Esprit Jouffret was a French

France

The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

 artillery

Artillery

Originally applied to any group of infantry primarily armed with projectile weapons, artillery has over time become limited in meaning to refer only to those engines of war that operate by projection of munitions far beyond the range of effect of personal weapons...

 officer, insurance actuary

Actuary

An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....

 and mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, author of Traité élémentaire de géométrie à quatre dimensions (Elementary Treatise on the Geometry of Four Dimensions, 1903), a popularization of Henri Poincaré

Henri Poincaré

Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...

's Science and Hypothesis in which Jouffret described hypercube

Hypercube

In geometry, a hypercube is an n-dimensional analogue of a square and a cube . It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.An...

s and other complex polyhedra

Polyhedron

In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...

 in four dimension

Dimension

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

s and projected them onto the two-dimensional page.

Maurice Princet

Maurice Princet

Maurice Princet was a French mathematician and actuary who played a role in the birth of cubism. He was an associate of Pablo Picasso, Guillaume Apollinaire, Max Jacob, Jean Metzinger, and Marcel Duchamp...

 brought Traite to Picasso's attention. Picasso's sketchbooks for Les Demoiselles d'Avignon

Les Demoiselles d'Avignon

He followed his success by developing into his Rose period from 1904 to 1907, which introduced a strong element of sensuality and sexuality into his work...

illustrate Jouffret's influence on the artist's work.