The April 2015 Nepal earthquake (also known as the Gorkha earthquake)[6][9] killed more than 9,000 people and injured more than 23,000. It occurred at 11:56 NST on 25 April, with a magnitude of 7.8Mw

[1] or 8.1Ms[2] and a maximum Mercalli Intensity of IX (Violent). Its epicenter was east of the

district of Lamjung, and its hypocenter was at a depth of approximately 8.2 km (5.1 mi).[1] It was the worst natural disaster to strikeNepal since the 1934 Nepal–Bihar earthquake.[10][11][12]

The earthquake triggered an avalanche on Mount Everest, killing at least 19,[13] making April 25, 2015 the deadliest day on the mountain in history.[14] The earthquake triggered another huge avalanche in the Langtang valley, where 250 people were reported missing.[15][16]

Hundreds of thousands of people were made homeless with entire villages flattened,[15][17][18] across many districts of the country. Centuries-old buildings were destroyed at UNESCO World Heritage sites in the Kathmandu Valley, including some at the Kathmandu Durbar Square, the Patan Durbar Square, the Bhaktapur Durbar Square, the Changu Narayan Temple and the Swayambhunath Stupa. Geophysicists and other experts had warned for decades that Nepal was vulnerable to a deadly earthquake, particularly because of its geology, urbanization, and architecture.[19][20]

Continued aftershocks occurred throughout Nepal at the intervals of 15–20 minutes, with one shock reaching a magnitude of 6.7 on 26 April at 12:54:08 NST.[5] The country also had a continued risk of landslides.[21]

A major aftershock occurred on 12 May 2015 at 12:51 NST with a moment magnitude(Mw) of 7.3.[22] The epicenter was near the Chinese border between the capital of Kathmandu and Mt. Everest.[23] More than 200 people were killed and more than 2,500 were injured by this aftershock.[24]

Avalanches on Mount Everest[edit]Main article: 2015 Mount Everest avalanches

This earthquake caused avalanches on Mount Everest. At least 19 died,[86] including Google executive Dan Fredinburg,[87] with at least 120 others injured or missing.[86]

Casualties[edit]Nepal

The earthquake killed nearly 9,000 in Nepal[7][83] and injured more than twice as many. The rural death toll may have been lower than it would have been as the villagers were outdoors, working when the quake hit.[84] As of 15 May, 6,271 people, including 1,700 from the 12 May aftershock, were still receiving treatment for their injuries.[54] More than 450,000 people were displaced.[57]

The Himalayan Times reported that as many as 20,000 foreign nationals may have been visiting Nepal at the time of the earthquake, although reports of foreign deaths were relatively low. [85]

India

A total of 130 deaths were reported in India - including 58 in Bihar, 16 in Uttar Pradesh, 3 in West Bengal and 1 in Rajasthan.[58]

China

27 dead and 4 missing, all from the Tibet Autonomous Region.[59]

Bangladesh

4 dead.[60]

DAMAGE:

Thousands of houses were destroyed across many districts of the country, with entire villages flattened, especially those near the epicenter.[15][17][18] The Tribhuvan International Airport serving Kathmandu was closed immediately after the quake, but was re-opened later in the day for relief

operations and, later, for some commercial flights.[94] It subsequently shut down operations sporadically due to aftershocks,[95] and on 3 May was closed temporarily to the largest planes for fear of runway damage.[96] Many workers were not at their posts, either from becoming earthquake casualties or because they were dealing with its after effects.[97]Flights resumed from Pokhara, to the west of the epicentre, on 27 April.[98]

Kalam started his career by designing a small helicopter for the Indian Army, but remained unconvinced with the choice of his job at DRDO.

Kalam was also part of the INCOSPAR committee working under Vikram Sarabhai, the renowned space scientist.[9] In 1969, Kalam was transferred to theIndian Space Research Organization (ISRO) where he was the project director of India's first indigenous Satellite Launch Vehicle (SLV-III) which successfully deployed the Rohini satellite in near earth orbit in July 1980.

Joining ISRO was one of Kalam's biggest achievements in life and he is said to have found himself when he started to work on the SLV project.

Kalam first started work on an expandable rocket project independently at DRDO in 1965. In 1969, Kalam received the government's approval and expanded the program to include more engineers.

In 1963–64, he visited Nasa's Langley Research Center in Hampton Virginia, Goddard Space Flight Center in Greenbelt, Maryland andWallops Flight Facility situated at Eastern Shore of Virginia.

During the period between the 1970s and 1990s, Kalam made an effort to develop the Polar SLV and SLV-III projects, both of which proved to be success.

In the 1970s, Kalam also directed two projects, namely, Project Devil and Project Valiant , which sought to develop ballistic missiles from the technology of the successful SLV programme. Despite the disapproval of Union Cabinet, Prime Minister Indira Gandhi allotted secret funds for these aerospace projects through her discretionary powers under Kalam's directorship.Kalam played an integral role convincing the Union Cabinet to conceal the true nature of these classified aerospace projects.

His research and educational leadership brought him great laurels and prestige in 1980s, which prompted the government to initiate an advanced missile program under his directorship.

Kalam and Dr. V. S. Arunachalam, metallurgist and scientific adviser to the Defense Minister, worked on the suggestion by the then Defense Minister, R. Venkataraman on a proposal for simultaneous development of a quiver of missiles instead of taking planned missiles one by one.R Venkatraman was instrumental in getting the cabinet approval for allocating 388 crore rupees for the mission, named Integrated Guided Missile Development Program (I.G.M.D.P) and appointed Kalam as the Chief Executive.

Kalam played a major part in developing many missiles under the mission including Agni, an intermediate range ballistic missile and Prithvi, the

tactical surface-to-surface missile, although the projects have been criticised for mismanagement and cost and time overruns. He was the Chief Scientific Adviser to the Prime Minister and the Secretary of Defence Research and Development Organisation from July 1992 to December 1999.

The Pokhran-II nuclear tests were conducted during this period where he played an intensive political and technological role. Kalam served as the Chief Project Coordinator, along with R. Chidambaram during the testing phase. Photos and snapshots of him taken by the media elevated Kalam as the country's top nuclear scientist.

In 1998, along with cardiologist Dr.Soma Raju, Kalam developed a low cost Coronary stent. It was named as "Kalam-Raju Stent" honouring them.

In 2012, the duo, designed a rugged tablet PC for health care in rural areas, which was named as "Kalam-Raju Tablet".

Scientific and Engineer

After graduating from the Madras Institute of Technology in 1960, Kalam joined the Aeronautical Development Establishment of the Defence Research and Development Organisation (DRDO) as a scientist. He started his career by designing a small helicopter for the Indian Army, but remained unconvinced by his choice of a job at DRDO. He also designed a hovercraft along with his teammates which proved to be a turning point in his life and gave him the much needed confidence to chase  his dreams.  Kalam was also part of the INCOSPAR committee working under Vikram Sarabhai, the renowned space scientist. In 1969, Kalam was transferred to the Indian Space Research Organisation (ISRO) where he was the project director of India's first Satellite Launch Vehicle (SLV-III) which successfully deployed the Rohini satellite in near-earth orbit in July 1980; Kalam had first started work on an expandable rocket project independently at DRDO in 1965. In 1969, Kalam received the government's approval and expanded the programme to include more engineers.

 Between the 1970s and 1990s, Kalam made an effort to develop the Polar Satellite Launch Vehicle (PSLV) and SLV-III projects, both of which proved to be successful.. In the 1970s, Kalam also directed two projects, Project Devil and Project Valiant, which sought to develop ballistic missiles from the technology of the successful SLV programme. Despite the disapproval of the Union Cabinet, Prime Minister Indira Gandhi allotted secret funds for these aerospace projects through her discretionary powers under Kalam's directorship. Kalam played an

integral role convincing the Union Cabinet to conceal the true nature of these classified aerospace projects. His research and educational leadership brought him great laurels and prestige in the 1980s, which prompted the government to initiate an advanced missile programme under his directorship. Kalam and Dr V S Arunachalam, metallurgist and scientific adviser to the Defence Minister, worked on the suggestion by the then Defence Minister, R. Venkataraman on a proposal for simultaneous development of a quiver of missiles instead of taking planned missiles one after another. R Venkatraman was instrumental in getting the cabinet approval for allocating ₹388 crores for the mission, named Integrated Guided Missile Development Programme (IGMDP) and appointed Kalam as the chief executive. Kalam played a major part in developing many missiles under the mission including Agni, an intermediate range ballistic missile and Prithvi, the tactical surface-to-surface missile. Kalam served as the Chief Scientific Adviser to the Prime Minister and the Secretary of the Defence Research and Development Organisation from July 1992 to December 1999. The Pokhran-II nuclear tests were conducted during this period in which he played an intensive political and technological role.  In 1998, along with cardiologist Soma Raju, Kalam developed a low cost coronary stent, named the "Kalam-Raju Stent". In 2012, the duo designed a rugged tablet computer for health care in rural areas, which was named the "Kalam-Raju Tablet".

Learning from failure

 One of the earliest such episodes from his  life happened when he was a student of aeronautics at the Madras Institute of Technology. His design teacher there was Professor Srinivasan, who was also the head of the institute. Once, the students were placed in teams of four students each, and our team had to design a low-level attack aircraft. He was in charge of coming up with the aerodynamic design. They worked very hard for weeks. His teammates were designing all the other components, like the propulsion, structure, control and instrumentation. Since his other course work was over at the time, he and his teammates spent long hours discussing our ideas and researching them. They were all keen to impress their professors with their project. They kept an eye on the progress and after a few days, Professor Srinivasan asked to see the design he had created. When he showed it to him, he examined it with his characteristic critical eye. Dr kalam stood by, waiting with bated breath to hear his verdict. The teacher looked at the paper spread out in front of him, then he straightened up and his next words stunned him. “This is just not good enough, Kalam,” he said. He turned stern eyes on Kalam and continued, “I expected much better from you. This is dismal work and I am disappointed that someone with your talent has come up with work like this.” He stared at the professor, dumbfounded. Kalam had always been the star pupil in any class and had never ever been pulled up by a teacher for anything. This feeling of embarrassment

and shame was a new experience for him, and he did not like it one bit. The professor shook his head some more and told him that he had to redo the entire design, starting from scratch and rethinking all his assumptions. Kalam agreed shamefacedly. Then his teacher broke the next bad news. Not only was he supposed to do the work again, he  had to finish it in three days! “Today is Friday afternoon, young man. I want to see a flawless configuration drawing by Monday evening. If you are unable to do so, your scholarship will be stopped.” He was even more dumbfounded now. The scholarship was the only way he could afford to be in college. Without it, Kalam would have to stop my studies. His own ambitions, the dreams of his parents, his sister and Jalalluddin dashed before his eyes and seemed to recede to a distance. It was unthinkable that the future could turn so bleak with a few words spoken by his professor. He got to work right away, determined to prove himself. He skipped dinner and remained at the drawing board through the night. Where earlier the components of his design were floating in his head, now they suddenly came together and took on forms and shapes he could work with. The concentrated work he put in seemed to brush away all the cobwebs of the mind. By the next morning, he was working like a man possessed. He took a short break to eat and freshen up, and went back to work again. By Sunday evening, his work was nearly complete an elegant, neat design that he was proud of. While he was putting  final touches to it, he sensed a presence in the room. It was the professor, still dressed in his tennis whites, on his way back from the club. He  didn’t know how long he had been standing there, watching me. Now, as their eyes met, he came forward. He looked critically at Kalam's work for many minutes. Then he straightened up and smiled. To Kalam's amazement, he hugged him affectionately. Then patting him on the back, he said, “I knew I was putting you under immense pressure when I rejected your work the other day. I set an impossible deadline—yet you have met it with work that I can only call outstanding. As your teacher, I had to push you to your limits so that you could recognise your own true potential.” After two days of extreme dejection, those words were music to his ears and revived his confidence and self-belief.That day Kalam learnt two lessons: a teacher who has his or her student’s progress in mind is the best possible friend, because the teacher knows how to make sure that you excel. And second, there is no such thing as an impossible deadline. I have worked on many tough assignments, some of which had the country’s top leaders watching over my work, but the assurance I gained in my capabilities at MIT thanks to Professor Srinivasan helped me later in life too. Kalam's attitude regarding "impossible deadlines" and the ability to challenge himself and rise from failure were instilled in him at a very young age by his father. Living in a village by the coastside his father used to ferry pilgrims and that boat was a huge source of income for  their family but one night a storm wrecked that boat but his father never gave up. Kalam then started selling newspapers along with his brother Samsuddin and collecting seeds which had come into  demand for some reason at the outbreak of the 2nd world war. This

taught him self reliance and is  a n example of how enterprising he had been even in his childhood.

Teaching

Kalam was always an educationist and visionary whose one love in life was to teach and interact with the youth of the nation so that he could guide them on the path of achieving their dreams. This quality coupled with his humility and charm endeared him  to all those who knew him. I remember listening to him in February at the Jaipur Literature Festival and his speech was the event which drew the maximum crowds. Such was the charisma of this man that even at the age of 80 something he refused to take it easy and made it a point to interact with the youth as much as possible. It is fitting that he died while giving a lecture to a gathering of students. I have no doubt in my mind that is the way he would have wanted to die.

Presidency

Kalam served as the 11th President of India, succeeding K. R. Narayanan. He won the 2002 presidential election with an electoral vote of 922,884, surpassing the 107,366 votes won by Lakshmi Sahgal. His term lasted from 25 July 2002 to 25 July 2007. During his term as president, he was affectionately known as the People's President, saying that signing the Office of Profit Bill was the toughest decision he had taken during his tenure. Kalam was criticised for his inaction in deciding the fate of 20 out of the 21 mercy petitions submitted to him during his tenure. Article 72 of the Constitution of India empowers the President of India to grant pardons, and suspend or commute the death sentence of convicts on death row. Kalam acted on only one mercy plea in his five-year tenure as president, rejecting the plea of rapist Dhananjoy Chatterjee, who was later hanged. Perhaps the most notable plea was from Afzal Guru, a Kashmiri terrorist who was convicted of conspiracy in the December 2001 attack on the Indian Parliament and was sentenced to death by the Supreme Court of India in 2004. While the sentence was scheduled to be carried out on 20 October 2006, the pending action on his mercy plea resulted in him remaining on death row. He also took the controversial decision to impose President's Rule in Bihar in 2005.In September 2003, in an interactive session in PGI Chandigarh, Kalam supported the need of Uniform Civil Code in India, keeping in view the population of the country.

Personal

Kalam's life and achievements especially in the field of aerospace engineering

have fueled the imagination of a generation including me who wishes to follow in his footsteps and become an aerospace engineer. He has set an example for all of us to follow and I hope we can make his dream a reality.

Hero of Alexandria (Greek: Ἥρων ὁ Ἀλεξανδρεύς, Heron ho Alexandreus; also known as Heron of Alexandria c. 10 – c. 70 AD) was a Greek mathematician and engineerwho was active in his native city of Alexandria, Roman Egypt. He is considered the greatest experimenter of antiquity[1] and his work is representative of the Hellenisticscientific tradition.[2]

Hero published a well recognized description of a steam-powered device called anaeolipile (sometimes called a "Hero engine"). Among his most famous inventions was awindwheel, constituting the earliest instance of wind harnessing on land.[3][4] He is said to have been a follower of the atomists. Some of his ideas were derived from the works of Ctesibius.

Much of Hero's original writings and designs have been lost, but some of his works were preserved in Arabic manuscripts.

Contents

  [hide] 

1   Career 2   Inventions

3   Mathematics 4   In media 5   Bibliography 6   See also 7   References 8   Further reading 9   External links

Career[edit]

It is almost certain that Hero taught at the Musaeum which included the famous Library of Alexandria, because most of his writings appear as lecture notes for courses in mathematics, mechanics, physics, and pneumatics. Although the field was not formalized until the twentieth century, it is thought that the work of Hero, his automated devices in particular, represents some of the first formal research into cybernetics.[5]

Inventions[edit]

Heron's Aeolipile

Hero described[6] the construction of the aeolipile (a version of which is known as Hero's engine) which was arocket-like reaction engine and the first-recorded steam engine (although Vitruvius mentioned the aeolipile in De Architectura some 100 years earlier than Hero). It was created almost two millennia before the industrial revolution. Another engine used air from a closed chamber heated by an altar fire to displace water from a sealed vessel; the water was collected and its weight, pulling on a rope, opened temple doors.[7] Some historians have conflated the two inventions to assert that the aeolipile was capable of useful work.[8]

Hero's wind-powered organ(reconstruction)

The first vending machine was also one of his constructions, when a coin was introduced via a slot on the top of the machine, a set amount of holy water was dispensed. This was included in his list of inventions in his book, "Mechanics and Optics". When the coin was deposited, it fell upon a pan attached to a lever. The lever opened up a valve which let some water flow out. The pan continued to tilt with the weight of the coin until it fell off, at which point a counter-weight would snap the lever back up and turn off the valve.[9]

A windwheel operating an organ, marking the first instance of wind powering a machine in history.[3][4]

Hero also invented many mechanisms for the Greek theater, including an entirely mechanical play almost ten minutes in length, powered by a binary-like system of ropes, knots, and simple machines operated by a rotating cylindrical cogwheel. The sound of thunder was produced by the mechanically-timed dropping of metal balls onto a hidden drum.

The force pump was widely used in the Roman world, and one application was in a fire-engine. A syringe-like device was described by Heron to control the delivery of air or liquids.[10]

In optics, Hero formulated the Principle of the Shortest Path of Light: If a ray of light propagates from point A to point B within the same medium, the path-length followed is the shortest possible. It was nearly 1000 years later that Alhacen expanded the principle to both reflection and refraction, and the principle was later stated in this form by Pierre de Fermat in 1662; the most modern form is that the path is at an extremum.

A standalone fountain that operates under self-contained hydrostatic energy. (Heron's fountain) A programmable cart that was powered by a falling weight. The "program" consisted of strings

wrapped around the drive axle.[11]

Mathematics[edit]

Hero described a method of iteratively computing the square root.[12] Today, however, his name is most closely associated withHeron's Formula for finding the area of a triangle from its side lengths.

In media[edit]

A 1979 Soviet animated short film focuses on Hero's invention of the aeolipile, showing him as a plain craftsman who invented theturbine accidentally[13]

A 2007 The History Channel television show Ancient Discoveries includes recreations of most of Hero's devices

A 2010 The History Channel television show Ancient Aliens episode "Alien Tech" includes discussion of Hero's steam engine

A 2014 The History Channel television show Ancient Impossible episode "Ancient Einstein"

Heron of Alexandria

Born: about 10 in (possibly) Alexandria, EgyptDied: about 75

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Sometimes called Hero, Heron of Alexandria was an important geometer and worker in mechanics. Perhaps the first comment worth making is how common the name Heron was around this time and it is a difficult problem in the history of mathematics to identify which references to Heron are to the mathematician described in this article and which are to others of the same name. There are additional problems of identification which we discuss below.

A major difficulty regarding Heron was to establish the date at which he lived. There were two main schools of thought on this, one believing that he lived around 150 BC and the second believing that he lived around 250 AD. The first of these was based mainly on the fact that Heron does not quote from any work later than Archimedes. The second was based on an argument which purported to show that he lived later that Ptolemy, and, since Pappus refers to Heron, before Pappus.

Both of these arguments have been shown to be wrong. There was a third date proposed which was based on the belief that Heron was a contemporary of Columella. Columella was a Roman soldier and farmer who wrote extensively on agriculture and similar subjects, hoping to foster in people a love for farming and a liking for the simple life. Columella, in a text written in about 62 AD [5]:-

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... gave measurements of plane figures which agree with the formulas used by Heron, notably those for the equilateral triangle, the regular hexagon (in this case not only the formula but the actual figures agree with Heron's) and the segment of a circle which is less than a semicircle ...

However, most historians believed that both Columella and Heron were using an earlier source and claimed that the similarity did not prove any dependence. We now know that those who believed that Heron lived around the time of Columella were in fact correct, for Neugebauer in 1938 discovered that Heron referred to a recent eclipse in one of his works which, from the information given by Heron, he was able to identify with one which took place in Alexandria at 23.00 hours on 13 March 62.

From Heron's writings it is reasonable to deduce that he taught at the Museum in Alexandria. His works look like lecture notes from courses he must have given there on mathematics, physics, pneumatics, and mechanics. Some are clearly textbooks while others are perhaps drafts of lecture notes not yet worked into final form for a student textbook.

Pappus describes the contribution of Heron in Book VIII of his Mathematical Collection. Pappus writes (see for example [8]):-

The mechanicians of Heron's school say that mechanics can be divided into a theoretical and a manual part; the theoretical part is composed of geometry, arithmetic, astronomy and physics, the manual of work in metals, architecture, carpentering and painting and anything involving skill with the hands.

... the ancients also describe as mechanicians the wonder-workers, of whom some work by means of pneumatics, as Heron in his Pneumatica, some by using strings and ropes, thinking to imitate the movements of living things, as Heron in his Automata and Balancings, ... or by using water to tell the time, as Heron in his Hydria, which appears to have affinities with the science of sundials.

A large number of works by Heron have survived, although the authorship of some is disputed. We will discuss some of the disagreements in our list of Heron's works below. The works fall into several categories, technical works, mechanical works and mathematical works. The surviving works are:

On the dioptra dealing with theodolites and surveying. It contains a chapter on astronomy giving a method to find the distance between Alexandria and Rome using the difference between local times at which an eclipse of the moon is observed at each cities. The fact that Ptolemy does not appear to have known of this method led historians to mistakenly believe Heron lived after Ptolemy;

The pneumatica in two books studying mechanical devices worked by air, steam or water pressure. It is described in more detail below;

The automaton theatre describing a puppet theatre worked by strings, drums and weights;

Belopoeica describing how to construct engines of war. It has some similarities with work by Philon and also work by Vitruvius who was a Roman architect and engineer who lived in the 1st century BC;

The cheirobalistra about catapults is thought to be part of a dictionary of catapults but was almost certainly not written by Heron;

Mechanica in three books written for architects and described in more detail below;

Metrica which gives methods of measurement. We give more details below;Definitiones contains 133 definitions of geometrical terms beginning with points, lines etc. In [15] Knorr argues convincingly that this work is in fact due to Diophantus;

Geometria seems to be a different version of the first chapter of the Metrica based entirely on examples. Although based on Heron's work it is not thought to be written by him;

Stereometrica measures three-dimensional objects and is at least in part based on the second chapter of the Metrica again based on examples. Again it is though to be based on Heron's work but greatly changed by many later editors;

Mensurae measures a whole variety of different objects and is connected with parts of Stereometrica and Metrica although it must be mainly the work of a later author;

Catoptrica deals with mirrors and is attributed by some historians to Ptolemy although most now seem to believe that this is a genuine work of Heron. In this work, Heron states that vision results from light rays emitted by the eyes. He believes that these rays travel with infinite velocity.

Let us examine some of Heron's work in a little more depth. Book I of his treatise Metrica deals with areas of triangles, quadrilaterals, regular polygons of between 3 and 12 sides, surfaces of cones, cylinders, prisms, pyramids, spheres etc. A method, known to the Babylonians 2000 years before, is also given for approximating the square root of a number. Heron gives this in the following form (see for example [5]):-

Since 720 has not its side rational, we can obtain its side within a very small difference as follows. Since the next succeeding square number  is 729, which has 27  for its side, divide 720 by 27. This gives 26 2/3. Add 27  to this, making 53 2/3, and take half this or 26 5/6. The side of 720 will therefore be very nearly 26 5/6.  In fact, if we multiply 26 5/6 by itself, the product is 720 1/36, so the difference in the square is  1/36.  If we desire to make the difference smaller still than  1/36, we shall take 720 1/36  instead of 729 (or rather we should take 26 5/6  instead of 27), and by proceeding in the same way we shall find the resulting difference much less than  1/36.

Heron also proves his famous formula in Book I of the Metrica :

if A is the area of a triangle with sides a, b and c and s = (a + b + c)/2  then      A2 = s (s - a)(s - b)(s - c).

In Book II of Metrica, Heron considers the measurement of volumes of various three dimensional figures such as spheres, cylinders, cones, prisms, pyramids etc. His preface is interesting, partly because knowledge of the work of Archimedesdoes not seem to be as widely known as one might expect (see for example [5]):-

After the measurement of surfaces, rectilinear or not, it is proper to proceed to solid bodies, the surfaces of which we have already measured in the preceding book, surfaces plane and spherical, conical and cylindrical, and irregular surfaces as well. The methods of dealing with these solids are, in view of their surprising character, referred to Archimedes by certain writers who give the traditional account of their origin. But whether they belong toArchimedes or another, it is necessary to give a sketch of these results as well.

Book III of Metrica deals with dividing areas and volumes according to a given ratio. This was a problem which Euclid investigated in his work On divisions of figures and Heron's Book III has a lot in common with the work of Euclid. Also in Book III, Heron gives a method to find the cube root of a number. In particular Heron finds the cube root of 100 and the authors of [9] give a general formula for the cube root of N which Heron seems to have used in his calculation:

a + b d/(b d + aD)(b - a), where a3 < N < b3, d = N - a3, D = b3 - N.

In [9] it is remarked that this is a very accurate formula, but, unless a Byzantine copyist is to be blamed for an error, they conclude that Heron might have borrowed this accurate formula without understanding how to use it in general.

The Pneumatica is a strange work which is written in two books, the first with 43 chapters and the second with 37 chapters. Heron begins with a theoretical consideration of pressure in fluids. Some of this theory is right but, not surprisingly, some is quite wrong. Then there follows a description of a whole collection of what might best be described as mechanical toys for children [1]:-

Trick jars that give out wine or water separately or in constant proportions, singing birds and sounding trumpets, puppets that move when a fire is lit on an altar, animals that drink when they are offered water ...

Although all this seems very trivial for a scientist to be involved with, it would appear that Heron is using these toys as a vehicle for teaching physics to his students. It seems to be an attempt to make scientific theories relevant to everyday items that students of the time would be familiar with.

There is, rather remarkably, descriptions of over 100 machines such as a fire engine, a wind organ, a coin-operated machine, and a steam-powered engine called an aeolipile. Heron's aeolipile, which has much in common with a jet engine, is described in [2] as follows:-

The aeolipile was a hollow sphere mounted so that it could turn on a pair of hollow tubes that provided steam to the sphere from a cauldron. The steam escaped from the sphere from one or

more bent tubes projecting from its equator, causing the sphere to revolve. The aeolipile is the first known device to transform steam into rotary motion.

Heron wrote a number of important treatises on mechanics. They give methods of lifting heavy weights and describe simple mechanical machines. In particular the Mechanica is based quite closely on ideas due to Archimedes. Book I examines how to construct three dimensional shapes in a given proportion to a given shape. It also examines the theory of motion, certain statics problems, and the theory of the balance.

In Book II Heron discusses lifting heavy objects with a lever, a pulley, a wedge, or a screw. There is a discussion on centres of gravity of plane figures. Book III examines methods of transporting objects by such means as sledges, the use of cranes, and looks at wine presses.

Other works have been attributed to Heron, and for some of these we have fragments, for others there are only references. The works for which fragments survive include one on Water clocks in four books, and Commentary on Euclid's Elementswhich must have covered at least the first eight books of the Elements. Works by Heron which are referred to, but no trace survives, include Camarica or On vaultings which is mentioned by Eutocius and Zygia or On balancing mentioned byPappus. Also in the Fihrist, a tenth century survey of Islamic culture, a work by Heron on how to use an astrolabe is mentioned.

Finally it is interesting to look at the opinions that various writers have expressed as to the quality and importance of Heron. Neugebauer writes [7]:-

The decipherment of the mathematical cuneiform texts made it clear that much of the "Heronic" type of Greek mathematics is simply the last phase of the Babylonian mathematical tradition which extends over 1800 years.

Some have considered Heron to be an ignorant artisan who copied the contents of his books without understanding what he wrote. This in particular has been levelled against the Pneumatica but Drachmann, writing in [1], says:-

... to me the free flowing, rather discursive style suggests a man well versed in his subject who is giving a quick summary to an audience that knows, or who might be expected to know, a good deal about it.

Some scholars have approved of Heron's practical skills as a surveyor but claimed that his knowledge of science was negligible. However, Mahony writes in [1]:-

In the light of recent scholarship, he now appears as a well-educated and often ingenious applied mathematician, as well as a vital link in a continuous tradition of practical mathematics from the Babylonians, through the Arabs, to Renaissance Europe.