| Title | Description |
|---|---|
| GeoGebra | This is a huge website where teachers and students share free math tools. You can drag lines and shapes around on the screen to see how changing a shape instantly changes its math equation. |
| PhET Interactive Simulations | Made by the University of Colorado Boulder, this site is full of free, game-like science and math labs. You get to move sliders and flip switches to see how changing variables alters real-time graphs. |
| Desmos | This website is most known for its easy-to-use digital graphing calculator. However, it has applets too that use simple slider bars that let you change numbers in an equation so you can watch math lines bend, shift, and move on a grid. |
| Wolfram Demonstrations Project | This is a more advanced site that helps visualize tough math and physics concepts. You can adjust variables with sliders, and the website instantly calculates and draws complex shapes and models for you. |
| Academo | This website is a collection of simple tools that explain engineering and science. It takes real-world things and turns them into visual experiments so you can see the exact math formulas that make them work. |
| Title | Description |
|---|---|
| GeoGebra Photography Composition Analysis | This applet lets you upload any picture and put a resizable Golden Ratio grid and spiral on top of it. By dragging the corners, you can check if the subject lines up perfectly with balanced geometric points. |
| PhET Geometric Optics Simulation | This applet mimics a camera lens. You can adjust the lens opening size (aperture) and thickness (focal length) to see how light rays bend. It shows the exact math a camera uses to flip an image upside down onto a digital sensor. |
| Desmos Geometric Optics Plotter | This applet plots camera lens mechanics directly onto an X/Y graph. You can move sliders for focal points and object distance to watch light lines shift on the grid. It calculates how image size changes with distance, showing the math behind why lenses stretch or flatten a subject's face. |
| Wolfram Optical Depth of Field Calculator | This applet charts how camera settings create a blurry background. You use sliders to calculate focus limits. It plots the exact points where an image shifts from sharp to blurry, showing that focus changes on a curved math scale rather than a straight line. |
| Academo Aperture Size and Depth of Field Demo | This applet shows how changing a camera's lens opening changes the amount of light that enters. It uses a simple fraction formula to show how the size of the opening alters background blur and image sharpness. |
| Title | Type | Description |
|---|---|---|
| Using Mathematics to Connect with Photography | Video | In this TED Talk, Kristi Odom explains how her background as a passionate math student helped her creative career. She breaks down how artists use lines, circles, and the Fibonacci spiral to guide a viewer's eye into a picture, showing that math is a secret language used to create beautiful artwork and wildlife photography |
| How Math Can Instantly Improve Your Photography | Podcast | This podcast episode breaks down simple mathematical tricks to take better pictures with a camera or phone. It explains how the geometry of grids like the Rule of Thirds balances an image, and how fractions and ratios are used in the "exposure triangle" to balance shutter speed, ISO, and aperture. |
| Mathematics of Photography | Blog | This math blog post breaks down the hidden mathematics used inside digital cameras. It explains how camera settings use geometric progressions for ISO speeds, fractions for shutter speeds, and the Inverse Square Law for flash lighting. |
| How to Use Math in a Photography Career | Framework/Guide | This online framework outlines the specific math required to work as a professional photographer. It breaks down why camera lens adjustments require calculating the geometric area of a circle, and how trigonometry and angles of view are used to map out composition shots. |
| Golden Ratio vs Rule of Thirds Layout Comparison | Instagram Reel | An Instagram reel comparing two major photography composition layouts. It uses diagram grids to contrast the simple 3x3 math division of the Rule of Thirds against the unequal 1:1.618 ratio grid of the Golden Ratio spiral. |