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Geometry And Mathematics In The Renaissance

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Published: Tue, 16 May 2017

Renaissance is one of the historical ages that truly had an impact on the modern civilization in terms of development in education, design and many other fields and also it did not ignore presenting out the most important figures during this age which had the same impact on modern civilization. This period of age started from the 14th century and ended on the 17th century starting in “Florence” in Italy and ending to the rest of Europe. Filippo Brunelleschi was one of its most important figures, shortly, the Renaissance style started to spread across Italian cities and some other countries like France, Germany, England, Russia and other parts of Europe at different dates and with varying degrees of impact. This paper will be discussing the impact of Renaissance on the development of mathematics and geometry in the modern age, its relation and the important figures that truly had an impact on this period. It will also discuss the important drawings and buildings that got affected by such innovations in this period of time.

Renaissance is one of the periods that had an impact on mathematic and geometry due to the brilliant figures that have been in this period of time which will be discussed in this paragraph. First of all, Geometry is simply a branch of mathematics that is concerned with shapes, size, position of figure, and properties of a space like for example, a square have a property of the flat equal-distance lines from all sides that gives it, its shape and the same goes for the other shapes like rectangle, hexagon, circle etc…Mathematics in general is the study of any types of structure, a space like a house, any designs etc., changes in velocity of an object, in general, anything that has to do with equations and calculations is categorized under mathematics. The most important figures that appeared in this period of age and had a true impact on Geometric and mathematics are” “Filippo Brunelleschi” dating from 1377 – 1446 he is the inventor of the mathematics of perspective in painting. “Paolo dal Pozzo Toscanelli” dating from 1397-1482 creating a huge sundial and making astronomical calculations and also giving a higher accuracy in calculating latitude at the sea and “luca pacioli” who wrote a number of theories and developed the geometrical proportions.” (Fletcher, 2000-11)

Renaissance buildings heavily relied on the use of geometry and the mathematics in their design which heavily impacted other modern designs till now. Renaissance type of buildings relied on curves, arches, triangle, circles and squares, which are the main elements of geometry, also needs to be defines as buildings like churches, castles and much more relied on those basic elements and developed it into arches, domes, rectangular segments inside and outside the buildings as many floor plans could describe it.

Renaissance building construction and how it was affected by such basic elements of geometry. The Renaissance great thinkers took the human being as a model for the universe being the perfect being made by god and used it in geometry and mathematics. This idea was developed by simply drawing this perfect figure which is the “Vitruvian man” standing in a square figure stretching his arms and legs forming a perfect circle around him. Based on these ideas, Leonardo made his own drawings based on the use of human proportions and the Vitruvius’s theory. In the renaissance age, it was their aim to put such ideas developed into practice in real buildings .What was done is that he blended the use of circles and squares much in his general layout of his plan and in the plan itself he divided it further into spaces through the use of columns plus having the advantage of supporting the roof and as for the circular part, he used it to act as a domes which was one of the most important figures in this period of time which gives the building its texture and unique style.

In this drawing, Leonardo made some adjustments to the Vitruvius measurement of the human figure which was inspired by his own studies and observation. Finally after adjustments and his own studies, he created the perfect image of the human figure with the best proportions. Leonardo had the belief that god was the perfect geometer and the one who created the universe based on proportions and numbers, he believed that the human body was one of his perfect creation, based on Leonardo’s thought, he drawn the Vitruvian man stretching his own legs and arms to form a perfect revolving circle around him and a square. However, in order to make this work, he had to place the circle centered but the center on the square is a bit lower. Through adjustments and researches of his own measurements based on studies of life models, the Vitruvian figure is not recognized as an ideal image and proportion of the human body. “Proportion is not only to be found in numbers and measures, but also in sounds, weights, intervals of time, and in every active force in existence.” stated by “Leonardo da Vinci” (University of the Arts).

The development of mathematics and calculations in the renaissance period is for sure one of the most important matters in this age. During the Renaissance, mathematicians and artists wrapped their arms around the questions of perspective, infinity, symbolic algebra and quartic equations, producing treatises on these subjects and offering fresh insights into the field of mathematics. The 15th through 17th centuries saw mathematical innovations in European countries like France and Italy, the impact of which extends to this day. These calculations were divided into different categories such as: Analysis vs. synthesis where the Renaissance saw the advancement of symbolic algebra. In his “Artem Analyticem Isogoge” of 1591, François Viéte took the ideas of Ancient Greeks Euclid, Diophantus and Pappus and sought to explain and clarify them through systematic algebraic notation. In doing so he could explain the concepts of analysis and synthesis. Analysis, or an assumption of something that is looked for and the arriving at something admitted to be true through its consequences, was to be distinguished from synthesis, which is an assumption of something that is admitted (conceded) and the arriving at something admitted to be true through its consequences. Moreover, he applied rules for calculating species “Viéte” further established rules for “species,” as opposed to numerical calculations. His first rule stipulates to “add a magnitude to a magnitude,” or to add only homogeneous magnitudes, such as apples to apples; his third and fourth rules instruct to multiply and divide magnitudes, respectively, which will result in heterogeneous kinds. For example, a side multiplied by a side is a plane, not another side. Expressed through species, operators and units, equations could now be handled more easily. Also, in the development of equations, cubic and quartic was main ingredients Two breakthroughs during the Renaissance in mathematics involved the solving of both cubic and quartic equations, which had beguiled mathematicians before and during the Renaissance. Although the work was not his own, Girolamo Cardano is credited with giving general solutions to both types of equations in the form of radicals. Previously, equations of the second degree were solved in this manner, but not cubic or higher equations. He published these findings in his work, “Artis Magnae,” in 1545. Finally, the imaginary and complex numbers, another advance for mathematics during the Renaissance period was the acknowledgment of the validity of imaginary or complex numbers. Cardano, in solving cubic equations, came upon the appearance of negative numbers under the radical sign. Predecessors either brushed these aside or were not able to solve such numbers. Cardano, although he incorporated these numbers in his calculations, admitted that he did not fully understand them. Nonetheless, his work with these new numbers brought mathematics to a higher level of abstraction.

After knowing the impact of mathematics and geometry in this period of time, renaissance did also impact modern age building design even though this period of age is so old but till nowadays it still impact us not in the design of the façade but in certain designs. We can see how did the Renaissance influenced architecture and its design all around us. The Use of symmetry, columns, and balance of windows in modern architecture, whether at a bank or courthouse, or even in an expensive home, all point to the influences of Renaissance architecture on modern buildings. Hence to effectively study the influence of Renaissance architecture on more modern architecture one should begin by more closely examining the elements and impact of Renaissance architecture and how those elements have been incorporated into architecture today. Renaissance architecture followed the Gothic period of architecture, which gave us the cathedral at Notre Dame, and was succeeded by the Baroque period, which is marked by highly ornate architectural designs and furnishings, and is often associated with the King Louis of France.

The Renaissance period strongly emphasized the following elements: Geometry which relied on having buildings, windows, and doors in square and rectangular shapes. Proportion, balance was critical in the Renaissance, and elements of the structure needed to be designed in proportion to other elements of the building. Symmetry relied on the use of geometric figures came an emphasis on symmetry and clean lines. Regularity which means that there is a little about the Renaissance style that is random or impulsive. A building must have recurring themes and elements. To accomplish these design goals, the Renaissance style employs many recurring elements, including: Columns, Pilasters, Lintels, Arches and arcades, Domes, Symmetrical windows and doors and finally Niches with sculptures. Each of these elements is used in proportion and with much attention given to order and balance.

Influence of the renaissance period came strongly in the 18th and early 19th centuries, which still many of these buildings still stand till today. Even later, in the 20th century, architects are reverting back to Renaissance designs when building grand homes much like the palaces found in Renaissance Italy and France. Various aspects of modern architecture find their roots in the Renaissance style. The features can include:

“Cube-shaped structure, Symmetrical façade, Smooth stone walls, made from finely-cut stone or with smooth stucco, Low-pitched roof, Roof topped with balustrade, Wide eaves with large brackets, Horizontal stone banding between floors, Segmental pediments, Ornately-carved stone window trim varying in design at each story, Smaller square windows on top floor and Quoins (large stone blocks at the corners)”. (What Influence Has Renaissance Architecture had on More Modern Architecture, 2011) We could also see many of these elements every day, all around you. Nowadays, designers do seek to blend the use of columns and style that dated 600 years old to use it till now .

Finally, to sum up, Renaissance time period showed a great improvement in the geometric and its use in the buildings as described in the paper and also the mathematical calculations used and how they were innovated and the name of the scientists who developed it. Moreover, we truly see the impact of geometry and proportions of space applied in their designs and how they made use of the basic elements such as circle, square, line etc…which later on impacted the modern age designs


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