Ancient Trig and History

1+ day, 7+ hour ago   (168+ words) Astrobiology Web [astro-ph.EP] Chondrule sizes are an important discriminant of chondrite groups and chondrule formation theories. Yet most studies report 2D sizes without attempting the somewhat tedious corrections to 3D proposed in the past literature. I show here that 3D size averages…...

6+ day, 15+ hour ago   (151+ words) Holes (Genus): 3 distinct holes passing through the figure 20 face pairs share a single edge. 8 face pairs share two edges. At every single vertex across the shape, exactly three faces meet. The most complex 3D shape that we come across in our…...

1+ week, 4+ hour ago   (109+ words) Published Sep 29, 2026 4:01 PM EDT While Mizhaev explains the genus-3 polyhedron’s geometry in a pre-print study detailed by New Scientist, it’s probably easiest to look at an example yourself. Pre-prints like these are research papers that have not been formally peer…...

1+ week, 6+ day ago   (306+ words) Imagine finding a planet billions of kilometres away because your calculations told you where to point the telescope. That’s essentially what happened on September 23, 1846, when Neptune was identified in one of astronomy’s great detective stories. Astronomers had noticed that Uranus…...

2+ week, 1+ day ago   (365+ words) "Written for the general reader, with no mathematical background required, The House of Algebra is not a book of grievance but a book of recovery." This is the ending to the introduction of Professor Ugail's new book. His work in…...

2+ week, 6+ day ago   (225+ words) At 12:00Z on 15 September, a bounded two-hour observation recorded 463 source rows and 463 unique events. Its useful result was not a fleet-wide health verdict. It was the boundary between incidents the record measured and explanations it could not support. The window captured…...

3+ week, 2+ hour ago   (202+ words) The previous post looked at how to interpret cosine similarity, or equivalently angles between word vectors. In a high-dimensional space, randomly chosen vectors are likely nearly perpendicular, and so relatively large angles, such as 50°, indicate very closely related words. Another…...