they built a wooden model to demonstrate their answer — although Bozóki notes that the model doesn’t verify the result because manufacturing errors are much greater than any errors the computer could have made. What's the point, when its not practically possible?
What's the point of what? Physical models have imperfections and distortions, so to absolutely know the answer you need the mathematics. Then having done the mathematics it's satisfying to build the physical model, to see it and to hold it.
Can you clarify your question? Try to avoid the word "it" because the referent might not be obvious.
This is going to sound like trolling, but it's not - I'm honestly curious. Why is this important? Is it just cool, or is there some real world application? Was someone paying for this research for some reason, or was it just a mathematician's hobby? EDIT: For the record, I don't have any problem with "just cool" research. I do that kind of research often (albeit, not as smart), and totally understand the value in it.…
When asked about this kind of topic I prefer to answer with the following joke:
'A mathematician, native Texan, once was asked in his class: "What is mathematics good for?" He replied: "This question makes me sick. Like when you show somebody the Grand Canyon for the first time, and he asks you `What's is good for?' What would you do? Why, you would kick the guy off the cliff".'
Great design for a no-gravity space station. Easy to go everywhere from everywhere.
I was going to make a vaguely snide comment about difficulty in routing and managing services (air, water, power, data, &c.), but the more I look at the model, the less firmly I'm convinced that there is an intractable topological problem involved. I'm still going to go with calling it the Villa Straylight, though.
You could dedicate a cylinder to utilities, and it will connect directly to all the others.
This is going to sound like trolling, but it's not - I'm honestly curious. Why is this important? Is it just cool, or is there some real world application? Was someone paying for this research for some reason, or was it just a mathematician's hobby? EDIT: For the record, I don't have any problem with "just cool" research. I do that kind of research often (albeit, not as smart), and totally understand the value in it.…
Exploring geometric puzzles made Professor Ernő Rubik the richest and most famous man in communist Hungary [1].
At least that's a concrete answer you can give to the "man in street" who's going to scoff at explanations about expanding mathematics. But money and fame, well, everybody understands that if it makes money or makes you famous it's justified.
This is just one of many puzzles and mathematical curiosities popularized by Martin Gardner. His books and columns make delightful light reading for anyone with a curious mind.
Ask HN: Is there an explanation somewhere of this "certification" that a layperson (college math and physics major, and self taught programmer) could understand?
It is not a matter of rational numbers, since the solution is likely to be an irrational number. The paper [1] describes a system of 20 polynomial equations with 20 variables (Equations 10--12) and solving them is no trivial task. To the end, authors first numerically found candidate solutions up to some ten decimal digits [2] and used specialized tools to prove (!) that there exists a real solution sufficiently clos…
Interesting. I would have thought that one could solve such things exactly by representing each unique known irrational that arises (root 2, pi, etc) by its own rational multiplier, and then overloading the relevant equality checks. Of course, you'd need to anticipate/implement each irrational type that might arise (roots, the geometric transcendental pi, and so on.) [Leaving the next sentence in, for comedy value. I…
How would you test whether two generic irrational numbers were equal? Obviously you can numerically approximate them and if you see any difference in the numerical approximation then they must be different - but if they seem the same up to e.g. 10 decimal places, what do you do next?
I was going to make a vaguely snide comment about difficulty in routing and managing services (air, water, power, data, &c.), but the more I look at the model, the less firmly I'm convinced that there is an intractable topological problem involved. I'm still going to go with calling it the Villa Straylight, though.
You could dedicate a cylinder to utilities, and it will connect directly to all the others.
That was more or less what I had in mind. On the other hand, it might be more cost-efficient in general to design the cylinders to connect endwise and form a hexagon; it'd increase travel time for the station's inhabitants, but reduce the need for unique construction tooling -- instead of seven types of cylinders, each of whose interconnections are placed differently from those of all the others, you build one type of cylinder and one type of connector, then fit out each unit according to the purpose it serves in a given station design. You can also enable more complex topologies simply by developing more complex connectors, whereas what I shall please myself by calling the "eccentric" design under discussion doesn't scale nearly as well.