*By Iftikhar U. Hyder*

Jul 10 2020

IN 1079 AD,
Omar Khayyam calculated the length of the year to be 365.24219858156 days,
astonishingly accurate to the sixth decimal, an inaccuracy of a fraction of a
second of the true length calculated in the 20th century using atomic clocks,
computers and the Hubble telescope. Yet, more than 900 years later, some of the
greatest academic works chronicling the contributions of Muslims to science,
mathematics, society, law, and the arts have been carried out by non-Muslims.

Most
Muslims admire Islamic art. However, it was only recently that a young
physicist made a discovery that many of the beautiful patterns in ancient
mosques were based on complex mathematics thought to have been first developed
in the mid-1970s.

In 2005, a
Harvard doctoral student Peter Lu, was visiting Uzbekistan. He noticed the
intricate patterns in some historic mosques. Lu recognised the tiling’s
patterns which were known by mathematicians as Penrose Tiles. At first, he
could not believe that the tiling was 500 years old since he knew that the
mathematics behind these was believed to have been first developed in 1974 by
the distinguished Oxford mathematician and physicist, Roger Penrose.

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**Also Read: ** **Science
and Religion**

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After
returning to Harvard, Lu collaborated with a world-renowned Princeton physicist
Paul Steinhardt, who in 1984 had proposed the existence of three-dimensional
analogs of Penrose Tiles, shrunk to the atomic level. Steinhardt had named such
structures ‘quasi-crystals’. After meticulously reviewing historic Islamic
mosaics and manuscripts, they published a paper in February 2007 in Science, a
journal published by American Academy for the Advancement of Science (AAAS) in
which they showed that Muslim mathematicians had made the geometric
breakthrough behind Penrose Tiles about 500 years before Penrose did. They
wrote in their paper, “....by the 15th century, the tessellation approach was
combined with self-similar transformations to construct nearly perfect quasi-crystalline
Penrose patterns, five centuries before their discovery in the West”.

Tessellations
are repeating patterns made of one or more shapes without gaps or overlaps.
They generally tend to be tilings in which patterns are repeated (‘periodic’),
meaning one can easily predict the next pattern. It was well known that
surfaces could be tiled with tiles with three, four or six sides but not with
only five-sided tiles.

Penrose had
shown that it was possible to build geometric patterns using a small set of
tile shapes that may have both fivefold rotational symmetry, ie shapes that
look the same if turned one-fifth of a circle such as a five-pointed star, and
reflectional symmetry, ie shapes whose reflection is the same as the pattern.
Penrose Tiles can also form a non-repeating (‘aperiodic’) pattern. Regardless
of how long one walks on tiles with aperiodic patterns, the next pattern cannot
be predicted.

In 1982,
Daniel Shechtman, a scientist at the US National Bureau of Standards announced
that he had discovered a crystal whose patterns at the atomic level seemed to
show fivefold symmetry similar to Penrose Tiles and its pattern was
non-repetitive. However, at that time, scientists had assumed that arrangement
of atoms in a crystal must have a repetitive pattern. After announcing his
discovery of crystals against the established scientific belief, Shechtman was
asked to leave his position. Nevertheless, he was able to publish his paper in
1984.

In 1987,
Shechtman’s discovery was verified by scientists using X-rays. He was awarded
the 2011 Nobel Prize in chemistry. The announcement of his Nobel Prize, said,
“Aperiodic mosaics, such as those found in the mediaeval Islamic mosaics of the
Alhambra Palace in Spain and the Darb-i-Imam Shrine in Iran, have helped
scientists understand what quasicrystals look like at the atomic level”.

Muslims in
Islam’s golden age knew that a surface cannot be tiled with just five-sided
tiles. Why then were they not content with designing elegant patterns using
tiles with three, four or six sides whose patterns are periodic, that is, whose
next patterns are predictable? Why it was important for them to use complex
mathematics for tilings with fivefold symmetry and which were aperiodic, ie
their next pattern could not be predicted? Perhaps, to them, fivefold symmetry
represented Islam’s five pillars of faith and the five daily prayers. And,
perhaps aperiodic tiling represented human beings’ limited ability, or even an
inability, to predict the future which was in the realm of God.

Designing
tiles which were in harmony with their faith was imperative, even if it
required the use of complex mathematics. It was possible in that era because
two-thirds of the world’s most renowned mathematicians who lived between 650AD
and 1300AD were Muslims. Such symbiosis between faith and learning existed for
centuries when Muslims treated learning as an act of faith.

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*Iftikhar U. Hyder is a finance professional
based in the US.*

**Original Headline: aith & mathematics**

**Source: ****The Dawn, Pakistan**

**URL: **https://newageislam.com/islam-science/muslims-treated-learning-act-faith/d/124214

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