Mathematics And Architecture 1700

′S Essay, Research Paper

A look at scientific/mathematical developments of the 1600’s and 1700’s helps place the Central European Baroque church in context: Desargues, Bernoulli, Leibniz and Scieferenna, all mathematician or architect, all dealt with theories of synthesis and convergence. The effect of the new mathematical ideas were on architecture was a gradual transformation of space from pure, static and isolated to composite, dynamic and interpenetrating.

Architects used geometrical methods as plan generators. Transformational operations were of utmost importance, including area, rotation, reflection, translation, and coordinate transformation. Although we have probably one of the greatest architectural minds in Michelangelo contributing work during these times, we’re going to look deeper into the roots of the architectural and mathematical advances during this era.

Let’s begin by looking at the work of the Jacob and Daniel Bernoulli, mathematicians during the times of mid 1600’s to late 1700’s.

Jacob (Jacques) Bernoulli

Born: 27 Dec 1654 in Basel, Switzerland

Died: 16 Aug 1705 in Basel, Switzerland

Jacob Bernoulli was one of the sons of Johann (II) Bernoulli. Following the family tradition he took a degree in law but his interests were in mathematics and mathematical physics. Jacob Bernoulli was the first to use the term integral. He studied the catenary, the curve of a suspended string. He was an early user of polar coordinates and discovered the isochrone.

Daniel Bernoulli

Born: 8 Feb 1700 in Groningen, Netherlands

Died: 17 March 1782 in Basel, Switzerland

Daniel Bernoulli was a Swiss scientist who was born in the year 1700. He discovered that fast moving air exerts less pressure than slow moving air. Daniel Bernoulli’s most important work considered the basic properties of fluid flow, pressure, density and velocity, and gave their fundamental relationship now known as Bernoulli’s principle. He also established the basis for the kinetic theory of gases. His most important work was Hydrodynamica, which considered the basic properties of fluid flow, pressure, density and velocity, and gave their fundamental relationship now known as Bernoulli’s principle. In this book he also gave a theoretical explanation of the pressure of a gas on the walls of a container. Bernoulli’s principle can be seen most easily through the use of a venturi tube (see Figure below). The venturi will be discussed again in the unit on propulsion systems, since a venturi is an extremely important part of a carburetor. A venturi tube is simply a tube which is narrower in the middle than it is at the ends. When the fluid passing through the tube reaches the narrow part, it speeds up. According to Bernoulli’s principle, it then should exert less pressure. Let’s see how this works.

These two mathematicians greatly influenced the era of building during their times. If not only in the elements of geometrical proportions and scale, but also with the human endeavor aspect of moving forth as a “technological” advancement. Jacob had discovered the isochronous curve, which when illustrated, shows the derivation of a complex mathematical curve from a simple hyperbola diagram. The experimentation that Jacob underwent during these periods pushed further the ideas and geometrical associations found in areas like the Piazza of St. Peter’s, in Italy (1656 1667) and el Piazza del Campidoglio, Rome, Italy (1650 to 1657)- done by Michelangelo and Bernini. The direct relationship between these mathematicians and the actual buildings are rare, yet the influence at the time is a rich co-dependency of each subject. A closer look at certain examples will lead us to different examples of how these geometries and influential advancements associate themselves with their buildings.

The Louvre

Architect: Pierre Lescot, Claude Perrault

Location: Paris, France

Built 1546 to 1878

Building Type: palace, art museum

Context: urban, river front

The Louvre is one of many buildings during this era

that demonstrated the geometrical proportions that

were being displayed through mathematical endeavor

The Karlskirche, begun in 1715, in Vienna, is dedicated

to Carlo Borromeo, the Italian cardinal and saint of the

Counter Reformation. What is most extraordinary about

this structure is the successful coherence of its design

despite a seemingly irreconcilable eclecticism. In front

of a longitudinally placed oval nave stands an unusually

wide facade composed of a bizarre combination of

elements. A Corinthian hexastyle temple portico on top

of a stepped podium, archaeological in its fidelity to

Roman temple fronts, represents the entrance to a vast

temple with the grandeur and power as that of Olympia

itself. In construction, the building possesses the many

distributing structural elements from a diagram that

seemed to have been derived from a geometrical diagram.

A look at the fa ade will show the pedimented main

accent and serene confidence of order, but will fail

to show the untraditional flat roof that the architects

chose to implement. The mathematical implementations