Vector Visual

Vector Visual is a tool for introducing vectors and how they relate to trigonometric formulas, the pythagorean theorem, the unit circle, the cartesian plane and other basic concepts in geometry.

Teachers or tutors may use Vector Visual like an electronic chalk board. For example, starting with a description of the shortest distance between two points (i.e. a line or vector), instructors can gradually guide students through drawing proper diagrams of right angle triangles. Vector Visual uses interactive animations, annotated with equations, to help students visualize relationships between the vector, the two points, the hypotenuse, and the opposite or adjacent legs of right triangles—in any quadrant of the cartesian plane.

Students may also use Vector Visual on their own, like a graphing calculator specialized for trigonometry, or a set of digital flash cards. This app is developed for mobile phone devices to make learning on the go more convenient. It can be used as a standalone application as well as an add-on study aid, with textbooks or narrated videos.

Vector Visual displays vectors along with their horizontal and vertical components in right triangle diagrams annotated with corresponding trigonometric and geometric formulas updating in real-time in response to touch screen interactions.

All 2D vectors, drawn on the Cartesian plane, can be decomposed into (the conventionally depicted) “horizontal” and “vertical” components. The vector, and its vertical and horizontal components are color-coded as purple, blue and red respectively. The color coding is intended to be a mnemonic device to help students remember basic vector addition by analogy, i.e. vectors are the combination of their horizontal and vertical components, just as purple is the combination of red and blue.

Toggle buttons below the diagram can be used to hide (or unhide) components of the diagram. This allows teachers and students to increase or decrease the complexity of a diagram step-by-step as lessons develop.

The most effective learning experiences are often hands on and involve exposing students to a sufficient number of examples of a concept, method, problem-type etc. Sometimes failure in academics (or even life in general) is simply the result of not having seen enough properly presented examples. Vector Visual provides the advantage of instantly constructing and adjusting vector diagrams annotated with their trigonometric parameters with one simple touch. Providing students with a practically infinite number of flash cards to help them study— with a teacher, tutor or independently.


According to a recent (Nov 2025) study coming out of UC San Diego, roughly 1 in 8 incoming freshmen, many with 4.0 high school math GPAs, cannot pass placement tests on elementary arithmetic. Vector Visual was developed to address gaps that may have been observed in high school or freshman physics.

Vectors are fundamental to science and engineering. Science and engineering are fundamental to technology, production and economy. Vector visual can be used to help build a foundation for students considering careers in science, engineering, medicine and other fields that rely on understanding the connections between these fundamental concepts in mathematics.