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Model Perspective

Jun 12, 2025 · Fundamentals

Why Did Newton Call Calculus ‘God’s Language’? The Story Behind the Equation

From a wartime interview where Feynman urged a novelist to learn calculus as the language of God, through Newton's plague‑ridden youth and his hidden use of infinitesimals, to the Leibniz‑Newton controversy and modern applications, this article traces how calculus became the indispensable tool of science and engineering.

Newtoncalculushistory of mathematics

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Why Did Newton Call Calculus ‘God’s Language’? The Story Behind the Equation

Model Perspective

Jan 23, 2025 · Fundamentals

Why Linear Algebra Powers AI, Graphics, Economics, Physics and More

This article explores how linear algebra—through matrices, vectors, and linear transformations—underpins diverse fields such as artificial intelligence, data science, computer graphics, economics, physics, engineering, and social network analysis, illustrating its practical impact on everyday technologies and scientific models.

Artificial Intelligenceapplicationscomputer graphics

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Why Linear Algebra Powers AI, Graphics, Economics, Physics and More

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Dec 25, 2024 · Fundamentals

How the Seven SI Base Units Evolved: From Earth’s Curve to Quantum Constants

Explore the fascinating evolution of the seven SI base units—meter, second, kilogram, kelvin, ampere, mole, and candela—detailing how each transitioned from historical, Earth‑based definitions to precise modern standards anchored in constants like the speed of light, atomic transitions, and quantum phenomena.

SI unitsmeasurementmetrology

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How the Seven SI Base Units Evolved: From Earth’s Curve to Quantum Constants

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Dec 21, 2024 · Fundamentals

How Differential Equations Shape the Universe, Weather, and Life

This article explores how differential equations serve as the mathematical language that describes phenomena ranging from planetary orbits and cosmic expansion to atmospheric dynamics, cellular reactions, ecological interactions, electrical circuits, and financial markets, highlighting their universal role in modeling change.

biologydifferential equationsmathematics

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How Differential Equations Shape the Universe, Weather, and Life

Python Programming Learning Circle

Nov 12, 2024 · Game Development

Implementing Automatic Missile Tracking in a Shooting Game Using Python and Pygame

This article explains the mathematical basis and step‑by‑step Python/Pygame implementation of an automatic missile‑tracking algorithm for a shooting game, covering time‑slice integration, angle calculation, image rotation handling, and provides complete source code for a functional demo.

Missile TrackingPygamealgorithm

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Implementing Automatic Missile Tracking in a Shooting Game Using Python and Pygame

Model Perspective

Sep 20, 2024 · Fundamentals

How Einstein’s Relativity Shapes Everyday Life: From GPS to Time Perception

This article explains how Einstein’s theory of relativity, through time dilation, gravitational effects, GPS timing adjustments, and nuclear energy, subtly influences everyday experiences such as travel, high‑rise living, navigation, and our perception of time.

GPSeveryday sciencenuclear energy

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How Einstein’s Relativity Shapes Everyday Life: From GPS to Time Perception

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Jul 8, 2024 · Fundamentals

Exploring the Diverse Forms of Numbers: From Natural to Hypercomplex

This article surveys the various kinds of numbers—natural, integers, rational, irrational, real, complex, hypercomplex, vectors, matrices, and tensors—explaining their definitions, mathematical significance, and practical applications in fields such as computer science, engineering, physics, graphics, and machine learning.

Computer Scienceapplicationsmathematics

0 likes · 8 min read

Exploring the Diverse Forms of Numbers: From Natural to Hypercomplex

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Jun 3, 2024 · Fundamentals

Unlock the Universe: 24 Fundamental Formulas Every Physics Enthusiast Should Know

This article reviews the book “24 Formulas that Rule the Universe,” summarizing key equations—from Euler’s identity and Gaussian distribution to Einstein’s field equation and the uncertainty principle—while highlighting their scientific significance and the level of physics knowledge required to grasp them.

cosmologyfundamental-formulasgeneral-relativity

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Unlock the Universe: 24 Fundamental Formulas Every Physics Enthusiast Should Know

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Mar 31, 2024 · Fundamentals

How Far Can the Tang Monk’s Tightening Spell Really Reach? A Sound‑Propagation Model

This article uses a simple acoustic attenuation model—combining geometric spreading and atmospheric absorption—to estimate the maximum distance at which Sun Wukong can hear the Tang monk’s tightening spell, arriving at an approximate effective range of about 311 meters.

acousticsjourney to the westmathematical modeling

0 likes · 5 min read

How Far Can the Tang Monk’s Tightening Spell Really Reach? A Sound‑Propagation Model

Model Perspective

Mar 18, 2024 · Fundamentals

How Long Does a Brick Take to Sink to the Ocean Bottom? A Physics Model

Confucius watches two children argue about a brick’s sinking time, then uses physics—gravity, buoyancy, drag—and a mathematical model with Python code to estimate how long the brick takes to reach the bottom of various oceans, highlighting differences due to depth and terminal velocity.

Pythonfluid dynamicsmathematical modeling

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How Long Does a Brick Take to Sink to the Ocean Bottom? A Physics Model

Model Perspective

Feb 16, 2024 · Game Development

Mastering Game Physics: Essential Math and Code Techniques

This article explores the fundamental physics and mathematics behind game development, covering object motion models, scrolling techniques, collision detection, ray casting, screen transition effects, and provides Python code examples to illustrate how these concepts are implemented in practice.

Pythonanimationcollision detection

0 likes · 22 min read

Mastering Game Physics: Essential Math and Code Techniques

Model Perspective

Jan 5, 2024 · Fundamentals

How Archimedes Shaped Mathematics, Physics, and Engineering: A Deep Dive

Archimedes, the ancient Greek mathematician, made groundbreaking contributions to geometry, calculus of areas and volumes, the principle of levers and buoyancy, invented devices like the Archimedean screw, and his legacy continues to influence modern science, engineering, and education.

ArchimedesEngineeringHistory of Science

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How Archimedes Shaped Mathematics, Physics, and Engineering: A Deep Dive

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Dec 7, 2023 · Fundamentals

Why Entropy Always Increases: Understanding the Second Law of Thermodynamics

The article explains the entropy increase law (the second law of thermodynamics), illustrating how isolated systems become more disordered, why heat flows from hot to cold, and how everyday examples like cooling coffee or refrigerators demonstrate local order at the cost of greater overall disorder.

entropyheat transferphilosophy

0 likes · 6 min read

Why Entropy Always Increases: Understanding the Second Law of Thermodynamics

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Nov 19, 2023 · Fundamentals

How Diffusion Models Explain Everyday Phenomena and Environmental Risks

This article introduces the fundamental concepts and mathematical description of diffusion, explores its wide-ranging applications from daily life to environmental engineering, and demonstrates its use through a detailed ink‑in‑water example and a lake‑spill case study.

Fick's lawdiffusionenvironmental science

0 likes · 10 min read

How Diffusion Models Explain Everyday Phenomena and Environmental Risks

Model Perspective

Oct 28, 2023 · Fundamentals

Understanding the 1D Heat Conduction Equation: Derivation and Solutions

This article explains the one‑dimensional heat conduction equation, covering its basic assumptions, derivation from energy conservation, relationship between heat flux and temperature gradient, and solution methods including separation of variables and numerical techniques, while highlighting the role of initial and boundary conditions.

energy conservationheat conductionpartial differential equations

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Understanding the 1D Heat Conduction Equation: Derivation and Solutions

Model Perspective

Oct 2, 2023 · Fundamentals

How the Inverse Square Law Shapes Physics and Social Phenomena

Exploring the inverse square law, this article explains its core mathematical expression, its pivotal role in gravity and electrostatic forces, and extends the concept as a metaphor to illustrate patterns in information diffusion, interpersonal relationships, and international trade within social sciences.

electrostaticsgravityinverse square law

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How the Inverse Square Law Shapes Physics and Social Phenomena

Model Perspective

Sep 13, 2023 · Fundamentals

What Einstein’s Simplicity Rule Teaches Us About Effective Mathematical Modeling

By exploring Einstein’s famous maxim that ‘things should be made as simple as possible, but not simpler,’ this article reveals how balancing simplification with realism guides the construction, validation, and refinement of mathematical models across physics and beyond.

Einsteinmathematical modelingmodel validation

0 likes · 6 min read

What Einstein’s Simplicity Rule Teaches Us About Effective Mathematical Modeling

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Aug 20, 2023 · Fundamentals

How Differential Equations Model Everything from Populations to Physics

From population growth and disease spread to radioactive decay, cooling laws, chemical reactions, and chaotic systems, this article explores how first‑order differential equations serve as a universal mathematical language that precisely describes dynamic processes across biology, physics, chemistry, and economics.

biologydifferential equationsmathematical modeling

0 likes · 8 min read

How Differential Equations Model Everything from Populations to Physics

Model Perspective

Feb 23, 2023 · Fundamentals

Why Derivatives Matter: From Motion to Modern Science

Derivatives, the core concept of calculus, originated from Newton’s instantaneous speed, Leibniz’s tangent, and Fermat’s extremum problems, and are defined as the limit of a function’s change ratio, linking continuity, geometry, and physics, while finding extensive applications across science, economics, and biology.

applicationscalculusderivative

0 likes · 10 min read

Why Derivatives Matter: From Motion to Modern Science

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Feb 10, 2023 · Fundamentals

Unraveling the Catenary: How a Kite’s String Shapes the Curve

This article explores the classic catenary curve—its definition, historical development, and mathematical derivation—while examining whether it can model a kite’s string under wind, highlighting the assumptions of the model and suggesting more realistic approaches such as advanced derivations or simulation.

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Unraveling the Catenary: How a Kite’s String Shapes the Curve