Math and Science In Your Life

Science, Math and Technology Resources at Empire State College

*Visualizing Mathematics

Featured Courses: Visualizing Mathematics


Visualization has been at the heart of how people learn and understand mathematics for over 2000 years.

course image Reasoning from experience led the ancient Greeks to the discovery of ideas that underlay mathematics we still use today.For example, building and architecture led to the formalization of many of the properties of basic shapes: rectangles, triangles, and circles. Once those properties were known, it was easy to find additional practical applications for the knowledge.The diagram shows how a staff of known length, its shadow, and knowledge of the basic properties of right triangles can be used to measure an object of unknown length.


Students in this course focus on visual representations of mathematical ideas. If you’ve struggled with math in the past, this visual approach may help make become reacquainted with math using visual representations of mathematical concepts and by relating those concepts to real life situations. The course is organized around four concepts that are central to mathematical understanding:

The course starts with a series of four videos; Similarity, The Theorem of Pythagoras, The Story of Pi, and The Tunnel of Samos, that help students see the patterns and relationships that underlie all of modern mathematics. The videos provide prerequisite mathematical knowledge in a way that is understandable and accessible to any student regardless of math background or previous results in mathematics.

From this foundation students work to develop a deeper understanding of a range of mathematical topics using interactive math tutorials that allow the student to solve math problems visually and interactively. In a final section of the course students learn how graphs and charts are used visualize the information found in data. Using visualization to see and understand the patterns found in data ties back into the math concepts presented earlier.

This course features the use of interactive math visualization tools. You can expreiment with a few of these tools here.

Similar Triangles

Similar Rectangles

The Geometry of Pi