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Islamic geometric patterns

Islamic geometric patterns is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Islamic geometric patterns rather than just read about it. In short: Islamic geometric patterns are one of the major forms of Islamic ornament, which tends to avoid using figurative images, as it is forbidden to create a representation of an important Islamic figure according to many holy scriptures. The geometric designs in Islamic art are often built on combinations of repeated squares and circles, which may be overlapped and interlaced, as can arabesques (with which they are often…

Islamic geometric patterns — main illustration
Islamic geometric patterns — illustration

Key takeaways

  • Islamic geometric patterns belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Islamic geometric patterns to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Islamic geometric patterns from memory before moving on to harder problems.

Reference excerpt

Islamic geometric patterns are one of the major forms of Islamic ornament, which tends to avoid using figurative images, as it is forbidden to create a representation of an important Islamic figure according to many holy scriptures. The geometric designs in Islamic art are often built on combinations of repeated squares and circles, which may be overlapped and interlaced, as can arabesques (with which they are often combined), to form intricate and complex patterns, including a wide variety of tessellations. These may constitute the entire decoration, may form a framework for floral or calligraphic embellishments, or may retreat into the background around other motifs. The complexity and variety of patterns used evolved from simple stars and lozenges in the ninth century, through a variety of 6- to 13-point patterns by the 13th century, and finally to include also 14- and 16-point stars in the sixteenth century. Geometric patterns occur in a variety of forms in Islamic art and architecture. These include kilim carpets, Persian girih and Moroccan zellij tilework, muqarnas decorative vaulting, jali pierced stone screens, ceramics, leather, stained glass, woodwork, and metalwork. Interest in Islamic geometric patterns is increasing in the West, both among craftsmen and artists like M. C. Escher in the twentieth century, and among mathematicians and physicists such as Peter J. Lu and Paul Steinhardt.

Background

Islamic decoration Islamic geometric patterns are derived from simpler designs used in earlier cultures: Greek, Roman, and Sasanian. They are one of three forms of Islamic decoration, the others being the arabesque based on curving and branching plant forms, and Islamic calligraphy; all three are frequently used together. From the 9th century onward, a range of sophisticated geometric patterns based on polygonal tessellation began to appear in Islamic art, eventually becoming dominant. Islamic art mostly avoids figurative images to avoid becoming objects of worship. This aniconism in Islamic culture caused artists to explore non-figural art, and created a general aesthetic shift toward mathematically based decoration.

Purpose Authors such as Keith Critchlow argue that Islamic patterns are created to lead the viewer to an understanding of the underlying reality, rather than being mere decoration, as writers interested only in pattern sometimes imply. In Islamic culture, the patterns are believed to be the bridge to the spiritual realm, the instrument to purify the mind and the soul. David Wade states that "Much of the art of Islam, whether in architecture, ceramics, textiles or books, is the art of decoration – which is to say, of transformation." Wade argues that the aim is to transfigure, turning mosques "into lightness and pattern", while "the decorated pages of a Qur’an can become windows onto the infinite." Against this, Doris Behrens-Abouseif states in her book Beauty in Arabic Culture that a "major difference" between the philosophical thinking of Medieval Europe and the Islamic world is exactly that the concepts of the good and the beautiful are separated in Arabic culture. She argues that beauty, whether in poetry or in the visual arts, was enjoyed "for its own sake, without commitment to religious or moral criteria".

Pattern formation

… excerpt ends here. Continue reading the full article.

Illustrations

Islamic geometric patterns illustration
Islamic geometric patterns illustration
Islamic geometric patterns illustration
Islamic geometric patterns illustration
Islamic geometric patterns illustration

Worked examples

Example 1 — a first encounter with Islamic geometric patterns

Start with the simplest possible case. Write down what Islamic geometric patterns claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Islamic geometric patterns before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Islamic geometric patterns ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Islamic geometric patterns

In research
Islamic geometric patterns appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Islamic geometric patterns in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Islamic geometric patterns is common in secondary-school and first-year university syllabi. It links to neighbouring topics Islamic architectural elements, Islamic art, Mathematics in the medieval Islamic world, so understanding it makes those chapters shorter.
In everyday life
Look for Islamic geometric patterns outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Islamic geometric patterns in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Islamic geometric patterns means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Islamic geometric patterns out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Islamic geometric patterns in simple terms?

Islamic geometric patterns are one of the major forms of Islamic ornament, which tends to avoid using figurative images, as it is forbidden to create a representation of an important Islamic figure according to many holy scriptures. The geometric designs in Islamic art are often built on combinatio…

Why does Islamic geometric patterns matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Islamic geometric patterns?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Islamic geometric patterns.

Tags

  • Islamic architectural elements
  • Islamic art
  • Mathematics in the medieval Islamic world
  • Patterns

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