees (thankfully, considering what follows, the rake is 0 degrees).

Easy enough right. Cut two 45s off the spandrel, tilt to the left a bit and you're off. Not so easy dear reader: that would create two mitre faces of uneven length, and the ones on the table were mostly certainly not uneven.

And this is where my crappy mathematics kicked my butt till the mid afternoon. Obviously the outside mitre needs to start longer, and the inside shorter, as the splay will lengthen the inside and shorten the outside mitre relative to the top line. Eventually, after a great deal of frustration and head scratching, googling and hassling my wife, "I" figured out that if you halve the splay angle, when you cut the splay angle off the top edge the difference is shared between the two mitres and they end up in plane with each other. I cannot describe the overwhelming feeling of relief when the penny finally dropped. That makes one mitre 44.25 degrees, and the other 44.75 degrees.

Onto the next head scratcher: how in the blue heck do you cut something at point two five degrees? On the same vein, how in the heck did they do this ONE THOUSAND YEARS AGO. Another thing I discovered today which is evidently new to me but not new to the world: rise and run. By using a +45 degree cross cut fence I can place a 2mm shim at 153mm from the blade to create a perfect 44.25 degree angle as the piece passes the blade. And to create the 45.75, I can just set the cross cut fence to 45 in the other direction (i.e. -45).

All the engineers in the room will be laughing at me but this has been a revelation. And what gets me is that people had figured this out so, so long ago. With the benefit of Google, computers, calculators and my brainy wife who made it make sense, it still took me hours to figure this out. The first time this style of table appeared, that we know of, is the Zhou Dynasty - between 1046 and 256 BC. Or, put another way, up to 3000 years give or take a Century. The historical record is not the beginning of human ingenuity. Not even close.

The heat coming off my skull could power a small generator. Time for something cold and refreshing.