Ancient Trig and History

1+ day, 22+ hour ago   (220+ words) Pascal’s triangle is the most famous triangular arrangement of numbers. I’ve written about other numerical triangles, such as Bell’s triangle and the trinomial triangle. There’s another well-known triangle that somehow I never heard of until recently: the harmonic triangle, first…...

3+ day, 13+ hour ago   (160+ words) You still have a body. You still have a brain. Unfortunately, the universe has decided to remove depth. Your body is now flat. Your veins have no volume, your organs have nowhere to exist, and turning sideways is no longer…...

3+ day, 11+ hour ago   (436+ words) This article will dive into the world of fractals, exploring their properties, how they are generated, and their presence in our world. Fractals are mathematical sets showing a repeating pattern that displays at every scale. They are known for their…...

4+ day, 15+ hour ago   (277+ words) Beyond faith and mysticism lies a blueprint of cosmic geometry. Exploring the Seven Lampstands as numerical tables on the Book 198 platform. What if the Seven Lampstands are not just dynamic metaphors, but literal structural blueprints of our universe? The Shift…...

1+ week, 2+ day 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…...

2+ week, 1+ day 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…...

2+ week, 1+ day 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…...

3+ week, 1+ 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…...

3+ week, 3+ 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…...

4+ week, 1+ 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…...