- owns the entire stack and creates high quality highly optimized systems
- creates closed lock-in systems without inter-operability and actively fights users from owning their devices
- do they give back enough to open source, or do they leech mostly?
Convex hull of all (Cartesian product power) D-tuples, e.g. in 3D:
( 1, 1, 1)
( 1, 1, -1)
( 1, -1, 1)
( 1, -1, -1)
(-1, 1, 1)
(-1, 1, -1)
(-1, -1, 1)
(-1, -1, -1)Basically the same as classical mechanics.
Ciro Santilli's hardware 2020-04 Giro Rumble VR Off Road Shoe by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-162021-01-28: used this show for the first time after wearing dhb Dorica MTB Shoe (2020-12) exclusively for a while. It felt much much more comfortable, the Dorica is too narrow. Also this one is much more recessed, and walking with it is much easier. Also, I notice that the intentional asymmetry I had put on cleats is not necessary anymore now that my saddle height is not way too high
At 5C feet are too cold. Compatible overshoes are basically impossible to find: bicycles.stackexchange.com/questions/73589/what-kind-of-overshoes-can-i-use-with-a-large-touring-spd-cycling-shoe-such-as-t
It is not possible to do long walks with this, unlike some websites suggests, especially on hard surfaces like rock, that would be very dangerous because the cleat area will slip. But it is good for shorter walks on grass/mud, and that does open up some good short walk exploration possibilities compared to a road shoe.
Color "Black/Red 20" (but it's actually orange), size 46 www.wiggle.co.uk/giro-rumble-vr-off-road-shoe (archive). Manual says to use Loctite 243 medium strength, first 2.4 Nm bolt torque to test it out and find good position, and then final bolt torque 5-6 Nm unless cleat says less. Starting with Shimano SM-SH56 cleats (archive), which also says provisional torque 2.5 Nm, tightening torque 5-6 Nm.
- Google Maps download offline maps. This works very reliably, you can select the area you want to download. The only downside is that Google maps can't reliably show a route offline, and it does not contain national cycle route routes. Or those features are impossible for a software engineer to get working after trying for about 2 hours.
- OpenStreetMap on browser with cycling layer: www.openstreetmap.org/#map=5/49.582/1.934&layers=C This is the best visualization of cycling routes I've found so far, contains both National Cycle Network and National Byway and a few others, and they are shown extremely clearly. But as a website it doesn't reliably work offline
- the OsmAnd app for Android is the best offline free-ish OpenStreetMap viewer I've found so far. You only have to pay after reaching 5 region downloads, and it is very cheap if you want to do so. The cycle route view is not amazing, the routes are not so clearly marked and mixed with very similarly colored big roads, but with a bit of effort you can make them out. No routing though
- I've heard Komoot can keep a predefined route (possibly auto planed) reliably offline, but haven't used it myself. I was not able to see National Cycle Route clearly marked anywhere on it
Consider this is a study in failed computational number theory.
The approximation converges really slowly, and we can't easy go far enough to see that the ration converges to 1 with only awk and primes:Runs in 30 minutes tested on Ubuntu 22.10 and P51, producing:
sudo apt intsall bsdgames
cd prime-number-theorem
./main.py 100000000
. It is clear that the difference diverges, albeit very slowly.
. We just don't have enough points to clearly see that it is converging to 1.0, the convergence truly is very slow. The logarithm integral approximation is much much better, but we can't calculate it in awk, sadface.
But looking at: en.wikipedia.org/wiki/File:Prime_number_theorem_ratio_convergence.svg we see that it takes way longer to get closer to 1, even at it is still not super close. Inspecting the code there we see:so OK, it is not something doable on a personal computer just like that.
(* Supplement with larger known PrimePi values that are too large for \
Mathematica to compute *)
LargePiPrime = {{10^13, 346065536839}, {10^14, 3204941750802}, {10^15,
29844570422669}, {10^16, 279238341033925}, {10^17,
2623557157654233}, {10^18, 24739954287740860}, {10^19,
234057667276344607}, {10^20, 2220819602560918840}, {10^21,
21127269486018731928}, {10^22, 201467286689315906290}, {10^23,
1925320391606803968923}, {10^24, 18435599767349200867866}}; Unlisted articles are being shown, click here to show only listed articles.