Re:To Live Your Best Life, Do Mathematics
by vanderZwan on Friday February 03, 2017 @06:49AM
(#13559149)
> My intellectual capacity was far improved only after doing first year Engineering Maths & Physics. I did terrible gradewise, but it has helped me visualize, juxtapose mental structures, quickly iterate on different concepts etc.
Same here, and thanks to the internet just remembering concepts is usually enough these days.
Yesterday I had to quickly guestimate for a project how much space overhead we'd have on the server if we pre-generated an image pyramid of tiles for leaflet.js[0], instead of generating a "PNG" in RAM on the fly each time and serving that. Then I realised the number of pixels shrinks by a quarter every time we zoom out, so the worst case would be the infinite sum of 1/4^n. While I vaguely remember from my first year of physics how to calculate that, it's been over a decade. But we have Wolfram Alpha these days[0], which told me it converges on 4/3. So I knew the upper boundary would be around 4/3 of our original data, plus negligible PNG header overhead, and assuming compression is about the same.
Same here, and thanks to the internet just remembering concepts is usually enough these days.
Yesterday I had to quickly guestimate for a project how much space overhead we'd have on the server if we pre-generated an image pyramid of tiles for leaflet.js[0], instead of generating a "PNG" in RAM on the fly each time and serving that. Then I realised the number of pixels shrinks by a quarter every time we zoom out, so the worst case would be the infinite sum of 1/4^n. While I vaguely remember from my first year of physics how to calculate that, it's been over a decade. But we have Wolfram Alpha these days[0], which told me it converges on 4/3. So I knew the upper boundary would be around 4/3 of our original data, plus negligible PNG header overhead, and assuming compression is about the same.
[0] http://leafletjs.com/
[1] https://www.wolframalpha.com/input/?i=sum+of+1%2F(4%5Ek)