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You could send them this: https://nohello.net/en/
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I don't own them, but this is probably the cheapest from a decent brand at £40.
https://www.kbaudio.co.uk/products/edifier-r19bt-2-0-pc-speakers-with-bluetooth -
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HP were so shit in the SOHO product space for so long that I wouldn't have trusted them to have gotten it back together
I think acquiring Samsung's printer business helped. I can't be bothered to look up the HP model number but I got a proper office grade machine with Ethernet for about £120, it has been faultless.
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Thanks @mmccarthy and @wence. I think I will play around with some basic graphics code. My maths isn't great though (e.g. I found Bresenham's circle drawing algorithm, but couldn't really read it) so needs to be fairly simple algorithms.
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Well doctor, it started when I dreamt I was in a snowstorm in a Minecraft-like world, and wondered what algorithm would be used to control the settling of cubic snowflakes on the landscape...
If a column of snowcubes start at cell X on a grid, and must each move to a randomly chosen neighbour cell including diagonals, how so you weight the choice so that you end up with roundish, not square snowdrifts?
When I said 'ratio in terms of pi' I'd assumed there was a simple-ish ratio.
Thanks for the exact answer @wence !
I now think a practical way of approximating it would be to draw a bigger version of the original diagram on a grid, and just count squares in the blue and red areas.
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[Lots of edits:] I think I have it by working out the generalisation for the red area, as the area of overlap between two quarter-circles of radius r.
If they are right on top of each other, overlap area A = r * pi / 4.
If one is moved exactly r in any direction x, then they stop overlapping and A = 0.
Given that for any* 2D shape, area is directly proportional to dimension, A varies linearly but inversely with x.
[Edit 2: * this isn't right here is it, as the shape isn't just changing size]So, generally A = - ( pi * x / 4 ) + pi / 4 [as long as r >= x >=0]
In the diagram, the distance between the two quarter-circle centres is sqrt(2).
So red area A = (pi / 4) - sqrt(2) * pi / 4
Blue area B = (pi / 4) -1.[Edit: FFS I have misplaced something somewhere, it doesn't add up.]
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Wasn't the bulk of Sunak's riches sourced from the state anyway? As I understood it, his hedge fund owned a stake in ABN Amro, which was acquired by RBS, which was then acquired by the UK government to stave off a collapse of the UK banking sector. Some, if not all, of his millions came from that bailout.
I think the problem is that this can't really be proved. It's alleged his firm inflated ABN shares and therefore their stake, making the sale to RBS more likely, at which point presumably the stake was sold for profit.
But to allege it was Sunak shorting (in the general sense of betting on a future price fall), or by encouraging the deal, contributing to the banking collapse, in which the UK government bought the shares at a higher price, or that by doing so the public purse effectively paid for almost all of the c. £500 million [edit: this was the sale price of the stake, not the gain]...
... would require alleging that Sunak personally knew ABN was overvalued. Which is difficult to do, especially when there were competing bidders in the sale, I think.
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It was a record 124 F in Palm Springs on Tuesday, which is over 50 C..!