Johann Heinrich Lambert

Johann Heinrich Lambert (1728–1777) was a Swiss-German mathematician, physicist, and astronomer who proved that π is irrational and helped establish photometry.

Irrational number: A real number that cannot be expressed as the ratio of two integers. Lambert’s proof placed π among numbers that no fraction can represent exactly.
Lambertian reflectance: An idealized reflection model in which a surface appears equally bright from every viewing direction. Lambert’s account of diffuse reflection became a standard model for matte surfaces.
Leonhard Euler: An eighteenth-century Swiss mathematician whose work shaped analysis, number theory, and mechanics. Euler’s results on trigonometric functions formed important background for Lambert’s proof about π.
Lambertian cosine law: The rule that diffuse radiance from an ideal Lambertian surface varies with the cosine of the viewing angle. It formalizes the angular behavior of the diffuse reflection Lambert studied.
Photometria: Lambert’s 1760 treatise that developed mathematical principles for measuring light. This book presented his systematic account of photometry and diffuse reflection.
Pi: The ratio of a circle’s circumference to its diameter, approximately 3.14159. Its irrationality was the subject of Lambert’s landmark 1761 proof.
Lambertian surface: An ideal diffuse reflector whose apparent brightness does not depend on viewing direction. This idealization carries Lambert’s optical work into modern graphics and illumination models.
Johann Bernoulli: A Swiss mathematician who advanced calculus and trained influential European mathematicians. Bernoulli’s mathematical tradition helped form the intellectual setting Lambert entered.
Computer graphics: The use of computation to create, manipulate, and display visual images. Lambertian reflection provides a simple baseline for shading virtual matte objects.
Irrationality of pi: The theorem that π cannot be expressed as a ratio of integers. Lambert proved this result in 1761 using properties of the tangent function.

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