/en/tags/math/Recent content in Math on Feynman's BlogHugoen-USTue, 25 Aug 2026 12:00:00 +0800/en/posts/threejs-glsl-math/Tue, 25 Aug 2026 12:00:00 +0800/en/posts/threejs-glsl-math/<blockquote class="blockquote-regular"> <p>Last lesson covered GLSL basics and ShaderMaterial data channels. This lesson dives deep into math functions — mix / step / smoothstep for gradients and boundaries, sin / cos for waves, dot / cross for lighting and Fresnel, fract / mod for repeating patterns. These functions form the core toolchain from &ldquo;a UV coordinate&rdquo; to &ldquo;a final image&rdquo;.</p> </blockquote> <h2 id="01-learning-objectives">01 Learning Objectives</h2> <p>This lesson focuses on practical applications of GLSL math functions:</p>/en/posts/trigonometry-guide/Sun, 05 Jul 2026 10:00:00 +0800/en/posts/trigonometry-guide/<blockquote class="blockquote-regular"> <p>Trigonometric functions are the core tool for describing periodic phenomena and the mathematical foundation for 3D graphics. This article starts from right triangles and systematically reviews the definitions, formulas, graphs, and inverse trigonometric functions.</p> </blockquote> <h2 id="01-basic-definitions">01 Basic Definitions</h2> <h3 id="right-triangle-definition">Right Triangle Definition</h3> <p>In a right triangle, let angle $\theta$ be an acute angle:</p> <ul> <li><strong>Sine</strong> (sin): $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$</li> <li><strong>Cosine</strong> (cos): $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$</li> <li><strong>Tangent</strong> (tan): $\tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{\sin\theta}{\cos\theta}$</li> </ul> <h3 id="opposite-adjacent-hypotenuse-computation-formulas">Opposite, Adjacent, Hypotenuse Computation Formulas</h3> <p>Given a trigonometric function value and one side, the other sides can be found:</p>