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# Math In Architecture

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## Kristin Walsh

on 10 November 2013

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#### Transcript of Math In Architecture

Mathematics is used by architects to express the design images on a drawing that can then be used to construct their vision. Mathematics is needed to analyze and calculate structural problems in order to engineer a solution that will assure that a structure will remain standing and stable. The sizes and shapes of the elements of a design are possible to describe because of mathematical procedures.
Calculus

Calculus can calculate things such as the area of planar geometric shapes or the volume of geometric solids. Architects use calculus to establish stable acoustics, lighting, heating, ventilation and electricity.
What Math Is Used?
Kristin Walsh
The Math of Architecture
Trigonometry

Trig uses functions such as sine, cosine and tangent and relates the measurements of angles to measurements of associated straight lines. Architects use trigonometry to calculate angles and corners of a structure. Trig also helps to show the relationship between corners of a building to the planes or walls so the structure will stand soundly. Trig also helps the architect calculate and convey the measurements of the walls and angles to the construction crew.
Analytical Geometry and Calculus

Architects use analytical geometry and calculus to determine coordinates and graphing of algebraic formulas. Analytical geometry and calculus uses Cartesian coordinate system to figure the location of a point in 3D space. Architects use this section of math to configure models of their structures while they are in the design process by scaling walls, angles and space.
Finite Math

Finite math uses mathematical analytical techniques with logic, probability, statistics and mathematical model building. Architects design buildings much like putting together a puzzle with the reasoning that everything must be in a specific place in order to function properly.
Tetrahedral-Shaped Church
The tetrahedron is a convex polyhedron with four triangular faces. It’s a striking and classic example of modernist architecture, with its row of 17 spires and massive tetrahedron frame that stretches more than 150 feet into the sky.
Pentagonal, Phyllotactic Greenhouse and Education Center

England’s Eden Project the world’s largest greenhouse. The architecture is composed of geodesic domes that are made up of hexagonal and pentagonal walls. Their interactive education center dubbed “The Core” incorporated Fibonacci numbers (a math sequence that also relates to the branching, flowering, or arrangement of things in nature) and phyllotaxis (the arrangement of leaves) in its design.
Experimental Math-Music Pavilion

The Philips Pavilion at the 1958 World’s Fair is home to the asymmetric hyperbolic paraboloids and steel tension cables. Philips Electronics Company wanted to create a unique and creative new look to the building, while maximizing acoustics, lighting, capacity, and effeciency of the building
Solar Algorithm Wizardry

Barcelona’s Endesa Pavillion used mathematical algorithms to design the cubic building’s geometry. The building was based on solar inclination and the structure’s proposed orientation. Algorithms can be used to create the perfect building for any location with the right computer program. For Endesa, the movement of the sun was tracked on site before an architect from the Institute for Advance Architecture of Catalonia stepped in to complete the picture. The algorithm essentially did all the planning for him, calculating the building’s optimal form for that particular location.
Magic Square Cathedral
The Sagrada Familia cathedral in Barcelona by Antoni Gaudí is constructed using hyperbolic paraboloid (pringle-shaped) structures ans Catenary arches (a geometric curve) are throughout its architecture.. The cathedral also contains a Magic Square — an arrangement of numbers that equal the same amount in every column, row, and diagonal. The magic number in Sagrada Familia’s case is 33, relating to religious meanings. (Jesus performed 33 recorded miracles, and most Christians believe he was crucified at 33 years old in 33 A.D.)
Golden Ratio
Pythagorean Theorem
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. Many artists and architects have proportioned their works based off of the golden ratio or the golden rectangle (in which the ratio of the longer side to the shorter is the golden ratio) believing this proportion to be aesthetically pleasing.
Hopefully no definition needed. The theorem is used in architecture in the planning and sketching off a building when the architect it establishing or calculating the lengths of a wall or structure. Also intertwines with Trig Identities to find angles of corners of the structure.