Geometric Bites

The Pythagram Defined Contributors over a 2.5 Year Period: Tiago Hands ( Final Construction ), Carlos Luna-Mota ( Egyptian Triangles ), Andrzej Kukla ( The Rhombus with Area of 3 ) 06 October 2025 Abstract The Pythagram is a planar geometric structure derived from the 3 : 4 : 5 right triangle and the orthographic projection of a cube. Its construction through defined Cartesian coordinates reveals six interrelated Pythagorean sub-figures that encode proportional symmetry across multiple dimensions. This document formalises the coordinates, connections, and geometric properties of the Pythagram as a reproducible mathematical entity. Coordinate Data Group 1 — Central Core A(16, 18), B(14, 18), C(12, 16), D(12, 14), E(14, 12), F(16, 12), G(18, 14), H(18, 16), I(15, 15), W(15, 17.5), X(12.5, 15), Y(15, 12.5), Z(17.5, 15) Group 2 — Inner Square L(15, 20), M(10, 20), N(10, 15), O(10, 10), P(15, 10), Q(20, 10), R(20...

Using a geometrical logo that can be reconstructed mathematically offers a variety of benefits, particularly in terms of design precision, versatility, and brand identity. Here's a detailed breakdown of these advantages: 1. Precision and Consistency Exact Reproduction : Mathematical definitions ensure that the logo can be reproduced exactly in any size or medium without distortion or loss of detail. Scalability : Geometrical designs based on mathematical constructs can scale seamlessly, maintaining their proportions and clarity from a tiny icon to a billboard. 2. Aesthetic Appeal Symmetry and Balance : Logos designed using geometric principles often incorporate symmetry and proportion, which are inherently pleasing to the human eye. Timelessness : Geometrical designs tend to feel clean and modern, yet timeless, making them less susceptible to trends. 3. Ease of Modification Flexible Adjustments : Since the logo's structure is based on mathematical principles, chang...

Understanding Heuristics: A Practical Guide to Smarter Problem Solving Image by:  https://pixabay.com/illustrations/data-robot-brain-humanoid-mind-7473235/ Introduction In our daily lives, we constantly make decisions, big and small. But how do we tackle complex problems without drowning in endless possibilities? Enter heuristics – a powerful set of mental shortcuts or "rules of thumb" designed to simplify decision-making. Heuristics are especially useful when time is limited, full information is unavailable, or a quick solution is needed. In this post, we'll delve into what heuristics are, how they work, and why they’re indispensable for efficient problem-solving. What Are Heuristics? Heuristics are simplified approaches or techniques that help us make quick, practical decisions. They don’t guarantee the optimal solution but offer a reasonable shortcut to finding workable answers. While heuristics are sometimes viewed as a compromise between accuracy and speed, ...

Falsifiability: The Cornerstone of Scientific Theory Karl Popper,  https://commons.wikimedia.org/wiki/File:Karl_Popper2.jpg In the quest to understand our world, science stands as a powerful tool, rigorously filtering ideas to identify the ones that best reflect reality. A crucial concept in this scientific process is falsifiability —the idea that, to be considered scientific, a theory must have the potential to be proven wrong. The principle of falsifiability, first popularised by philosopher Karl Popper in the 20th century, plays a key role in distinguishing science from non-science, helping us separate knowledge grounded in evidence from beliefs that evade scrutiny. What is Falsifiability? Falsifiability is the notion that a hypothesis or theory must have testable predictions that, if proven false, would invalidate the theory. In other words, there must be conceivable evidence or an experiment that could show the hypothesis to be incorrect. A theory that doesn’t allow for th...

Pseudoscience: Separating the Real from the Fake in Science Tarot cards: Image by  https://pixabay.com/photos/tarot-cards-tarot-cards-5511610/ In a world where information is at our fingertips, it's not surprising that the lines between genuine science and pseudoscience are sometimes blurred. While science is a structured approach to understanding reality, pseudoscience mimics this structure without adhering to scientific standards. Understanding the difference between the two is crucial for anyone seeking to make well-informed decisions and to avoid falling prey to false claims masked as “scientific truths.” What is Pseudoscience? Pseudoscience consists of beliefs, practices, or claims that appear to be based on scientific principles but lack the core elements that make something truly scientific. These fields and ideas often sound plausible, use scientific jargon, and may even appear in professional-looking journals or presentations. However, pseudoscience ultimately lacks th...

What is a Theory in Science? Image by:  https://pixabay.com/illustrations/universe-cosmos-astrophysics-7118741/ In science, a theory is a well-substantiated explanation for a broad set of observations and experimental results. It is developed through extensive research, testing, and evidence collection and is generally accepted within the scientific community as the best explanation available for a particular phenomenon. Theories are more comprehensive and reliable than hypotheses or conjectures because they integrate and explain a wide range of data and observations. They’re built on hypotheses that have been repeatedly tested and confirmed across various conditions, often by different researchers. Unlike in everyday language, where a "theory" might imply a guess or assumption, in science, a theory is a robust framework that helps scientists understand complex aspects of the natural world. For example, the theory of gravity explains the force of attraction between obj...