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Chapter 5: Problem 113

The following topics related to irrational numbers are appropriate for either individual or group research projects. A report should be given to the class on the researched topic. The Golden Rectangle in Art and Architecture

Short Answer

Expert verified
The Golden Ratio is an irrational number (approximately 1.618) obtained by dividing a line into two parts such that the ratio of the whole line to the larger part equals the ratio of the larger part to the smaller one. A Golden Rectangle, which uses the Golden Ratio in its dimensions, is a rectangle that achieves an aesthetically pleasing balance, and has been widely used in both art (like in Leonardo Da Vinci's paintings) and architecture (like the Parthenon in Greece and designs of modern architect Le Corbusier).

Step by step solution

01

Understanding the Golden Ratio

The Golden Ratio, commonly denoted by Greek letter \(\phi\) (Phi), is an irrational number approximately equal to 1.61803398875... It is obtained when a line is divided into two parts in such a way that the ratio of the whole line to the longer part is the same as the ratio of the longer part to the shorter one.
02

Golden Rectangle and its Properties

A Golden Rectangle is a rectangle with sides of unequal length such that the ratio of the longer side to the shorter one is the golden ratio. If we draw a square inside this rectangle, the remaining rectangle will also be a Golden Rectangle.
03

Golden Rectangle in Art and Architecture

The Parthenon in Greece and the Pyramids of Egypt are often cited as examples of the use of the golden rectangle in architecture. In modern times the Swiss architect Le Corbusier used the golden ratio in his designs. He believed that this ratio brought mathematical harmony to his buildings.
04

Giving the Report

The final step is to present this information in a clear and concise manner. The report must include what the Golden Ratio and Golden Rectangle are, properties of the Golden Rectangle and specific examples of their application in art and architecture.

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Most popular questions from this chapter

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(0.0004,-0.004,0.04,-0.4, \ldots\)

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(0.0007,-0.007,0.07,-0.7, \ldots\)

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Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(0.0004,-0.004,0.04,-0.4, \ldots\)
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