Tag: Geometry

Exploring the Divine Geometry and Cosmic Harmony of India’s Grand Temples

A Temple is called a Devsthan, or a place where Deity resides. It is also called Devaalaya: A commonly used name for a temple that can also mean “devotional place” or “residence of God”. However in regular parlance the temple is called Mandir. The word mandir is made up of th...

The Stunning Beauty of Islamic Geometry

For creative individuals, life is all about seeking new, challenging experiences that pique their interest. When they find their passion in art, it’s not just about creating something pretty to look at; it’s about connecting with something deeper within us all. Art has the power to ...

Could Not Converge Geometry Optimization

In the code, I am finding convergence with mp2 that includes the electron correlation. This might be difficult to converge if there is a lot of interactions and dispersion effects where you might have to fall back to a lower level of theory hartree-fock . The same argument can be...

‘Probably The Hardest Geometry Equation In The World’

Inthe movie Rushmore, eccentric 15-year-old scholarship student Max Fischer participates extensively in extracurricular activities at the prestigious Rushmore Academy in Houston, but struggles academically. the hardest geometry equation in the world!? One day, Max daydr...

Introduction to Geometry

As I wander through the world of shapes and lines, I feel like I’m on a cool adventure. Geometry, to me, is like a game filled with puzzles waiting to be solved. Every time I draw a shape or figure out how big something is, it’s like unlocking a new level in my favorite video game. I ...

Non-Euclidean Dressmaking and Flounce Forms in Nature's Frilly Hyperbolic Geometry

I adore a flounce. It's one of my favorite ornaments on my clothes. I have tiny boobies and a little po, my curves, although feminine, are subtle and understated, so i dress to enhance them. And flounces, both in a textile art sense, and in a precise mathematical sense, are all about curvature. ...

What is Fractals Geometry

Fractals are fascinating geometric shapes that exhibit self-similarity at different scales. They are infinitely complex patterns that are created by repeating a simple process over and over again. In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small...

A 7-Circle Geometry Problem

Geometry is a beautiful intellectual pursuit. I believe that solving geometry puzzles is one of the greatest hobbies anyone can do. Whether you liked math in school or not, I hope this problem will make your day just a little better  Here’s a hint: rearrange the shaded … I re...

The Stunning Beauty of Islamic Geometry

Unraveling the beauty of Fractal Geometry in Technology

What exactly is Fractal Geometry?’ Well, let’s dive in to explore this intricate concept and its significant role in technology and engineering. If you’re a tech aficionado, engineer, or simply a curious mind, you’re in for an exciting ride! Fractal Geometry, as you might ...

Visualizing fractional geometry

I am a visual thinker. Taking intelligence tests with a grain of salt, in 9th grade I was given a multiple intelligences I/Q test and the results indicated that my visual-spatial intelligence was a full 20 points higher than my intelligences in other areas. Things just make sense when you can visual...

A Simple and Fun Geometry Problem

Here’s a math puzzle about Thanom’s roll of paper. Hmm, perhaps he has made a mess in the kitchen!?  Here’s a hint: a diagram will come in handy … I recommend you pause the article, grab your pen and paper, and give this a go. When you are ready, keep reading for ...

Reality Check: Euclidean Geometry Debunks the Simulation Hypothesis

Euclidean Geometry, developed by the ancient Greek mathematician Euclid, forms the foundation of our understanding of space and shapes. It describes a two-dimensional plane where points, lines, and angles interact according to specific rules. These rules, known as Euclid’s axioms, govern the b...

The Secret Meaning Behind the Flower of Life: A Guide to Understanding Sacred Geometry

Introduction Life is a curious adventure, and if you approach it with a little bit of humour, sarcasm, and a lot of heart, you can’t help but be amazed at the wonders of the world around us. Sacred Geometry: A Giant “I Spy” Game Sacred Geometry, for instance, is like a gia...

The geometry of shooting

A key principle in my approach to football analytics is to make sure that all data is related back to the game itself. We should never introduce a number, a statistic or a metric unless we can say what it means in terms of a player’s actions and coaching decisions. We have already seen this pr...

The Mystical Geometry of the Most Basic Concepts of Existence

Following on from our recent exploration of the rules and logic of spirituality found in geometry, in this article, we examine the spirituality to be discovered in the geometry of tesselating circle patterns. We propose that three overlapping circles, the trefoil, contain the geometry of the most ba...

The Sacred Geometry of the Circle, Sphere, Cone, its Sections, and the Wave in Kabbalah & Gothic Cathedrals

In this article, we meditate on the spiritual symbolism of the development of the circle and its geometric analogues, the sphere, cone, its sections and the wave. We consider the kabbalistic and mystical aspects of these geometric shapes and then how they are applied in the design of Gothic cathedra...

Exploring the Elegance of Ceva’s Theorem in Euclidean Geometry

the theorem provides deep insights into the relationships among cevians in a triangle. In geometry, a cevian is a line segment that connects a vertex of a triangle to a point on the opposite side or its extension. Essentially, it’s a line drawn from any vertex of a triangle to a point on the o...

What is DeepMind Alpha-Geometry?

This innovative neuro-symbolic system combines the strengths of a neural language model with those of a symbolic deduction engine, allowing it to mimic human-like reasoning capabilities. By generating “fast, intuitive” ideas through the neural model and refining them with the “deli...

Introducing scikit-geometry

As one can imagine, these types go a long way to define all sorts of geometries, and query for properties or generate new ones based on programmatic construction using intersections or other algorithms. The following example shows how easy it is to use the geometric primitives to find all pairwis...

How did Einstein interpret Euclidean geometry?

Everyone knows that one of the greatest theories proposed by Albert Einstein was the Theory of Relativity. You’ve certainly heard of it, whether through the famous formula E= MC² or even the concept of Space-Time. What most people don’t know is that the theory of relativity is la...

Geometry effects of a building in a SAR image, compared to an optical image

Where 3D rendering engines can work vectorially, projecting all faces in the camera plane in increasing order of distance to the sensor, in radar this approach is not possible. The projection plane of the image is not the plane of the sensor, and therefore the calculation of the faces that...

Another “Radical” Geometry Problem from IMO

As always, try solving this problem for yourself, before reading the solution. Even though this is an IMO problem, you still might be able to solve it, don’t give up too easily, and remember that it is always recommended to work on such problems for at least a few hours. Even if you don’...

Olympiad Geometry Solved by AI

Google DeepMind has developed an AI system called AlphaGeometry that can solve complex geometry problems, including those from the International Mathematical Olympiad (IMO)[2][3][4]. This represents a significant step towards machines with more human-like reasoning skills[2]. AlphaGeometry was te...

Math for Transforming 3D Geometry

The positions of things in graphics are usually represented by vectors. The first number in a vector is called the x-coordinate and the second number is called the y-coordinate. Each number represents a dimension; a 3-dimensional vector has an additional coordinate called z. Here are two diff...

Revolutionizing Problem-Solving: AI Masters Complex Geometry

In the rapidly evolving landscape of artificial intelligence, a milestone has been reached as Google DeepMind unveils an AI system with the capacity to tackle complex geometry problems. Dubbed AlphaGeometry, the system stands as a significant leap toward the development of more human-like reasoning ...

A Very Smart Solution On Oxford University Geometry Problem

Around 10 days ago, I wrote up a solution to an Oxford University MAT geometry problem. Specifically, I came up with my own solution by finding the individual radii of the circles. However, I found out that we can reach the solution much quicker. Here’s the question again! Here&rsquo...

The Geometry of War: Indian Chakravyuha and Roman Testudo

From time immemorial, the transcendent forms encoded in sacred art and geometry have guided humanity’s understanding of our place in the cosmos. The elegant permanence of the circle reflects the harmonic ordering of chaos into a unified equilibrium, symbolizing spiritual concepts of unity, inf...

Decoding the Mathematics and Geometry Hidden in the Torah — An Introduction to the Evolution of the Soul

The Hidden Geometry in the Torah This synthesis of spiritual, esoteric, and mathematical concepts hidden in the Torah presents a unique challenge. To understand this better from the start, let’s break down the components of these topics and explore how they might interconnect within the ...

Hidden Geometry in Music as a Healing Mechanism

The relationship between music and geometry is a mesmerizing dance, a language shared by these seemingly disparate realms. While perfect geometric shapes like triangles and squares often get touted as the ultimate representation of musical harmony, the reality is far more nuanced and scientifically ...

The Ineffable Geometry

Okay, let’s run a hypothetical thought experiment. In this experiment, you are participating in a tribe’s discussion. But, there’s a catch. You don’t understand their vocabulary, and they don’t understand your. Where do you begin? Such is the challenge of underst...

Unlocking the Mysteries of the Universe: How Geometry Reveals the Key to Reality

Introduction For centuries, mankind has been fascinated by the mysteries of the universe. From the vastness of space to the tiniest particles that make up our world, we have sought to understand the fundamental nature of reality. One intriguing aspect that has emerged is the role of geometry in u...

What is differential geometry and why do we care about it?

In a nutshell, the main idea in differential geometry is the following: we want to study curved spaces of a certain dimension, taking advantage of many useful tools from calculus. Okay, great but… 1- What kind of spaces? 2- What does it mean “certain dimension”? 3- Why would...

Ethereal Geometry : the Mystical Tapestry of Mathematical Beauty

Ethereal Geometry is a captivating and mesmerizing intersection where the rigor and precision of mathematics converge with the boundless realm of artistic expression. At its core, this concept delves into the exploration and representation of geometric patterns that transcend the purely analyti...

A Journey Beyond Traditional Geometry with Fractals

The concept of fractals was formalized by Benoit Mandelbrot in the 1970s. Mandelbrot’s work, particularly his book “The Fractal Geometry of Nature,” revolutionized the way we understand complex geometric shapes. Mandelbrot Set: Named after Benoit Mandelbrot, the Mandel...

Another purportedly hard geometry puzzle

One can rotate Figure 1 anticlockwise by 90° and flip it horizontally without changing the radius of the smaller circle. The hope is that this will make the problem easier to solve. This is Figure 3 below. Figure 3: Rotated and flipped version of the problem Notice ...

Now you can solve geometry, physics, and calculus problems with Google Search | TheOrcTech

Google recently improved its search engine and Lens tool to make it easier for you to understand and solve complex problems in subjects like geometry, physics, trigonometry, and calculus. The update lets you type math equations or take pictures of them using Google Lens tool. It then gives y...

Geometry and Trigonometry: Solving Triangles (AI’s Insights on Mathematics #5–3)

Venturing further into the captivating world of trigonometry, we find ourselves at the intersection of geometry and trigonometry: solving triangles. This article is a pivotal part of our mathematical journey. Triangles are the simplest polygons, yet they hide a world of complexity and fascinating pr...

Top 20 Uses Of Geometry In Daily Life

Have you ever noticed how shapes and patterns are everywhere in your day? That’s the magic of geometry! It’s not just about school lessons or complicated math — it’s the cool way shapes and spaces come together to make our world interesting. Imagine buildings reaching for ...

Geometry Across Dimensions (AI’s Insights on Mathematics #4–2)

Welcome to the fascinating world of Geometry Across Dimensions. As we venture further into our journey, we’ll explore a realm that takes us beyond the simplicity of flat planes and into the intricate complexities of three-dimensional space and even beyond. In this article, we delve int...

Visionary Art and Sacred Geometry

What is Visionary Art? Leonardo da Vinci was known to incorporate the aesthetic harmony of mathematical formulas in his art, and the tradition of painting visions may go all the way back to cave-paintings. Mystics used mandalas, Buddhist Tankas, and luscious visual compositions to deepen their ow...

Euclid: Illuminating the Universe with Geometry and Reason

In the ancient city of Alexandria, where the scent of papyrus mingled with the salt-laden breeze from the Mediterranean, Euclid walked the hallowed halls of the Library, a sanctuary of wisdom and enlightenment. His presence was marked by a quiet intensity, a mind always aglow with the sparks of math...

Understanding Quartic Curves in Classical Algebraic Geometry

Algebraic geometry is a captivating branch of mathematics that studies solutions to polynomial equations. One of the fundamental objects of study in this field is algebraic curves, which are defined by polynomial equations in two variables. Among these curves, the quartic curve holds a special place...

Intuition Can Be Cultivated, But Is There A Limit? — Insights from Chinese School Geometry Education

Drawing from my decade-long experience as a math teacher, I've observed that the introduction of geometric proof often marks a fresh beginning for middle school students. Interestingly, students who are good at algebra may not necessarily excel in geometry, while those under performers in elemen...