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Double date

7 Aug

After breaking fast together at Ramen Tan, we headed for the movies!

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Captain America was indeed a great action movie. Some parts about the Nazis reminded me of the x-men movie.

There is something about movies taken about (in the) past which attracts me!

The time of the nazi also reminded me of some of the ghastly movies, sound recordings and photos I saw in the House of Terror in Budapest. After my trip to the museum, I exited the building feeling very disturbed and my mind wandered back sometimes. It was a scary time! I heard from other travelers that their visits to the concentration camps in Poland and Berlin were worse.

Back to Captain America! Captivating and pulled me into the story from the very beginning. I liked the specks of humor and romance here and there. I hated that his best friend had to die 😦

Yet I felt the movie was similar to many Other such movies like spiderman, xmen, superman… There is this obsession to conquer the world and to do so, they absorb as much power as possible.

Entertaining nonetheless!

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X – MEN

17 Jun

I never watched any x-men movies before and i admit, i wanted to watch this because Mr Q liked such movies. I think my brother did urge me to watch the other movies before but i refused.

It was enjoyable and thrilling. What i particularly liked was the way the movie begun, how Magneto emerged. I must say i just like anything of the past, taken during the war or in the countryside where people reared animals in their farms and i think you got the idea.

I remember my childhood days watching x-men cartoons, i think again my brother influenced me into watching that kind of cartoon. They had powers and they saved the world, who doesnt like such cartoons? 

The rest of the movie was great, action and twists were great, not as i expected. This is the first X-men movie of the series i think because the professor was just setting up his academy at the end of the movie. *spoilers*

My only exposure to x-men is

 

Arabic science episodes

28 Jan

I enjoyed them so very much, there are 3 episodes. If you watch it on youtube, one episode consist of 6 parts, 10 minutes each. He would go to Cairo, Damascus, Cordoba, Tehran and Baghdad to look at the discoveries of ancient Islamic Scholars.

Islamic Scholar: Al-Haytham

22 Jan

 

A devout Muslim, Ibn al-Haitham believed that human beings are flawed and only God is perfect. To discover the truth about nature, Ibn a-Haitham reasoned, one had to eliminate human opinion and allow the universe to speak for itself through physical experiments. “The seeker after truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them,” the first scientist wrote, “but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration.”

In his massive study of light and vision, Kitâb al-Manâzir (Book of Optics ), Ibn al-Haytham submitted every hypothesis to a physical test or mathematical proof. To test his hypothesis that “lights and colors do not blend in the air,” for example, Ibn al-Haytham devised the world’s first camera obscura, observed what happened when light rays intersected at its aperture, and recorded the results. Throughout his investigations, Ibn al-Haytham followed all the steps of the scientific method.

Kitab al-Manazir was translated into Latin as De aspectibus and attributed to Alhazen in the late thirteenth century in Spain. Copies of the book circulated throughout Europe. Roger Bacon, who sometimes is credited as the first scientist, wrote a summary of Kitab al-Manazir entitled Perspectiva (Optics) some two hundred years after the death of the scholar known as Alhazen.

Ibn al-Haytham conducted many of his experiments investigating the properties of light during a ten-year period when he was stripped of his possessions and imprisoned as a madman in Cairo. How Ibn al-Haytham came to be in Egypt, why he was judged insane, and how his discoveries launched the scientific revolution are just some of the questions Bradley Steffens answers in Ibn al-Haytham: First Scientist, the world’s first biography of the Muslim polymath.

Source.

Ibn al-Haytham’s writings are too extensive for us to be able to cover even a reasonable amount. He seems to have written around 92 works of which, remarkably, over 55 have survived. The main topics on which he wrote were optics, including a theory of light and a theory of vision, astronomy, and mathematics, including geometry and number theory. We will give at least an indication of his contributions to these areas.

A seven volume work on optics, Kitab al-Manazir, is considered by many to be ibn al-Haytham’s most important contribution. It was translated into Latin as Opticae thesaurus Alhazeni in 1270. The previous major work on optics had been Ptolemy‘s Almagest and although ibn al-Haytham’s work did not have an influence to equal that of Ptolemy‘s, nevertheless it must be regarded as the next major contribution to the field. The work begins with an introduction in which ibn al-Haytham says that he will begin “the inquiry into the principles and premises”. His methods will involve “criticising premises and exercising caution in drawing conclusions” while he aimed “to employ justice, not follow prejudice, and to take care in all that we judge and criticise that we seek the truth and not be swayed by opinions”.

Also in Book I, ibn al-Haytham makes it clear that his investigation of light will be based on experimental evidence rather than on abstract theory. He notes that light is the same irrespective of the source and gives the examples of sunlight, light from a fire, or light reflected from a mirror which are all of the same nature. He gives the first correct explanation of vision, showing that light is reflected from an object into the eye. Most of the rest of Book I is devoted to the structure of the eye but here his explanations are necessarily in error since he does not have the concept of a lens which is necessary to understand the way the eye functions. His studies of optics did led him, however, to propose the use of a camera obscura, and he was the first person to mention it.

Book II of the Optics discusses visual perception while Book III examines conditions necessary for good vision and how errors in vision are caused. From a mathematical point of view Book IV is one of the most important since it discusses the theory of reflection. Ibn al-Haytham gave [1]:-

… experimental proof of the specular reflection of accidental as well as essential light, a complete formulation of the laws of reflection, and a description of the construction and use of a copper instrument for measuring reflections from plane, spherical, cylindrical, and conical mirrors, whether convex or concave.

Alhazen’s problem, quoted near the beginning of this article, appears in Book V. Although we have quoted the problem for spherical mirrors, ibn al-Haytham also considered cylindrical and conical mirrors. The paper [36] gives a detailed description of six geometrical lemmas used by ibn al-Haytham in solving this problem. Huygens reformulated the problem as:-

To find the point of reflection on the surface of a spherical mirror, convex or concave, given the two points related to one another as eye and visible object.

Huygens found a good solution which Vincenzo Riccati and then Saladini simplified and improved.

Book VI of the Optics examines errors in vision due to reflection while the final book, Book VII, examines refraction [1]:-

Ibn al-Haytham does not give the impression that he was seeking a law which he failed to discover; but his “explanation” of refraction certainly forms part of the history of the formulation of the refraction law. The explanation is based on the idea that light is a movement which admits a variable speed (being less in denser bodies)

Ibn al-Haytham’s study of refraction led him to propose that the atmosphere had a finite depth of about 15 km. He explained twilight by refraction of sunlight once the Sun was less than 19° below the horizon.

Abu al-Qasim ibn Madan was an astronomer who proposed questions to ibn al-Haytham, raising doubts about some of Ptolemy‘s explanations of physical phenomena. Ibn al-Haytham wrote a treatise Solution of doubts in which he gives his answers to these questions. They are discussed in [43] where the questions are given in the following form:-

What should we think of Ptolemy‘s account in “Almagest” I.3 concerning the visible enlargement of celestial magnitudes (the stars and their mutual distances) on the horizon? Is the explanation apparently implied by this account correct, and if so, under what physical conditions? How should we understand the analogy Ptolemy draws in the same place between this celestial phenomenon and the apparent magnification of objects seen in water? …

There are strange contrasts in ibn al-Haytham’s work relating to Ptolemy. In Al-Shukuk ala Batlamyus (Doubts concerning Ptolemy), ibn al-Haytham is critical of Ptolemy‘s ideas yet in a popular work the Configuration, intended for the layman, ibn al-Haytham completely accepts Ptolemy‘s views without question. This is a very different approach to that taken in his Optics as the quotations given above from the introduction indicate.

One of the mathematical problems which ibn al-Haytham attacked was the problem of squaring the circle. He wrote a work on the area of lunes, crescents formed from two intersecting circles, (see for example [10]) and then wrote the first of two treatises on squaring the circle using lunes (see [14]). However he seems to have realised that he could not solve the problem, for his promised second treatise on the topic never appeared. Whether ibn al-Haytham suspected that the problem was insoluble or whether he only realised that he could not solve it, in an interesting question which will never be answered.

In number theory al-Haytham solved problems involving congruences using what is now called Wilson‘s theorem:

if p is prime then 1 + (p – 1) ! is divisible by p .

In Opuscula ibn al-Haytham considers the solution of a system of congruences. In his own words (using the translation in [7]):-

To find a number such that if we divide by two, one remains; if we divide by three, one remains; if we divide by four, one remains; if we divide by five, one remains; if we divide by six, one remains; if we divide by seven, there is no remainder.

Ibn al-Haytham gives two methods of solution:-

The problem is indeterminate, that is it admits of many solutions. There are two methods to find them. One of them is the canonical method: we multiply the numbers mentioned that divide the number sought by each other; we add one to the product; this is the number sought.

Here ibn al-Haytham gives a general method of solution which, in the special case, gives the solution (7 – 1)! + 1. Using Wilson‘s theorem, this is divisible by 7 and it clearly leaves a remainder of 1 when divided by 2, 3, 4, 5, and 6. Ibn al-Haytham’s second method gives all the solutions to systems of congruences of the type stated (which of course is a special case of the Chinese Remainder Theorem).

Another contribution by ibn al-Haytham to number theory was his work on perfect numbers. Euclid, in the Elements, had proved:

If, for some k > 1, 2k – 1 is prime then 2k-1(2k – 1) is a perfect number.

The converse of this result, namely that every even perfect number is of the form 2k-1(2k – 1) where 2k – 1 is prime, was proved by Euler. Rashed ([7], [8] or [27]) claims that ibn al-Haytham was the first to state this converse (although the statement does not appear explicitly in ibn al-Haytham’s work). Rashed examines ibn al-Haytham’s attempt to prove it in Analysis and synthesis which, as Rashed points out, is not entirely successful [7]:-

But this partial failure should not eclipse the essential: a deliberate attempt to characterise the set of perfect numbers.

Ibn al-Haytham’s main purpose in Analysis and synthesis is to study the methods mathematicians use to solve problems. The ancient Greeks used analysis to solve geometric problems but ibn al-Haytham sees it as a more general mathematical method which can be applied to other problems such as those in algebra. In this work ibn al-Haytham realises that analysis was not an algorithm which could automatically be applied using given rules but he realises that the method requires intuition. See [18] and [26] for more details.

Article by: J J O’Connor and E F Robertson

Source.

Using math in physics and astronomy, Ibn Al-Haytham wrote treaties on the light of the Moon, in which he argues that the moon shines like a self luminous object, though its light is borrowed from the Sun.

He wrote on the Halo and Rainbow, on Spherical Burning Mirrors, on Paraboloidal Burning Mirrors, and on the Shape of an eclipse, which examines the camera obscura phenomena.

Camera Obscura
Karmal al-Din al-Farisi
Istanbul, Fourteenth Century

source.

Islamic scholar: Al-Battani

21 Jan

Al-Battani is sometimes known by a latinised version of his name, variants being Albategnius, Albategni or Albatenius. His full name was Abu Abdallah Mohammad ibn Jabir ibn Sinan al-Raqqi al-Harrani al-Sabi al-Battani.

Al-Battani was born in Harran, called Carrhae in earlier times by the Romans, which lies on the Balikh River, 38 km southeast of Urfa. His family had been members of the Sabian sect, a religious sect of star worshippers from Harran. Being worshipers of the stars meant that the Sabians had a strong motivation for the study of astronomy and they produced many outstanding astronomers and mathematicians. However, for “Abu Abdallah Mohammad” indicates that he was certainly a Muslim.Although the identification is not absolutely certain, it is probable that al-Battani’s father was Jabir ibn Sinan al-Harrani who had a high reputation as an instrument maker in Harran. The name certainly makes the identification fairly certain and the fact that al-Battani himself was skilled in making astronomical instruments is a good indication that he learnt these skills from his father.Al-Battani made his remarkably accurate astronomical observations at Antioch and ar-Raqqah in Syria. The town of ar-Raqqah, where most of al-Battani’s observations were made, became prosperous when Harun al-Rashid, who became the fifth Caliph of the Abbasid dynasty on 14 September 786, built several palaces there. The town had been renamed al-Rashid at that time but, by the time al-Battani began observing there, it had reverted to the name of ar-Raqqah. The town was on the Euphrates River just west of where it joins the Balikh River (on which Harran stands).The Fihrist (Index) was a work compiled by the bookseller Ibn an-Nadim in 988. It gives a full account of the Arabic literature which was available in the 10th century and it describes briefly some of the authors of this literature. The Fihrist describes al-Battani as (see for example [1]):-

… one of the famous observers and a leader in geometry, theoretical and practical astronomy, and astrology. He composed a work on astronomy, with tables, containing his own observations of the sun and moon and a more accurate description of their motions than that given in Ptolemy‘s “Almagest”. In it moreover, he gives the motions of the five planets, with the improved observations he succeeded in making, as well as other necessary astronomical calculations. Some of his observations mentioned in his book of tables were made in the year 880 and later on in the year 900. Nobody is known in Islam who reached similar perfection in observing the stars and scrutinising their motions. Apart from this, he took great interest in astrology, which led him to write on this subject too: of his compositions in this field I mention his commentary on Ptolemy‘s Tetrabiblos.

Other information about al-Battani contained in the Fihrist is that he observed between the years 877 and 918 and that his star catalogue is based on the year 880. It also describes the end of his life which seems to have occurred during a journey he made to Baghdad to protest on behalf of a group of people from ar-Raqqah because they had been unfairly taxed. Al-Battani reached Baghdad and put his arguments but died on the return journey to ar-Raqqah.The Fihrist also quotes a number of works by al-Battani. There is his Kitab al-Zij which is his major work on astronomy with tables, referred to above. We shall examine this in more detail in a moment. There is also the commentary on Ptolemy‘s Tetrabiblos referred to above and two other titles: On ascensions of the signs of the zodiac and On the quantities of the astrological applications. One of the chapters of the Kitab al-Zij has the title “On ascensions of the signs of the zodiac” and so the Fihrist may be wrong in thinking this is a separate work. This point still appears unclear.Al-Battani’s Kitab al-Zij is by far his most important work and we should examine briefly the topics which it covered. The work contained 57 chapters. It begins with a description of the division of the celestial sphere into the signs of the zodiac and into degrees. The necessary background mathematical tools are then introduced such as the arithmetical operations on sexagesimal fractions and the trigonometric functions. Chapter 4 contains data from al-Battani’s own observations. Chapters 5 to 26 discuss a large number of different astronomical problems following to some extent material from the Almagest. The motions of the sun, moon and five planets are discussed in chapters 27 to 31, where the theory given is that of Ptolemy but for al-Battani the theory appears less important than the practical aspects.After giving results to allow data given for one era to be converted to another era, al-Battani then gives 16 chapters which explain how his tables are to be read. Chapters 49 to 55 cover problems in astrology, while chapter 56 discusses the construction of a sundial and the final chapter discusses the construction of a number of astronomical instruments.What are the main achievements of al-Battani’s Zij? He catalogued 489 stars. He refined the existing values for the length of the year, which he gave as 365 days 5 hours 46 minutes 24 seconds, and of the seasons. He calculated 54.5″ per year for the precession of the equinoxes and obtained the value of 23° 35′ for the inclination of the ecliptic.Rather than using geometrical methods, as Ptolemy had done, al-Battani used trigonometrical methods which were an important advance. For example he gives important trigonometric formulae for right angled triangles such as

b sin(A) = a sin(90° – A).

Al-Battani showed that the farthest distance of the Sun from the Earth varies and, as a result, annular eclipses of the Sun are possible as well as total eclipses. However, as Swerdlow points out in [8], the influence of Ptolemy was remarkably strong on all medieval authors, and even a brilliant scientist like al-Battani probably did not dare to claim a different value of the distance from the Earth to the Sun from that given by Ptolemy. This was despite the fact that al-Battani could deduce a value for the distance from his own observations that differed greatly from Ptolemy‘s.In [1] Hartner gives a somewhat different opinion of the way that al-Battani is influenced by Ptolemy. He writes:-

While al-Battani takes no critical attitude towards the Ptolemaic kinematics in general, he evidences … a very sound scepticism in regard to Ptolemy‘s practical results. Thus, relying on his own observations, he corrects – be it tacitly, be it in open words – Ptolemy‘s errors. This concerns the main parameters of planetary motion no less than erroneous conclusions drawn from insufficient or faulty observations, such as the invariability of the obliquity of the ecliptic or of the solar apogee.

Al-Battani is important in the development of science for a number of reasons, but one of these must be the large influence his work had on scientists such as Tycho Brahe, Kepler, Galileo and Copernicus. In [5] there is a discussion on how al-Battani managed to produce more accurate measurements of the motion of the sun than did Copernicus. The author suggests that al-Battani obtained much more accurate results simply because his observations were made from a more southerly latitude. For al-Battani refraction had little effect on his meridian observations at the winter solstice because, at his more southerly site of ar-Raqqah, the sun was higher in the sky.Al-Battani’s Kitab al-Zij was translated into Latin as De motu stellarum (On the motion of the stars) by Plato of Tivoli. This appeared in 1116 while a printed edition of Plato of Tivoi’s translation appeared in 1537 and then again in 1645. A Spanish translation was made in the 13th century and both it and Plato of Tivoli’s Latin translation have survived.Article by: J J O’Connor and E F Robertson

Source: website

Picture taken from the link (press here) of Ptolemy’s Almagest

Picture above from here.

Also of the Ptolemy Almagest which is the The Mathematike Syntaxis (The Mathematical Compilation)

 

One man holds a quadrant while another sights the eclipsed sun.  An assistant tracks the time with a portable sundial. Source: https://eee.uci.edu/clients/bjbecker/ExploringtheCosmos/lecture3.html

 

A modern illustration depicting the universe described by Dante Alighieri (1265-1321) in his Divine Comedy (1306-1321)

The universe depicted in The Nuremberg Chronicle (1493)

Source: https://eee.uci.edu/clients/bjbecker/ExploringtheCosmos/lecture3.html

A few other Islamic Scholars

20 Jan

Meteorology

In the 9th century, Al-Kindi (Alkindus) was the first to introduce experimentation into the Earth sciences.[57] He wrote a treatise on meteorology entitled Risala fi l-Illa al-Failali l-Madd wa l-Fazr (Treatise on the Efficient Cause of the Flow and Ebb), in which he presents an argument on tides which relates them to temperature change. He describes the following clear and precise laboratory experiment in order to prove his argument:[58]

“One can also observe by the senses… how in consequence of extreme cold air changes into water. To do this, one takes a glass bottle, fills it completely with snow, and closes its end carefully. Then one determines its weight by weighing. One places it in a container… which has previously been weighed. On the surface of the bottle the air changes into water, and appears upon it like the drops on large porous pitchers, so that a considerable amount of water gradually collects inside the container. One then weighs the bottle, the water and the container, and finds their weight greater than previously, which proves the change. […] Some foolish persons are of opinion that the snow exudes through the glass. This is impossible. There is no process by which water or snow can be made to pass through glass.”

In the 10th century, Ibn Wahshiyya‘s Nabatean Agriculture discusses the weather forecasting of atmospheric changes and signs from the planetary astral alterations; signs of rain based on observation of the lunar phases, nature of thunder and lightning, direction of sunrise, behaviour of certain plants and animals, and weather forecasts based on the movement of winds; pollenized air and winds; and formation of winds and vapours.[59] As weather forecasting predictions and the measurement of time and the onset of seasons became more precise and reliable, Muslim agriculturalists became informed of these advances and often employed them in agriculture, making it possible for them to plan the growth of each of their crops at specific times of the year.[citation needed]

In 1021, Ibn al-Haytham (Alhazen), an Iraqi scientist, introduces the scientific method in his Book of Optics.[60] He writes on the atmospheric refraction of light, for example, the cause of morning and evening twilight.[61] He endeavored by use of hyperbola and geometric optics to chart and formulate basic laws on atmospheric refraction.[62] He provides the first correct definition of the twilight, discusses atmospheric refraction, shows that the twilight is due to atmospheric refraction and only begins when the Sun is 19 degrees below the horizon, and uses a complex geometric demonstration to measure the height of the Earth’s atmosphere as 52,000 passuum (49 miles),[63] which is very close to the modern measurement of 50 miles (80 km). He also realized that the atmosphere also reflects light, from his observations of the sky brightening even before the Sun rises.[64] Ibn al-Haytham later publishes his Risala fi l-Daw’ (Treatise on Light) as a supplement to his Book of Optics. He discusses the meteorology of the rainbow, the density of the atmosphere, and various celestial phenomena, including the eclipse, twilight and moonlight.[65]

In the late 11th century, Abu ‘Abd Allah Muhammad ibn Ma’udh, who lived in Al-Andalus, wrote a work on optics later translated into Latin as Liber de crepisculis, which was mistakenly attributed to Alhazen. This was a short work containing an estimation of the angle of depression of the sun at the beginning of the morning twilight and at the end of the evening twilight, and an attempt to calculate on the basis of this and other data the height of the atmospheric moisture responsible for the refraction of the sun’s rays. Through his experiments, he obtained the accurate value of 18°, which comes close to the modern value.[66]

In 1121, Al-Khazini, a Muslim scientist of Byzantine Greek descent, publishes The Book of the Balance of Wisdom, the first study on the hydrostatic balance.[67] In the late 13th century and early 14th century, Qutb al-Din al-Shirazi and his student Kamāl al-Dīn al-Fārisī continued the work of Ibn al-Haytham, and they were the first to give the correct explanations for the rainbow phenomenon.[68]

Source: wikipedia

More on Abū Rayhān Bīrūnī

19 Jan

Among his writings on geology, Abū Rayhān Bīrūnī (974-1048) observed the geology of India and discovered that the Indian subcontinent was once a sea, hypothesizing that it became land through the drifting of alluvium. He wrote:

“But if you see the soil of India with your own eyes and meditate on its nature, if you consider the rounded stones found in earth however deeply you dig, stones that are huge near the mountains and where the rivers have a violent current: stones that are of smaller size at a greater distance from the mountains and where the streams flow more slowly: stones that appear pulverised in the shape of sand where the streams begin to stagnate near their mouths and near the sea – if you consider all this you can scarcely help thinking that India was once a sea, which by degrees has been filled up by the alluvium of the streams.”[48]

In his Book of Coordinates, Biruni described the existence of shells and fossils in regions that once housed seas and later evolved into dry land. Based on this discovery, he realized that the Earth is constantly evolving. He thus viewed the Earth as a living entity, which was in agreement with his Islamic belief that nothing is eternal and opposed to the ancient Greek belief that the universe is eternal. He further proposed that the Earth had an age, but that its origin was too distant to measure.[citation needed]

Biruni writes the following on the geological changes on the surface of the Earth over a long period of time:

“they take a long period of time, the limits of which cannot be ascertained, nor can the mode of the change be described. The centre of gravity of the earth also changes its position according to the position of the shifting of matter on its surface. If the centre rises, it causes its surrounding areas to compress and the waters become scanty, etc. Hence it is said that this deterioration is due to old age, and the deteriorated land is called ‘growing and becoming young’. For this reason, hot regions become cold and the cold ones become hot.”[49]

As an example, he cites the 9th century Persian astronomer Abu’l Abbas al-Iranshahri who discovered the roots of a palm tree under dry land, to support his theory that sea turns into land and vice versa over a long period of time. He then writes:[49]

“But if such changes took place on earth before the appearance of man, we are not aware of them; if they came after his appearance, then they were not recorded.”

Another example he cites is the Arabian desert which, like southern Sindh, was also a sea at one time. He writes that the Arabian desert was a sea at one time and became land as it became filled by sand. He then goes on to discuss paleontology, writing that various fossils have been found in that region, including bones and glass, which could not have been buried there by anyone. He also writes about the discovery of:[49]

“stones which if broken apart, would be found to contain shells, cowry-shells and fish-ears.”

It should be noted that he used the term “fish-ears” to refer to fossils. He then writes about how, a long time ago, the ancient Arabs must have lived on the mountains of Yemen when the Arabian desert was a sea. He also writes about how the Karakum Desert between Jurjan and Khwarezm must have been a lake at one time, and about how the Amu Darya (Oxus) river must have extended up to the Caspian Sea.[49] This is in agreement with the modern geological theory of a Mesozoic Sea, the Tephys, covering the whole of Central Asia and extending from the Mediterranean Sea to New Zealand.[50]

Source: wikipedia

Islamic Scholars: Al Ma’mum and Al Bairuni

18 Jan

 

 Ibn al-Wardi‘s atlas of the world, a manuscript copied in 17th century

Mathematical geography and geodesy

The Muslim scholars who held to the spherical Earth theory used it in an impeccably Islamic manner, to calculate the distance and direction from any given point on the earth to Mecca. This determined the Qibla, or Muslim direction of prayer. Muslim mathematicians developed spherical trigonometry which was used in these calculations.[32]

Around 830, Caliph al-Ma’mun commissioned a group of astronomers to measure the distance from Tadmur (Palmyra) to al-Raqqah, in modern Syria. They found the cities to be separated by one degree of latitude and the distance between them to be 66 2/3 miles and thus calculated the Earth’s circumference to be 24,000 miles (39,000 km).[33] Another estimate given was 56 2/3 Arabic miles per degree, which corresponds to 111.8 km per degree and a circumference of 40,248 km, very close to the currently modern values of 111.3 km per degree and 40,068 km circumference, respectively.[34]

In a passage about the sea route to China in his Kitab al-Masalik wa ’l-Mamalik (Book of Roads and Kingdoms), Ibn Khordadbeh (820–912.AD) gives an estimate of the size of the Indian Ocean: “The length of this sea, from Qulzum [at the head of the Red Sea] to Waqwaq, is 4500 farsakhs.” He also states that the distance from Qulzum to the Mediterranean port of Farama is 25 farsakhs. The latter distance, he writes, corresponds to the length of one degree on the meridian; thus, the 4500-farsakh distance to Waqwaq corresponds to 180 degrees. Therefore Waqwaq lies exactly halfway around the world from Qulzum. With its outlandish name and incredible distance eastward, Waqwaq seems to belong to legend rather than commercial geography.

In mathematical geography, Abū Rayhān al-Bīrūnī, around 1025, was the first to describe a polar equi-azimuthal equidistant projection of the celestial sphere.[35] He was also regarded as the most skilled when it came to mapping cities and measuring the distances between them, which he did for many cities in the Middle East and western Indian subcontinent. He often combined astronomical readings and mathematical equations, in order to develop methods of pin-pointing locations by recording degrees of latitude and longitude. He also developed similar techniques when it came to measuring the heights of mountains, depths of valleys, and expanse of the horizon, in The Chronology of the Ancient Nations. He also discussed human geography and the planetary habitability of the Earth. He hypothesized that roughly a quarter of the Earth’s surface is habitable by humans, and also argued that the shores of Asia and Europe were “separated by a vast sea, too dark and dense to navigate and too risky to try” in reference to the Atlantic Ocean and Pacific Ocean.[citation needed]

Abū Rayhān al-Bīrūnī is also considered the father of geodesy for his important contributions to the field,[36][37] along with his significant contributions to geography and geology. At the age of 17, al-Biruni calculated the latitude of Kath, Khwarazm, using the maximum altitude of the Sun. Al-Biruni also solved a complex geodesic equation in order to accurately compute the Earth‘s circumference, which were close to modern values of the Earth’s circumference.[38] In his Masudi Canon,[39] His estimate of 6,339.9 km for the Earth radius was only 16.8 km less than the modern value of 6,356.7 km. In contrast to his predecessors who measured the Earth’s circumference by sighting the Sun simultaneously from two different locations, al-Biruni developed a new method of using trigonometric calculations based on the angle between a plain and mountain top which yielded more accurate measurements of the Earth’s circumference and made it possible for it to be measured by a single person from a single location.[40][41][42] Biruni’s method was intended to avoid “walking across hot, dusty deserts” and the idea came to him when he was on top of a tall mountain in India,[42] From the top of the mountain, he sighted the dip angle which, along with the mountain’s height (which he calculated beforehand), he applied to the law of sines formula. This was the earliest known use of dip angle and the earliest practical use of the law of sines.[41][42] He also made use of algebra to formulate trigonometric equations and used the astrolabe to measure angles.[39] His method can be summarized as follows:

Abu Rayhan Biruni accurately determined the Earth radius by formulating a trigonometric equation relating the dip angle (between the true horizon and astronomical horizon) observed from the top of a mountain to the height of that mountain.

He first calculated the height of the mountain by going to two points at sea level with a known distance apart and then measuring the angle between the plain and the top of the mountain for both points. He made both the measurements using an astrolabe. He then used the following trigonometric formula relating the distance (d) between both points with the tangents of their angles (θ) to determine the height (h) of the mountain:[43]

h = \frac{d \ tan{\theta_1} tan {\theta_2} }{tan {\theta_2} - tan{\theta_1} }

He then stood at the highest point of the mountain, where he measured the dip angle using an astrolabe.[43] He applied the values he obtained for the dip angle and the mountain’s height to the following trigonometric formula in order to calculate the Earth’s radius:[43]

R = \frac{h \ \cos{\theta} }{1 - \cos{\theta} }

where[43]

John J. O’Connor and Edmund F. Robertson write in the MacTutor History of Mathematics archive:

“Important contributions to geodesy and geography were also made by al-Biruni. He introduced techniques to measure the earth and distances on it using triangulation. He found the radius of the earth to be 6339.6 km, a value not obtained in the West until the 16th century. His Masudic canon contains a table giving the coordinates of six hundred places, almost all of which he had direct knowledge.”[44]

Al-Biruni had, by the age of 22, also written several short works, including a study of map projections, Cartography, which included a method for projecting a hemisphere on a plane. Biruni’s Kitab al-Jawahir (Book of Precious Stones) described minerals such as stones and metals in depth, and was regarded as the most complete book on mineralogy in his time. He conducted hundreds of experiments to gauge the accurate measurements of items he catalogued, and he often listed them by name in a number of different languages, including Arabic, Persian, Greek, Syriac, Hindi, Latin, and other languages. In the Book of Precious Stones, he catalogued each mineral by its color, odor, hardness, density and weight. The weights for many of these minerals he measured were correct to three decimal places of accuracy, and were almost as accurate as modern measurements for these minerals.[citation needed]

Muslim astronomers and geographers were aware of magnetic declination by the 15th century, when the Egyptian Muslim astronomer ‘Izz al-Din al-Wafa’i (d. 1469/1471) measured it as 7 degrees from Cairo.[45]

The Tabula Rogeriana, drawn by Muhammad al-Idrisi for Roger II of Sicily in 1154. Note that the north is at the bottom, and so the map appears “upside down” compared to modern cartographic conventions

Source: Wikipedia

automated garage

3 Oct
Imagine having to park your car in your garage after a tired day at work. Worst still, after driving for over 20 hours from another city and back. I am talking about Singapore here.*

Presenting to you the AUTOMATED GARAGE where all you need to do is press the button and jump out of your car, and stroll into your house.
When you need to go out, all you need to exert is a little energy to press teh button again and within minutes, your car will be down next to you and in the correct direction, all ready for you to jump in and off you go.
I heard this from my Management teacher in school like 2 days ago and when i received an email from a super lazy friend of mine, i thought to myself, this is worth posting. So here you go super lazy friend.
If you want to do something crazy, you have till January and YOU HAVE to have a bucket full of “kaching“! (not cacing-worms) Just book a plane and fly here to Finland.