Tag Archives: Measures

Mitad del Mundo

Photography by Carlos Dorce

Photography by Carlos Dorce

Mitad del Mundo is a touristic attraction built in 1979 by order of Patricio Romero barberia with the intent of promoting Ecuador’s identity and the European 18th-century geodesic missions. The main entrance is a large corridor with some sculptures with the most important men who took measures in the first geodesic mission like La Condamine or…

Photography by Carlos Dorce

Photography by Carlos Dorce

PEDRO VICENTE MALDONADO (Riobambam 1704 – London, 1748)

  • Thanks to his ample knowledge of geodesy and geography, he was one of the key members of the First Geodesic Mision.
  • He was the first latin american to join the Paris Academy of Sciences.
  • He drew the first geographical map of the Royal Audiencia of Quito.
  • He is attributed with building the commercial route between Quito and Esmeraldas.
  • Due to his notable work, he was dubbed “Knight of the Royal Chamber” by King Philip V of Spain in 1746.
  • His remains lie in St. James’s Church of England.
Photography by Carlos Dorce

Photography by Carlos Dorce

ANTONIO DE ULLOA (Sevilla, 1716 – Isla de León, 1795)

  • He was one of the sailors sent by King Philip V of Spain to form part of the Geodesic Mission.
  • He went to Paris with La Condamine where he became a member of the Academy of Sciences.
  • Due to his scientific work, he published “Noticias de America” (News of the Americas) in 1772.
  • Together with Jorge Juan y Santacilia, he wrote the famous report entitled “Noticias Secretas” (Secret News) to the King of Spain about the state of his colonies.
Photography by Carlos Dorce

Photography by Carlos Dorce

JORGE JUAN Y SANTA CILIA (Alicante, 1713 – Madrid, 1773)

  • He was a Spanish scientist, mathematician, naval officer and mariner. He was appointed member of the French Geodesic Mission by the King of Spain, Philip V.
  • He remained in South America for many years with the purpose of studying the political and social situations in the Spanish territories.
  • He wrote “Relación Histórica del Viaje a la América Meridional” (History of the Journey to Meridional America) with Antonio de Ulloa. It was published in Madrid in 1748.

The expedition was former by the French scientists La Condamine, Godin, Jussieu, Bouguer, Morinville, Verguin, Godin des Odonnais, Seniergues and Hugot, and the Spaniards Jorge Juan and Antonio de Ulloa. They left La Rochelle on May 16th, 1735 and arrived at Manta on March 9th, 1736. La Condamine separated himself from the others and performed the first measurements and observations on the coast of Manabi and on June, the members of the mission met again to select the most adequate place for a base that would be used for the necessary triangulation.

Photography by Carlos Dorce

Photography by Carlos Dorce

On the top of the main monument there is a big world with a rounding equatorial line…

Photography by Carlos Dorce

Photography by Carlos Dorce

… and inside you can see that the rotation of the water is determined by other factors like the initial rotational direction (Coriolis effect!):

Photography by Carlos Dorce

Photography by Carlos Dorce

CORIOLIS

It is the effect

It is the effect observed in a rotating reference system when an object is moving respect to that system. Its influence can be detected in the rotation of hurricanes, ocean currents and trade winds.

The place is lovely and the views from the top of the monument are wonderful!

Photography by Carlos Dorce

Photography by Carlos Dorce

There also are some sundials like these ones:

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

In the different museums, it is possible to learn more things about the geodesic mission and the instruments of measurement used by the scientists:

Photography by Carlos Dorce

Photography by Carlos Dorce

Of course, if you go to Mitad del Mundo you must play with your feet and the equatorial line: one foot in the North and one foot in the South!

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Mitad del Mundo (map)

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The Catalan Cane

This column measures 1 cane

This column measures 1 cane

In the corner of Santa Llúcia and Bisbe Streets, we find a corious thing that does not call the atention of any of the tourists who walk around the cathedral of Barcelona. On the romanic chapel of Santa Llúcia, erected three decades before the construction of the Cathedral, we find this semicircular column sculpted in stone on the wall which measures exactly one “destre cane”.

Photography by Robert Salla

Photography by Robert Salla

The word “cane” is engraved on the wall next to the column so everybody in the Medieval barcelona could check that this was the standard measure of longitude in the market.

A cane (from the latin qana) was an ancient unit of mesurement used on the Crown of Aragon, part of France and the north of Italy. Before the Internacional Sistem of Units it was a way to have a fixed reference of lenght. This unit was used for building specific sticks of wood that were used on the market tents to have a reference when they were selling. In Barcelona, it was equivalent to eight palms, six feet or two steps, that is about 1.55 meters, although it wasn’t exactly the same measure everywhere. For example, in Tortosa it was equivalent to 1.59 meters but the reference to the whole Catalan countries was the same as in Montpellier, equivalent to 1.99 meters. Furthermore there were the square cane which was used to measure surfaces: in Barcelona it was equivalent to 2.44 square meters, 2.42m. in Girona , 2.43m in Tarragona and in 2,45m in Mallorca. Surprisingly we see that there is less diference between the square canes than in the lenght measures. As we’ve said, it was the unit of longitude used in the markets next to the cathedral in the Middle Ages althought the Catalan “destre cane” was also used. It was equivalent to twelve palms and this is exactly the height of the column that we find next to the cathedral.

This post has been written by Ander Castillo and Robert Salla in the subject Història de les Matemàtiques (History of Mathematics, 2014-15)

Location: Carrer de la Pietat 2 (map)

Meters and feet

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Photography by Carlos Dorce

Next to Birmingham Town Hall…

Photography by Carlos Dorce

Photography by Carlos Dorce

… there is this line on te floor. Almost everybody in Victoria Square walk near it but only a few people notice that this stone line shows the equivalence between the metrical system and the British one.

So you can see some plaques indicating the distances measured in meters and also in feet:

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

It’s a good opportunity to improvise a Maths class, isn’t it?

Location: Birmingham Town Hall (map)

The Royal Observatory in Greenwich (II)

Photography by Carlos Dorce

Photography by Carlos Dorce

The Royal Observatory of Greenwich was commisioned in 1675 by Charles II and the building was completed in the summer of 1676. John Flamsteed (1646-1719) was the first Astronomer Royal so the building was often given the title “Flamsteed House” in reference to its first occupant.

In one of the walls, the observatory has the Sepherd 24-hour Gate Clock which is the earliest electrically driven public clocks. It was installed in 1852 ans the dial always shows Greenwich Mean Time (GMT):

Photography by Carlos Dorce

Photography by Carlos Dorce

In the small plate under the clock (G 1692) is an Ordnance Survey bench mark dating from the 1940s. The height above the sea level has been measured and recorded. There are also the British Imperial Standards of Length which were mounted here some time before 1866.

The observatory is also known as the location of the prime meridian of Greenwich meridian:

Photography by Carlos Dorce

Photography by Carlos Dorce

All the tourist want to have a picture with a foot in each side of the meridian:

Photography by Carlos Dorce

Photography by Carlos Dorce

and there is always a large queue to take a picture next to the meridian line which is graved ion the terrace:

Photography by Carlos Dorce

Photography by Carlos Dorce

Another characteristic thing of the obervatory is the Time Ball. The red time ball on top of Flamsteed House is one of the world’s first visual time signals. It was installed in 1833 to enable navigators on ships in the Thames to check their marine chronometers.

The Time Ball drops daily at 13:00hrs (GMT in winter […]). It is raised halfway up the mast at 12:55hrs as a preparatory signal and to the top 2 minutes before it drops.

Photography by Carlos Dorce

Photography by Carlos Dorce

 Let’s start our visit through the gardens of the observatory where we can imagine the great English astronomers looking at the night sky! Ofcourse we find a sundial: 

Photography by Carlos Dorce

Photography by Carlos Dorce

Sundials are the oldest known device for telling the time. As the Earth rotates and the Sun appears to move accross the sky, the shadow cast on the scale indicates the time of the day.

This dial constructed in 1968, represents a globe made from a series of rings. The rings are called ‘armillae’ in Latin, so it is called an armillary dial. The hour scale is on the northern half of the ring representing the equator.

There is also the well where Flamsteed 100-foot telescope was located:

Photography by Carlos Dorce

Photography by Carlos Dorce

Flamsteed used a 30,5 m. well on this site to accomodate a very long telescope:

ROG09

The astronomer sat at the bottom of the well and observed stars that passed directly overhead. It was hoped that placing the telescope in the well would make it possible to create a steady long-focus instrument for very fine measurements. Flamsteed made a few observations from here in 1679, but the damp underground conditions soon made the telescope impossible to use.

A remaining section of a 12 m. reflecting telescope built for the astronomer William Herschel is also in the gardens:

Photography by Carlos Dorce

Photography by Carlos Dorce

The telescope was the largest in the world and cost over 4.000 pounds, paid for by King George III. Completed in 1789 and erected at Herschel’s home near Slough, about 30 miles (48 km) west of Greenwich, it soon became a tourist attraction. Some people likened it to the Colossus of Rhodes, and it was even marked on the 1830 Ordnance Survey map of the area.

Sadly, the Herschels did not use the great telescope for much serious astronomy since it was difficult to set up and mantain. William’s son had it dismantled in 1840. Most of the tube was destroyed when a tree fell on it 30 years later.

On the walls of Flamsteed House is marked  the Bradley Merdian which was the first British National Meridian. The Greenwich meridian was set according to the location of the telescope used by the Astronomer Royal to establish the time. So the Greenwich meridian was in the graved line when James Bradley, the 3rd Astronomer Royal between 1742 and 1762 was in the observatory. When the Airy Transit Circle Telescope was erected in 1850, the Greenwich Meridian was moved approximately 19 feet east to its present location.

Before visiting Flamsteed House there is still time for look at the Dolphin Sundial designed by Christopher St. J. H. Daniel and commisioned by the National Maritime Museum in 1977:

Photography by Carlos Dorce

Photography by Carlos Dorce

So let’s go now to Flamsteed House!

LocationGreenwich Observatory (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)

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!