Activity for ziggurism
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #290305 |
Yes, the 11- and 57- cells apparently do have those very high dimensional realizations. And apparently with the right definitions every abstract polytope has a realization? Ok, but I would expect the general realization of a general abstract polytope to be pretty divorced from their geometry.
Wha... (more) |
— | 6 months ago |
| Comment | Post #290318 |
the set of normal numbers in $[0,1]$ is measure 1. Which means the non-normal numbers are a null set. Of course, contradictorily, the set of numbers which we can prove to be normal is probably countable. (more) |
— | 6 months ago |
| Comment | Post #290305 |
Ok I have read some of the sources linked on wikipedia, like [these two](https://people.eecs.berkeley.edu/~sequin/PAPERS/2007_SIGGRAPH_57Cell.pdf) and [pdfs](https://people.eecs.berkeley.edu/~sequin/PAPERS/2007_ISAMA_11Cell.pdf) by Sequin and Hamlin, and a [related powerpoint] and [this](https://en.w... (more) |
— | 6 months ago |
| Comment | Post #290305 |
ok if that's what the atlas link shows, then my answer is completely wrong. I notice that the atlas link lists neither the 11-cell (schäfli symbol {3,5,3}) nor the 57-cell (schäfli symbol {5,3,5}) so I don't know what to make of that list (more) |
— | 6 months ago |
| Comment | Post #290305 |
right, i think i may have overlooked the class of projective polytopes. thanks for the correction. But the point remains that unshackling yourself from any specific geometry unlocks two new regular polytopes. (more) |
— | 6 months ago |
| Comment | Post #290291 |
i tried to answer the question "why is homological orientation equivalent to the smooth definition of orientation". But upon re-reading the question, I'm wonder whether what you're really asking about is Betti numbers? (more) |
— | 6 months ago |
| Comment | Post #290291 |
OP asked for a first principles explanation, but i have left a lot of details vague in my answer. It is not complete at this stage and I would like to come back later and flesh it out. (more) |
— | 6 months ago |
| Comment | Post #287820 |
the Lagrange interpolation formula is an explicit formula for the polynomial of degree $n$ matching $n$ given values. https://en.wikipedia.org/wiki/Lagrange_polynomial (more) |
— | over 1 year ago |
| Comment | Post #287674 |
You may think that 60 is too unwieldy a number to count to, to learn the positional number system, but if you're willing to use a sub-base, like apparently Kaktovik does, so that needn't be a problem.
According to wikipedia, the motivating reason for using Kaktovik is compatibility with Inupiaq la... (more) |
— | over 1 year ago |
| Comment | Post #287674 |
Apparently the the Kaktovik numerals are a base 20 system with a sub-base of 5. Personally changing my own numeral system would be a huge task that I wouldn't undertake unless there were huge benefits. And of course the threshold to change the standards used for education and communication with other... (more) |
— | over 1 year ago |
| Comment | Post #286907 |
Although @#53398 is correct, that you cannot use mathematical induction to prove an identity for all real numbers, what you can do is prove Bernoulli's inequality for the natural numbers, using mathematical induction, which is straightforward. Then you can extend it to negative exponents, and rationa... (more) |
— | over 1 year ago |