Einthoven's Triangle Revisited: A Mathematical Proof

TL;DR

This paper provides a formal mathematical proof of why Einthoven's triangle is used in ECG interpretation and explores conditions for alternative lead configurations, enhancing understanding of cardiac electrical axis determination.

Contribution

It offers the first formal proof of Einthoven's triangle and establishes geometric criteria for alternative bipolar ECG lead systems.

Findings

Proof confirms the equilateral triangle assumption in ECG lead placement

Defines geometric conditions for alternative ECG lead configurations

Enhances understanding of cardiac electric axis determination

Abstract

Willem Einthoven is widely considered the father of the electrocardiogram (ECG). In 1912, he proposed a method of determining the electric axis of the heart by using an imaginary equilateral triangle connecting the limb leads, now known as Einthoven's triangle. In 1924, Einthoven was awarded the Nobel Prize in Physiology or Medicine for his discovery of the mechanisms of the electrocardiogram. More than a century later, Einthoven's triangle is still at the heart of ECG interpretation. It defines the axes of the ECG leads in the frontal plane, that in turn, determines the axis of the cardiac electric dipole. The method is ubiquitously taught in lectures and applied in clinical settings. But Einthoven did not provide a proof for choosing the equilateral triangle. Future medical literature have not explored its origins. This paper provides a formal proof of its derivation to complete this important chapter in medical history and medical education. In addition, the proof determines the geometric conditions for alternative systems of bipolar ECG lead configurations in the frontal plane.