Today, the ancient Mayans are particularly famous by their incredible calendar. In fact, Mayans made a really powerful calendar inspired by astronomical events, as they really were essentially farmers and very superstitious. This is the reason why they didn’t have an unique counting system in their calendar, that is, they had ‘sub-calendars’ which different periods as reference. For example, they had a holy calendar (called Tzolkin), which had 260 days, and also a civil solar calendar (called Haab) with 365 days (it’s not clear what was the motivation for the Tzolkin). Tzolkin means “division of days” was probably based on the 224-day Venus sidereal period although there are some hypothesis which defend that it is related with the human gestation period. The Haab calendar consisted in 18 months of 20 days each plus an additional period of five days at the end of the year. It was first used around 500 BC. Mayans were so religious and these astronomical calendars were exposed in their most important buildings like the World-wide famous Temple of Kukulkan (“Feathered serpent”) in the archeological site of Chichen Itza. The temple was founded around 525 AD although the current building was completed between the 9th and the 12th centuries. The pyramid has four sides, each one with 91 steps, which adds up to 364 steps. If we count the last platform as a step we get 365 steps, which is equal to the days we find in the Haab calendar.
But the most famous thing about the Kukulkan’s temple is the descent of Kukulkan: during the autumn and spring equinoxes the late afternoon Sun strikes off the northwest corner of the pyramid and casts a series of triangular shadows against the northwest balustrade, creating the illusion of a feathered serpent ‘crawling’ down the pyramid. We should remark that the balustrade and corners of the pyramid are perfectly aligned, which makes us admire even more the work that Mayans had on the building:
The pyramid also shows us that Mayans had some knowledge about acoustics. If you stand in front of any of the four stairway and clap your hands, the pyramid reflects the sound in such way that you hear the sing of a quetzal, a bird from the jungle. It’s fascinating! Isn’t it? Moreover, the shaman was known as ‘the man with the great voice’, because when people met for a ritual, he didn’t have to speak loudly, as everybody could hear him perfectly.
From all these facts, we can easily conclude that mathematics in the ancient Mayan world wasn’t only a help for agriculture but a tool through which the leaders could control the population. In fact, in the picture below we can see the ruins of a Mayan school. Only those from the upper class had access to the education, and we can see from the building they truly wanted to keep it as a privilege!
The hole at the right of the picture was made by an adventurer who thought gold was hiding inside it and used dynamite to enter the building.
This post has been written by Roberto Lara Martín in the subject Història de les Matemàtiques (History of Mathematics, 2014-15).
Location: Chichen Itzá (map)
Another mathematical building located in Birmingham is the Rotunda. I think that it’s not necessary to say anything more!
Location: Rotunda (map)
The forntispiece of Museo del Prado of Madrid is full of allegorical figures of the muses and the arts. If we watch it carefully, we’ll notice Urania with a compass and a globe in her hands counting on a parchment:
The building was designed by the architect Juan de Villanueva (1739-1811) and it had to host the Royal Observatory, a Science Room, the Botanic Gardens, schools, laboratories,… The Spanish king yhought that it could be a very good example of the new illustrated Spain. However, it never was used in this way:
Nowadays thousands of tourists visit the pictures in the Museo del Prado and only a few ones visit outside the building. Among all the statues which decorate this neoclassical structure there are the Architecture…
…and the Symmetry:
There are also some medallions with busts of famous Spanish scientist and writers on each of these statues. Of course, Juan de Herrera is also here:
Today I’ve seen this picture taken in the cathedral of Wells. It’s a typical vault in the English Cathedrals and it’s impossible to say that it’s a very mathematical image, isn’t it?
This bridge was designed by William Etheridge and built by James Essex in 1749 and it has been rebuilt in 1866 and 1905. It is composed of straight timbers in a very curious design and this is the reason because it is called “mathemtical”.
A tale says that Newton was able to build one mathematical bridge with straight timbers without the use of bolts but I think this is not really true.
Location: the Mathematical Brisge (map)
St. Paul’s Cathedral is the masterpiece of Sir Christopher Wren. It was built between 1675 and 1710 after its predecessor was destroyed in the Great Fire of London, and services began in 1697.
A lot of very important English men like Lord Nelson or the Duke of Wellington are buried here but among all these names we notice that the great Christopher Wren was also buried here under the crypt:
On the wall next to the grave there is this plaque written in Latin:
Christopher Wren is buried under the founder of this church and of the city. He lived beyond the age of ninety, not to himself but for the public good reader. If you seek his monument, look around you.
Died February 25, 1723, s. 91.
There is also a memorial plaque for “one of the most ingenious men who ever lived”: Robert Hooke.
It’s forbidden to take pictures in the cathedral but it’s always possible to find a guard who allows you to take a pair of them. Thank you very much anonymous guard!
This is the All Souls College in Oxford. It’s next to Radcliffe camera and very near the Bodleian Library. The College of All Souls of the Faithful Departed was founded by Henry VI and Henry Chichele (fellow of New College and Archbishop of Canterbury), in 1438. Sir Christopher Wren studied here and the big sundial (1658) in its main garden is attributed to him:
A former screen in the chapel is also attributed to Wren although it was replaced by a newer one designed by Sir James Thornhill in 1716.
Why are we taliing about the All Souls College? The only reason is Sir Christopher Wren (20 October 1632 – 25 February 1723), a very important figure who will appear more times in these Holidays. According to Wikipedia:
Sir Christopher Wren was born in East Knoyle in Wiltshire, the only surviving son of Christopher Wren Sr. (1589–1658) and Mary Cox, the only child of the Wiltshire squire Robert Cox from Fonthill Bishop. Christopher Sr. was at that time the rector of East Knoyle and later Dean of Windsor. It was while they were living at East Knoyle that all their children were born; Mary, Catherine, and Susan were all born by 1628 but then several children were born who died within a few weeks of their birth. Their son Christopher was born in 1632 then, two years later, another daughter named Elizabeth was born. Mary must have died shortly after the birth of Elizabeth, although there does not appear to be any surviving record of the date. Through Mary, however, the family became well off financially for, as the only heir, she had inherited her father’s estate.
As a child Wren “seem’d consumptive”. Although a sickly child, he would survive into robust old age. He was first taught at home by a private tutor and his father. After his father’s royal appointment as Dean of Windsor in March 1635, his family spent part of each year there, but little is known about Wren’s life at Windsor. He spent his first eight years at East Knoyle and was educated by the Rev. William Shepherd, a local clergyman.
Little is known of Wren’s schooling thereafter, during dangerous times when his father’s Royal associations would have required the family to keep a very low profile from the ruling Parliamentary authorities. The story that he was at Westminster School between 1641 and 1646 is substantiated only by Parentalia, the biography compiled by his son, a fourth Christopher, which places him there “for some short time” before going up to Oxford (in 1650); however, it is entirely consistent with headmaster Doctor Busby’s well-documented practice of educating the sons of impoverished Royalists and Puritans alike, irrespective of current politics or his own position. Some of Wren’s youthful exercises preserved or recorded (though few are datable) showed that he received a thorough grounding in Latin and also learned to draw. According to Parentalia, he was “initiated” in the principles of mathematics by Dr William Holder, who married Wren’s elder sister Susan (or Susanna) in 1643. During this time period, Wren manifested an interest in the design and construction of mechanical instruments. It was probably through Holder that Wren met Sir Charles Scarburgh whom Wren assisted in his anatomical studies.
On 25 June 1650, Wren entered Wadham College, Oxford, where he studied Latin and the works of Aristotle. It is anachronistic to imagine that he received scientific training in the modern sense. However, Wren became closely associated with John Wilkins, the Warden of Wadham. The Wilkins circle was a group whose activities led to the formation of the Royal Society, comprising a number of distinguished mathematicians, creative workers and experimental philosophers. This connection probably influenced Wren’s studies of science and mathematics at Oxford. He graduated B.A. in 1651, and two years later received M.A.
Receiving his M.A. in 1653, Wren was elected a fellow of All Souls College in the same year and began an active period of research and experiment in Oxford. His days as a fellow of All Souls ended when Wren was appointed Professor of Astronomy at Gresham College, London in 1657. He was provided with a set of rooms and a stipend and was required to give weekly lectures in both Latin and English to all who wished to attend; admission was free. Wren took up this new work with enthusiasm. He continued to meet the men with whom he had frequent discussions in Oxford. They attended his London lectures and in 1660, initiated formal weekly meetings. It was from these meetings that the Royal Society, England’s premier scientific body, was to develop. He undoubtedly played a major role in the early life of what would become the Royal Society; his great breadth of expertise in so many different subjects helping in the exchange of ideas between the various scientists. In fact, the report on one of these meetings reads:
Memorandum November 28, 1660. These persons following according to the usual custom of most of them, met together at Gresham College to hear Mr Wren’s lecture, viz. The Lord Brouncker, Mr Boyle, Mr Bruce, Sir Robert Moray, Sir Paule Neile,Dr Wilkins, Dr Goddard, Dr Petty, Mr Ball, Mr Rooke, Mr Wren, Mr Hill. And after the lecture was ended they did according to the usual manner, withdraw for mutual converse.
In 1662, they proposed a society “for the promotion of Physico-Mathematicall Experimental Learning.” This body received its Royal Charter from Charles II and “The Royal Society of London for Improving Natural Knowledge” was formed. In addition to being a founder member of the Society, Wren was president of the Royal Society from 1680 to 1682.
In 1661, Wren was elected Savilian Professor of Astronomy at Oxford, and in 1669 he was appointed Surveyor of Works to Charles II. From 1661 until 1668 Wren’s life was based in Oxford, although his attendance at meetings of the Royal Society meant that he had to make occasional trips to London.
The main sources for Wren’s scientific achievements are the records of the Royal Society. His scientific works ranged from astronomy, optics, the problem of finding longitude at sea, cosmology, mechanics, microscopy, surveying, medicine and meteorology. He observed, measured, dissected, built models and employed, invented and improved a variety of instruments. It was also around these times that his attention turned to architecture.
It was probably around this time that Wren was drawn into redesigning a battered St Paul’s Cathedral. Making a trip to Paris in 1665, Wren studied the architecture, which had reached a climax of creativity, and perused the drawings of Bernini, the great Italian sculptor and architect. Returning from Paris, he made his first design for St Paul’s. A week later, however, the Great Fire destroyed two-thirds of the city. Wren submitted his plans for rebuilding the city to King Charles II, although they were never adopted. With his appointment as King’s Surveyor of Works in 1669, he had a presence in the general process of rebuilding the city, but was not directly involved with the rebuilding of houses or companies’ halls. Wren was personally responsible for the rebuilding of 51 churches; however, it is not necessarily true to say that each of them represented his own fully developed design.
Wren was knighted 14 November 1673. This honour was bestowed on him after his resignation from the Savilian chair in Oxford, by which time he had already begun to make his mark as an architect, both in services to the Crown and in playing an important part in rebuilding London after the Great Fire.
Additionally, he was sufficiently active in public affairs to be returned as Member of Parliament for Old Windsor in 1680, 1689 and 1690, but did not take his seat.
By 1669 Wren’s career was well established and it may have been his appointment as Surveyor of the King’s Works in early 1669 that persuaded him that he could finally afford to take a wife. In 1669 the 37-year-old Wren married his childhood neighbour, the 33-year-old Faith Coghill, daughter of Sir John Coghill of Bletchingdon. Little is known of Faith’s life or demeanour, but a love letter from Wren survives, which reads, in part:I have sent your Watch at last & envy the felicity of it, that it should be soe near your side & soe often enjoy your Eye. … .but have a care for it, for I have put such a spell into it; that every Beating of the Balance will tell you ’tis the Pulse of my Heart, which labors as much to serve you and more trewly than the Watch; for the Watch I beleeve will sometimes lie, and sometimes be idle & unwilling … but as for me you may be confident I shall never …
This brief marriage produced two children: Gilbert, born October 1672, who suffered from convulsions and died at about 18 months old, and Christopher, born February 1675. The younger Christopher was trained by his father to be an architect. It was this Christopher that supervised the topping out ceremony of St Paul’s in 1710 and wrote the famous Parentalia, or, Memoirs of the family of the Wrens. Faith Wren died of smallpox on 3 September 1675. She was buried in the chancel of St Martin-in-the-Fields beside the infant Gilbert. A few days later Wren’s mother-in-law, Lady Coghill, arrived to take the infant Christopher back with her to Oxfordshire to raise.
In 1677, 17 months after the death of his first wife, Wren married once again. He married Jane Fitzwilliam, daughter of William FitzWilliam, 2nd Baron FitzWilliam and his wife Jane Perry the daughter of a prosperous London merchant.
She was a mystery to Wren’s friends and companions. Robert Hooke, who often saw Wren two or three times every week, had, as he recorded in his diary, never even heard of her, and was not to meet her till six weeks after the marriage. As with the first marriage, this too produced two children: a daughter Jane (1677–1702); and a son William, “Poor Billy” born June 1679, who was developmentally delayed.
Like the first, this second marriage was also brief. Jane Wren died of tuberculosis in September 1680. She was buried alongside Faith and Gilbert in the chancel of St Martin-in-the-Fields. Wren was never to marry again; he lived to be over 90 years old and of those years was married only nine.
Bletchingdon was the home of Wren’s brother-in-law William Holder who was rector of the local church. Holder had been a Fellow of Pembroke College, Oxford. An intellectual of considerable ability, he is said to have been the figure who introduced Wren to arithmetic and geometry.
Wren’s later life was not without criticisms and attacks on his competence and his taste. In 1712, the Letter Concerning Design of Anthony Ashley Cooper, third Earl of Shaftesbury, circulated in manuscript. Proposing a new British style of architecture, Shaftesbury censured Wren’s cathedral, his taste and his long-standing control of royal works. Although Wren was appointed to the Fifty New Churches Commission in 1711, he was left only with nominal charge of a board of works when the surveyorship started in 1715. On 26 April 1718, on the pretext of failing powers, he was dismissed in favour of William Benson.
He was married to 3 different women but only had children with 2 of them.
The Wren family estate was in the area of Hampton Court. It had been bought by Wren many years before as part of a legacy for his son Christopher Wren, Jr. For convenience Wren also leased a house on St James’s Street in London. According to a 19th-century legend, he would often go to London to pay unofficial visits to St Paul’s, to check on the progress of “my greatest work”. On one of these trips to London, at the age of ninety, he caught a chill which worsened over the next few days. On 25 February 1723 a servant who tried to awaken Wren from his nap found that he had died.
Wren was laid to rest on 5 March 1723. His remains were placed in the south-east corner of the crypt of St Paul’s beside those of his daughter Jane, his sister Susan Holder, and her husband William. The plain stone plaque was written by Wren’s eldest son and heir, Christopher Wren, Jr.
Therefore, I think that Wren will be a very used tag in this blog!
In the Jorcks Passage in the centre of Copenhagen there are some allegorical representations which are difficult t distinguish. One of them is a woman with a plan of a big house and a compass in the other. Is she the allegorical representation of the Architecture?
Whatever there is a very interesting shop in one of the corners dedicated to games where it’s possible to find dice, Rubbik cubes, etc.
Location: Jorcks Passage (map)