Tag Archives: Counting

Counting with Count Von Count

I know that this is not the correct place for a doodle dedicated to Count Von Count but five years ago this doodle was published to celebrate the 40th anniversary of Sesame Street. I watched it when I was a child I and I loved Count Von Count who taught children to count. Do you remembere it? There were thunders and lightnings after each number!

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Shakuntala Devi’s doodle

Shakuntala Devi (November 4, 1929 – April 21, 2013) was a mental calculator who travel around the World showing her arithmetic talent.

According to Wikipedia:

Examples of the problems presented to Devi included calculating the cube root of 61,629,875, and the seventh root of 170,859,375. […] Devi provided the solution to the aforementioned problems (395 and 15, respectively) before [prof. Arthur] Jensen could copy them down in his notebook.

In the 1982 Guinness Book of Records is mentioned that on June 18, 1980, she demonstrated the multiplication of two 13-digit numbers—7,686,369,774,870 × 2,465,099,745,779—picked at random by the Computer Department of Imperial College, London. She correctly answered 18,947,668,177,995,426,462,773,730 in 28 seconds.

Source: Wikimedia Commons

This doddle was published last year to commemorate Devi’s 84th birthday in a lot of countries of the World.

Whipple Museum of the History of Science (and V)

Photography by Carlos Dorce

Photography by Carlos Dorce

The last post dedicated to Whipple Museum is for the calculators and their predecessors. All these objects are located in the next room which contains a lot of things in shelves and drawers as if they were in a store. There are calculators and a drawer dedicated to the Napier’s rods or bones:

Photography by Carlos Dorce

Photography by Carlos Dorce

There also are some interesting abacus like this one:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, different slide rules fill some drawers. You must be very patient and it’s a pity that this museum isn’t located in a larger building. 

WM27

Photography by Carlos Dorce

I have more pictures but you must go there if you want to have a real idea of the exhibition. It’s impossible to summarize it in some photos!

LocationWhipple Museum of the History of Science in Cambridge (map)

Whipple Museum of the History of Science (IV)

Photography by Carlos Dorce

Photography by Carlos Dorce

Some mathematical objects also exhibited here like this Gunter’s square made in 1567. Gunter also invented his scale for computing adapting the new logarithms invented by Napier in 1614. Hence, it’s time to start our visit to all the Napier’s rods and slide rules of the exhibition. Let’s have a look to a couple of them, like these English Napier’s rods from 1720…

Photography by Carlos Dorce

Photography by Carlos Dorce

or this other ivory set made from the 17th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

From Gunter scales the slide rules were invented and this spiral logarithmic scale by John Holland (1650) is a very good example of the great inventions of the men from the Renaissance:

Photography by Carlos Dorce

Photography by Carlos Dorce

After the slide rules and before the computers, ihis fragment of the ‘Difference Engine No. 1’ by Charles Babbage (1832-3)  assembled by his son Henry Babbage (c.1880) must also be exhibited:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, a very curious mathematical object: this magic cube made by A. H. Frost in 1877:

Photography by Carlos Dorce

Each row, each column and each diagonal have the same sum!

Photography by Carlos Dorce

LocationWhipple Museum of the History of Science in Cambridge (map)

The Science Museum in London (IV)

Photography by Carlos Dorce

Photography by Carlos Dorce

John Napier invented published his Mirifici Logarithmorum Canonis Descriptio in 1614 and the invention of the logarithms was the beginning of a new method of computing. Henry Briggs met Napier in Edimburg in the summer of 1615 and 1616 and these two men together decided to improve the invention creating the decimal logarithms which were published by Briggs some years later. In 1620 Edmund Gunter published his Canon Triangulorum where he described one of the first attempts to create a slide rule:

Photography by Carlos Dorce

Photography by Carlos Dorce

After the Gunter’s scale was invented, some other descriptions of the rule appeared like the one made by Wingate in paris in 1624. Gunter’s scale was very popular because all the trigonometrical resolutions of the triangles were reduced to additions and substractions on the rule:

Photography by Carlos Dorce

Photography by Carlos Dorce

The slide rule was invented by William Oughtred who designed both a circular and a straight form of slide rule in about 1621 but did not publish his work until much later. Richard Delamain, one of his former pupils, published a description of a circular slide rule in 1630, and claimed priority of invention although he copied Oughtred’s ideas. In 1660’s Thomas Browne invented the spiral slide rule consisting in fixed scales and moveable index arms similar to Oughtred’s circles of proportion:

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationScience Museum in London (map)

Babbage’s Difference Machine No. 1

Photography by Carlos Dorce

Photography by Carlos Dorce

This is not going to be the only post dedicated to Babbage in the Science Museum. I’ve visited this museum in my birthday and I am going to write some posts about the mathematical section. However, the first thing that I saw after the exhibition about Turing is this Babbage’s Difference Machine No. 1.

This trial portion of the Difference Engine is one of the earliest automatic calculators and is a celebrated icon in the prehistory of the computer.

Charles Babbage was a brillant thinker and mathematician. He divised the Difference Engine to automate the production of error-free mathematical tables. In 1823 he secured 1500 pounds from the government and shortly afterwards he hired the engineer Joseph Clement.

The Difference Engine was designed to perform fixed operations automatically. During its development Babbage’s mind leapt forward to the design of the Analytical Engine, which using punched cards could be programmed to calculate almost any function. This design embodied almost all the conceptual elements of the modern electronic computer.

The project collapsed in 1833 when Clement downed tools. By then, the government had spent over 17.000 pounds to build the machine -equivalent to the price of two warships. The collapse of the venture was traumatic for Babbage and, in old age, he became embittered and disillusioned.

Historians have suggested that the design was beyond the capability of contemporany technology and would have required greater accuracy than contemporany engineering could have provided. However, recent research has shown that Clement’s work was adequate to create a functioning machine. In fact, the scheme founderer on issues of economics, politics, Babbage’s temperament and his style of directing the enterprise.

 LocationScience Museum in London (map)

The Museum of the History of Science (III)

Photography by Carlos Dorce

Photography by Carlos Dorce

The mathematicalinstruments are also part of the collection. For example, there is a 17th-century box with some wooden polyhedra and some models for the study of Spherical Trigonometry:

Photography by Carlos Dorce

Photography by Carlos Dorce

And more wooden models in this mathematical box:

Photography by Carlos Dorce

Photography by Carlos Dorce

John Rowley was one of the leading London instrument makers in the late 17th and early 18th centuries and there are some mathematical compasses and instruments made by him in the collection:

Photography by Carlos Dorce

Photography by Carlos Dorce

Object number 1 is a proportional compass meanwhile number 5 is a ruler with pencil and dividers and number 6 is a slide rule.

Of course, if we are in a museum where the History of the Mathematics is exhibited, Napier’s rods must be here:

Photography by Carlos Dorce

Photography by Carlos Dorce

Unsigned, English, c. 1679

Photography by Carlos Dorce

Photography by Carlos Dorce

Unsigned, English, 17th century?

Photography by Carlos Dorce

Photography by Carlos Dorce

Charles Cotterel’s Arithmetical Compendium, Unsigned, English, c.1670

As in the Pitt Rivers Museum, the abacus also have their space in the showcases:

Oriental abacuses use beads on rods to represent numbers. Addition and substraction can be quickly performed by flicking the beads to and fro. Rather than ten beads in each column, the Chinese abacus uses five ‘unit’ beads and two ‘five’ beads (1 and 2). The Japanese abacus has just four ‘unit’ beads and one ‘five’ in each column (3).

Photography by Carlos Dorce

Photography by Carlos Dorce

The next Arithmetical instrument was made in the 18th century for counting. Addition was performed by turning the brass discs but since there isn’t no mechanism it was up to the user to carry tens:

Photography by Carlos Dorce

Photography by Carlos Dorce

I am going to finish this post with this reproduction of the Measurers by the Baroque painter Van Balen (1575 – 17 July 1632) which can be seen upstairs:

The Measurers. Hendrick van Balen

Location: The Museum of the History of Science (map)

The Pitt Rivers Museum

The Pitt Rivers Museum Photography by Carlos Dorce

The Pitt Rivers Museum
Photography by Carlos Dorce

The Pitt Rivers Museum cares for the University of Oxford’s collection of anthropology and world archaeology. It is next to the Oxford University Museum of Natural History which was closed in August and it was very surprising for me and also for my kids (I think it’s an idela museum for children!).

Photography by Carlos Dorce

Photography by Carlos Dorce

There are some interesting mathematical objects in the collection and I am going to list some of them. First of all, we must focus our interest in the showcase dedicated to “counting”:

Photography by Carlos Dorce

Photography by Carlos Dorce

There are some old counting strings:

Photography by Carlos Dorce

Photography by Carlos Dorce

and this “swampan”:

Photography by Carlos Dorce

Photography by Carlos Dorce

“Swampan” or calculating board with sliding beads, used in casting accounts. The two upper balls on each bar = 5 each, the lower balls = units, similar to the roman abacus. China.

There also is the typical “soroban” which is next to a icture of a Roman abacus and in the upper right corner of the next picture:

Photography by Carlos Dorce

Photography by Carlos Dorce

“Soroban” or calculating board for casting accounts, similar to and derived from the Chinese “swampan”. Japan.

There is also a picture of a “quipu”.

There also are astrolabes and clocks. For example, there are a brass astrolabe dated in 1673 and sme interesting portable sundials:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally there is some showcases dedicated to games, dice, chess,… in the upper floor:

Photography by Carlos Dorce

Photography by Carlos Dorce

Before finishing this post, look at the next picture and try to guess who is this great man:

Photography by Carlos Dorce

Photography by Carlos Dorce

The Oxford University Museum of Natural History was closed but it was possible to walk around the inner yard and it was possible to see one of the famous statues dedicated to the great scientific men. So it was possible to take a photography of Gottfried Wilhelm Leibniz!

Location: Pitt Rivers Museum (map)

Two traders counting money

Photography by Carlos Dorce

Photography by Carlos Dorce

Here we have the representation of two traders counting coins with a balance above them. This is a little picture that you can find in the building located in Nygade Street nr 1 in Copenhagen.

Location: Nygade 1 (map)

A capital in Doge’s Palace in Venice

Doge's palace Photography by Carlos Dorce

Doge’s palace
Photography by Carlos Dorce

Doge’s Palace in Piazza San Marco is one of the most touristic attractions of Venice. The palace (XIVth c.) is very beaytiful and there is a hidden mathematical secret in one of the capitals of its columns. The capitals of the columns of the palace are dedicated to some biblical passages, quotidian Medieval scenes and… there is one capital dedicated to the Liberal Arts!  So we can find here our famous three most representative figures of the Arithmetic, the Geometry and the Astronomy:

Pythagoras Photography by Carlos Dorce

Pythagoras
Photography by Carlos Dorce

Euclid Photography by Carlos Dorce

Euclid
Photography by Carlos Dorce

Venice08

Ptolemy
Photography by Carlos Dorce

Pythagoras is counting money and next to his coins we can read the number 1399 and Euclid has a compass in one of his hands. The column is the first one next to the corner in front of the sea:

Photography by Carlos Dorce

Photography by Carlos Dorce

You must see this column in Venice!

Location: Piazza San Marco (map)