Tag Archives: Figures

The Palmerston Number Sculpture

The Palmerston Number Sculpture. Photography by Loxias (TravelPod)

This is a new mathematical sculpture found in the net and dedicated to numbers. It was designed by Anton Parsons and represents a great monument to our loved Mathematics.

Location: The Palmerston Number Sculpture (map)

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A cuneiform tablet in Pergamon Museum

Photography by Carlos Dorce

Photography by Carlos Dorce

This map is dated inthe 21st century BC and can be seen in the Pergamon Museum of Berlin. As you can see, there is a plane of some lands and the cuneiform figures tell us the dimensions of it. Of course, this is a small piece of clay rouded by the great Mesopotamian treasures that you can admire in this wonderful museum but… can we forget focussing our attention in this cuneiform tablet? I don’t think so!

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Pergamon Museum in Berlin (map)

The frontispiece of Museo del Prado

Photography by Carlos Dorce

Photography by Carlos Dorce

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:

Photography by Carlos Dorce

Photography by Carlos Dorce

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:

Photography by Carlos Dorce

Photography by Carlos Dorce

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…

Photography by Carlos Dorce

Photography by Carlos Dorce

…and the Symmetry:

Photography by Carlos Dorce

Photography by Carlos Dorce

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:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Museo del Prado (map)

Egyptian Mathematics in the BM

Photography by Carlos Dorce

Photography by Carlos Dorce

I am going to begin my Egyptian visit to the British Museum with the limestone game-board in the form of a coiled snake used for the game called “mehen” (2890-2686 BC). The body of the coiled snake is divided into rectangular spaces but the number of these spaces is not important for the game.

Game-boards in the form of coiled snakes are known from the Early Dynastic period whengames became a regular item of tomb equipment. Several examples were discovered in the excavation of the Second-Dinasty tomb of King Khasekhemwy at Abydos. The game for which the snake-board was used was called mehen and although the exact method of play is not known, later representations show that it involved two players. The game-pieces consisted of spherical stone marbles and small figures of lions and lionesses usually made of bone or ivory.

The other popular game in Ancient Egypt was the ‘senet’ and there is one ivory sene board with a drawer for storing the gaming pieces with the glazed gaming pieces. This second board is in the special exhibition dedicated to the tomb-chapel of Nebamun (1350 BC):

Photography by Carlos Dorce

Photography by Carlos Dorce

The secnond mathematicl object found in the British Museum is this sandstone stela of the Egyptian Viceroy of Kush, Merymose, who served under Pharaoh Amenhotep III (c.1400 BC). A hieroglyphic text describes his campaign against the Nubians of Ibhet:

Photography by Carlos Dorce

Photography by Carlos Dorce

The hieroglyphic text is full of numbers and figures:

Photography by Carlos Dorce

Photography by Carlos Dorce

Other hieroglyphic numbers are found in the limestone relief of Rahotep (c.2600 BC) which was fixed in the offering-chapel of a brick mastaba tomb.

Photography by Carlos Dorce

Photography by Carlos Dorce

The relief shows Rahotep seated before offerings which are detailed in a formal list on the right of the slab and all these offerings are accompanied of the number of them. We can see the ‘lotus’ for the thousands…

Photography by Carlos Dorce

Photography by Carlos Dorce

and a lot of examples of units, tens and hundreds:

Photography by Carlos Dorce

Photography by Carlos Dorce

It’s also interesting this bone identifying label from an item of funerary equipment (3100 BC). The front of the label bears the name of Queen Neithhotep and on the back is the numeral 135:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, the limestone false door stela of Niankhre (2450 BC) from Saqqara which comes from the mastaba-tomb of the superintendant of the hairdressers of the Palace Niankhre. You can see the number 4.000 in the top of the stela:

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationBritish Museum in London (map)

Mesopotamian Mathematics in the BM

Photography by Carlos Dorce

Photography by Carlos Dorce

This is the famous Royal Game of Ur (2600-2300 BC). This wooden game board was in at least six graves in the Royal Cemetery so it’s an early example of a game that was played all over the ancient Near East for about 3.000 years.

The game is a race for two players using dice with seven identical pieces each. All playing squares are decorated, but on later boards only the five ‘rosette’ squares are marked. […] Pieces are ‘at war’ along the central path but turn off to their own side to exit.

Playing pieces were discs of shell or lapis lazuli. The tetrahedrical dice of the game are also exhibited.

Apart of the Royal Game of Ur, the only exhibited objects which are related with Mespotamian mathematics are the Archaic and Cuneiform tablets. For example, look at this tablet containing a five day ration list (Jemdet Nasr, 3000-2900 BC):

Photography by Carlos Dorce

Photography by Carlos Dorce

Each line contains rations for one day and the sign for ‘day’ and numbers 1, 2, 3, 4 and 5 are easily identificable (at the beginning of the line!).

Photography by Carlos Dorce

Photography by Carlos Dorce

This Gypsum tablet with Archaic numbers (Uruk, 3300 BC) has 3 units (round impressions) and 3 ‘tens’ (elongated impressions).

Photography by Carlos Dorce

Photography by Carlos Dorce

This tablet above contains the daily barley beer ration for the workers (3300-3100 BC). Here there are also identificable all the marks representing units and tens and it’s the same in the next tablet containig food rations (3300-3100 BC):

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, there is another tablet from the Late Uruk Period (3300-3100 BC):

Photography by Carlos Dorce

Photography by Carlos Dorce

However, mathematical tables are not only clay tablets with figures and numbers. For example, the next tablet contains a set of problems relating to the calculation of volume, together with the solutions.

Photography by Carlos Dorce

Photography by Carlos Dorce

You can see the details of the tablet in the next two pictures:

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

There is also a tablet recording observations of the planet Venus from c.1700 BC:

Photography by Carlos Dorce

Photography by Carlos Dorce

Astronomical tablets were so common in Mesopotamia and here we have a representation of the heavens in eight segments which include drawings of the constellations.

Photography by Carlos Dorce

Photography by Carlos Dorce

The next piece of cuneiform tablet contains a star chart which was found in Ashurbanipal’s library:

Photography by Carlos Dorce

Photography by Carlos Dorce

According the British Museum’s web…

Ashurbanipal, whose name (Ashur-bani-apli) means, ‘the god Ashur is the creator of the heir’, came to the Assyrian throne in 668 BC. He continued to live in the Southwest Palace of his grandfather, Sennacherib, in Nineveh, which he decorated with wall reliefs depicting his military activity in Elam. He also had a new residence built at Nineveh, known today as the North Palace. The famous lion hunt reliefs, some of which are now in The British Museum, formed part of the new palace’s decorative scheme.

Throughout his reign, Ashurbanipal had military problems, mainly at the borders of the empire. He also continued his father’s policy of attacking Egypt. Campaigns in 667 and 664 BC led to the defeat of the Egyptian Twenty-fifth Dynasty and the appointment of a pro-Assyrian ruler in the Nile Delta. Assyria also attacked Elam, possibly in 658-57 BC, following the receipt of insulting letters from the Elamite king. In 652 BC Shamash-shum-ukin, Ashurbanipal’s brother, and ruler of Babylonia, revolted against Assyria with the support of the Elamites. The Assyrian army invaded Elam and Babylonia. Babylon was captured in 648 BC and the following year the Elamite city of Susa was destroyed. There is little surviving evidence that can help us to reconstruct the last years of Ashurbanipal’s reign. Ashurbanipal boasted of his ability to read the cuneiform script, and was responsible for the collection and copying of a major library of contemporary literary and religious texts

LocationBritish Museum in London (map)

The Ashmolean Museum in Oxford (III)

There also are some Mesopotamian astronomical and mathematcal tablets in the Ashmolean Museum. For example, these two tablets are two proto-cuneiform clay tablets from an administrative building. They contain receipts of objects and grain, accounts and possibly rations and it’s possible to distinguish the units, the tens and the sixties:

Photography by Carlos Dorce

Photography by Carlos Dorce

Next clay tablet records date palms, orchards and gardeners in Akkadian cuneiform (2350-2150 BC):

Photography by Carlos Dorce

Photography by Carlos Dorce

Perhaps, the next clay tablet is the most interesting mathematical one because of its diagram. It’s a school tablet from 1900-1600 BC with a mathematical exercise showing a triangle with the incorrect calculation of the area of a field:s

Photography by Carlos Dorce

Photography by Carlos Dorce

In Eleanor Robson’s Mathematical cuneiform tablets in the Ashmolean Museum, Oxford, we find an explanation about this tablet:

Type IV tablet with upper right portion missing and reverse blank where preserved. Geometrical diagram of a triangle, showing the two lengths and an erroneous value for the area. Found in Trench C-10, 1 metre from surface level, 2 metres from plain level, with two other Type IV tablets bearing elementary exercises […].

The correct answer is 3;45 · 1;52,30 · 0;30 = 3;30,56,15

The error appears to have arisen through misplacing the sexagesimal place of one part of an intermediate calculation […]

Source: Robson's Mathematical cueniform tablets...

Source: Robson’s Mathematical cueniform tablets

There also is a clay prism with table of linear measures and squares roots (1950-1700 BC) from Southern Iraq:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, I took a photography of the clay tablet with astronomical observations copied by a scribe in the early 8th century BC from Iraqian Kish. It gives the dates of the rising and settings of Venus in the reign of Ammizaduqa, king of Babylon in the 17th century BC:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: The Ashmolean Museum in Oxford (map)

The Ashmolean Museum in Oxford (II)

Statue of King Khasekhrm Photography by Carlos Dorce

Statue of King Khasekhem
Photography by Carlos Dorce

There also is this statue in the Ashmolean Museum. Khasekhem was the last king of the 2nd Dinasty (2850-2700 BC) and he is wearing the White Crown of Upper Egypt and is wrapped in a long robe. His right fist is drilled to attach a separate object, perhaps a mace handle or sceptre. The king’s name is inscribed in front of his feet written inside a representation of the palace façade topped by the falcon god Horus. The base of the statue records a military campaign against the northern rebels referring to the inhabitants of the Nile Delta, alongside the bodies of slain enemies, numbered on the front as 47.209:

Photography by Carlos Dorce

Photography by Carlos Dorce

There also are some other Egyptian objects in which it’s possible to read the Hieroglific figures. One example is the limestone cornice from a false door in the mastaba of Sheri, overseer of mortuary priests tending the cults of the 2nd Dynasty Kings Sened and Persibsen (c.2700 BC):

Photography by Carlos Dorce

Photography by Carlos Dorce

Framed between two facades, Sheri and his wife Kentyetka are seated at a table laden with food offerings and we can see four numbers “1.000” below it:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, there is a set of funerary stelae in which can be noticed some Egyptian figures:

Photography of Carlos Dorce

Photography of Carlos Dorce

For example, look at this limestone stela (c.1200 BC) of the Lector Priest Dedusobek, official of the pyramid and town of Senwosret II at Lahun. Dedusobek and his father Menkau are each seated before a table of offerings. You can see two set of four number “1.000” over the table:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: The Ashmolean Museum in Oxford (map)

Without metrical system

Photography by Cristina Martínez

Photography by Cristina Martínez

I am used to the decimal metric system for measuring the distances! In Great Britain there isn’t the metro and the kilometer as the unit length so when you drive through its roads and motorways, you must to learn all about miles, yards,… So let me begin:

1 mile = 1,609344 km = 1760 yards

1 yard = 0,9144 m.

In Continental Europe we are used to write 500 m in spite of 1/2 Km because the decimal system is very comfortable for us. In Britain, it’s better to say 1/4, 1/2 or 3/4 miles than 415, 830 or 1245 yards, respectively. Here we have a case in which fractions are very useful!

Where is number 13?

bristol01

Photography by Carlos Dorce

I was in the Premier Inn hotel in Bristol and I think that this have been the tallest hotel where I’ve ever slept. There was this plaque next to the lifts and… can you notice anything strange?

Of course… where is number 13? The supestition has won!

Location: Premier Inn in Bristol (map)

The Ashmolean Museum in Oxford (I)

The Ashmolean Museum Photography by Carlos Dorce

The Ashmolean Museum
Photography by Carlos Dorce

The Ashmolean Museum is the World’s first university museum. Its first building was built in 1678–1683 to house the cabinet of curiosities Elias Ashmole gave Oxford University in 1677. The collection includes that of Elias Ashmole which he had collected himself, including objects he had acquired from the gardeners, travellers and collectors John Tradescant the elder and his son of the same name. The collection included antique coins, books, engravings, geological specimens, and zoological specimens—one of which was the stuffed body of the last dodo ever seen in Europe; but by 1755 the stuffed dodo was so moth-eaten that it was destroyed, except for its head and one claw. The museum opened on 24 May 1683, with naturalist Robert Plot as the first keeper. The first building, which became known as theOld Ashmolean, is sometimes attributed to Sir Christopher Wren or Thomas Wood.

One of the first room that you visit after the main entrance is the one dedicated to the Minoic and the Ancient Greek period and we can find the Minoic figures there.

Linear B is one of the Minoic scriptures. The script has about 90 signs ans a number of pictorial signs. Some of these old tablets have survived and they are the tablets that were baked in fires that destroyed the Minoic buildings. Linear B tablets as number 21 reconstruct the various stages of the textile production supervised in Knossos. This in a record of 58 castrated male sheep, 2 female sheep and a shortfall of 50 sheep, about 1375 BC, burnt clay. Can you guess the minoican figures for numbers 58, 2 and 50?

Photography by Carlos Dorce

Photography by Carlos Dorce

Of course! Each vertical line represents number “one” and each horizontal line represents number “ten”. Another example is the tablet number 20 which records women workers along with girls and boys (probably their children) from about 1375 BC:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, other examples of the Linear B escripture:

Photography by Carlos Dorce

Photography by Carlos Dorce

Number 11 is a record of raw materials including wild goat horns probably needed for chariot building (c.1375 BC) and number 14 records issues of wool to women for the production of a particular type of cloth (c. 1375 BC).

From the Ancient Greece we also find two mazes carved in two respectively coins:

Photography by Carlos Dorce

Photography by Carlos Dorce

The  first one is an Ancient Greek silver drachma found Kossos (300-270 BC) and the second is also a silver Knossos coin (300-200 BC) with a minotaur inside.

Location: The Ashmolean Museum in Oxford (map)