This paper introduces Euclidean Constructive Geometry (ECG). ECG is a field of modern mathematics that is based on the traditions of ruler and compass geometry that emerge from the ancient Greek geometer Euclid. This type of mathematics is unique in that is emerges directly the basic categories of space and time. ECG relates directly with mathematical objects. Unlike arithmetic or algebraic mathematics, geometry does not require the additional step of abstraction into numeral or variable.
Communication through ECG is direct and does not require encoding or decoding messages. Therefore, it is the most appropriate form of communication with ETI. Surprisingly, nearly all SETI messages use pictographic or numeral-based mathematics, which requires translation, abstraction, and decoding processes.