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Awesome! You can get another beautiful bagel by plotting the roots of polynomials with integer coefficients: https://math.ucr.edu/home/baez/roots/ https://math.
by bubblyworld 3y ago
Awesome! You can get another beautiful bagel by plotting the roots of polynomials with integer coefficients: https://math.ucr.edu/home/baez/roots/ https://math.ucr.edu/home/baez/roots/
(edit: hang on, am I crazy or do these bagels look remarkably similar? despite very different definitions)
- jerf 3y agoIt might be worth emailing the two groups of people and putting them in contact with each other. Nobody can know everything and be everywhere at once.
- Jarmsy 3y agoThe author of the article linked in the comment above yours has been discussing this here: https://mathstodon.xyz/@gregeganSF/112007010957379619 https://mathstodon.xyz/@gregeganSF/112007010957379619
- 3abiton 3y agoThis finding is so funny, it's like despite the interconnectedness in the 21st century things like this still happen.
- koliber 3y agoAbsolutely! The bagel 3D-like image and the 3rd image in your link are showing the same thing. Look at the inside of the ring and compare the images side by side. The features align in both images.
- madcaptenor 3y agoNot just you. I knew I'd seen these somewhere before.
- vinnyvichy 3y agoThe qm article says "A number is totally real if it satisfies a polynomial equation with integer coefficients" etc but I love your spirit and it's totally on quantamags for not stating their inputs up front
- 9991 3y agoAs always, Quanta Magazine reporting is just garbage. The name for such numbers is ‘algebraic’.
- gjm11 3y agoThe quotation from Quanta was incomplete, and the Quanta article doesn't in fact claim that "totally real" means what "algebraic" actually means. Here's what the article actually says (added emphasis mine): > A number is totally real if it satisfies a polynomial equation with integer coefficients that only has real roots. Nothing wrong with that.
- JadeNB 3y ago> As always, Quanta Magazine reporting is just garbage. The name for such numbers is ‘algebraic’. Any popularization is inevitably going to run into some inaccuracies—or else it's just re-publishing the technical papers—but the opinions of most mathematicians I know are that, far from being garbage, Quanta's reporting is distinctly better than most.
- throwaway81523 3y agoNo it's narrower than algebraic. If I have this right, the number is totally real if it's a root of a polynomial with integer coefficients, all of whose roots are real. So for example, the (real) cube root of 2 is not totally real, because x^3-2 has one real root and two complex roots. The idea of totally real is that not only is the root real, but all of its images under the polynomial's Galois group are also real. See: https://en.wikipedia.org/wiki/Totally_real_number_field https://en.wikipedia.org/wiki/Totally_real_number_field Added: in fact the Quanta article gets this right. It says "A number is totally real if it satisfies a polynomial equation with integer coefficients that only has real roots." Also, Jordana Cepelowicz is a knowledgeable math writer and I believe she has a PhD in math.
- bubblyworld 3y agoYeah, you've got it right, the Quanta article covered this accurately. For instance, 'i' is algebraic but not totally real (it isn't a real number!), since it satisfies 'x^2 + 1'.
- deleted 3y ago[deleted]
- DanielGeisler 3y agoI contacted Dr. Tiozzo about the similarity of the two fractals and he replied, From Giulio Tiozzo "Of course, the similarity between the set of zeros of Littlewood polynomials and Thurston’s entropy bagel is striking. In fact, I proved a few years ago that the two fractal sets the same inside the unit disk! The difference is that Baez’s set is symmetric under circle inversion, while Thurston’s set is not: the parts outside of the unit disk are completely different."
- bubblyworld 3y agoThanks for contacting him! I'll do some diving into his work, that's super cool =)