Pen-based Proofs in Euclidean Geometry

The concept of digital ink has the potential to dramatically transform and enhance the teaching and learning process by becoming widely used in classrooms - replacing the use of desktops or laptops. One of the potential advantages of the new technology is that it allows the expression and exchange of ideas in an interactive environment using sketch based interfaces.

The project combines the concept of geometrical sketching on tablets with an automated theorem proving systems.

The goal of the work is to promote an intuition for problem solving and a way of algorithmic thinking on examples from planar geometry. Choosing the pen-based interface, we will expose students to contemporary software design and development. Integrating elements of formal proofs by definitions and axioms will propel students into a higher level of geometrical thinking. The idea of proving will be developed and refined as the above cycle progresses (revolves) until students obtain a strong grasp on a logical construction.


  1. Pen-Based Problem-Solving Environment for Computational Science, International Conference on Intelligent User Interfaces, February 24-27, 2014, Haifa, Israel.
  2. Pen-based Proofs in Euclidean Geometry, Workshop on the Impact of Pen and Touch Technology on Education, March 12-15, 2014, Texas A&M University, College Station, TX.

Victor S. Adamchik
Computer Science Department, 
Carnegie Mellon University, Pittsburgh, PA.