6+ mon, 2+ week ago   (291+ words) I ran across an old article [1] that gave a sort of multiplication table for trig functions and inverse trig functions. Here’s my version of the table. I made a few changes from the original. First, I used LaTeX, which didn’t…...

6+ mon, 3+ week ago   (352+ words) Scientists are extending the reach of artificial intelligence beyond standard data formats. New techniques allow machine learning to analyse complex, non-Euclidean data such as networks and manifolds. This development promises to unlock insights from increasingly diverse and challenging datasets, with…...

8+ mon, 2+ week ago   (459+ words) Have you ever tried to visualize 5 dimensions? Usually, you get shown a tesseract—a 4-dimensional hypercube spinning inside another cube. It’s mathematically accurate, but visually? It often looks like a tangled mess of wireframes. And once you try to go to…...

8+ mon, 2+ week ago   (929+ words) is nothing but 'all sin tan cos' rule in trigonometry. The 'all sin tan cos' rule can be remembered easily using the following phrases. All Sliver Tea Cups All Students Take Calculus ASTC formula has been explained clearly in the…...

8+ mon, 3+ week ago   (700+ words) This article details the implementation of non-linear classification models from a foundational standpoint. It is based on technical coursework from the PyTorch for Deep Learning Bootcamp. A common misconception is that deeper networks(two or more hidden layers) automatically solve…...

9+ mon, 2+ day ago   (942+ words) I have always been fascinated by elementary algorithms that create complex patterns. There is something fundamentally intriguing about such algorithms. One such algorithm is the Perfect Shuffle. Let's explore its unusual properties and create some striking fractals using this algorithm....

9+ mon, 1+ week ago   (313+ words) 📣 Superhive Black Friday sale is live! Get 25% off thousands of assets, tutorials and addons. In this example, edge 4 connects the bottom-right vertex to the top-left one. At the bottom-right vertex (‘Vertex 1’), the next edge in rotational order is 0 and the…...

9+ mon, 2+ week ago   (236+ words) In spherical geometry, the interior angles of a triangle add up to more than π. And in fact you can determine the area of a spherical triangle by how much the angle sum exceeds π. On a sphere of radius…...

9+ mon, 2+ week ago   (1718+ words) Complex systems often appear chaotic or incomprehensible, yet closer examination reveals that such complexity can frequently be reduced to a simple underlying mechanism. By systematically removing layers of emergent behavior, one can uncover a fundamental rule or equation from which…...

9+ mon, 3+ week ago   (62+ words) Five posts on Pythagorean triangles and Pythagorean triples Primitive Pythagorean triangles with the same area Sparse binary Pythagorean triples Matrix Pythagorean triples Approximation by Pythagorean triangles Fibonacci meets Pythagoras The post Pythagorean triples first appeared on John D. Cook. Five posts…...