Another interesting museum located in the Collegius Maius of the Jagiellonian University is an exhibition about mathematics where children can play and learn a lot! There are old calculators from the 20th century…
…abacus and slide rulers:
Children can play with Geography and learn that straight lines in a map are not the shortest ways for the planes:
They can also learn the theorem of Pythagoras scrolling this interesting figure:
There are polyhedra and a lot of geometrical and topological games:
The museum is very small but all the tourist are inside Collegius Maius so you can be very quiet watching all the exhibited objects and toys, like the Rodin’s Thinker:
Finally… here you have my two children playing with Eulerian graphs! They are lovely! Aren’t they?
Location: Collegius Maius (map)
Yesterday I didn’t remember to show Kircher’s Organum Mathematicum:
Organum Mathematicum was invented in 1661 by the Jesuit astronomer and mathematician Athanasius Kircher. This device is a comprehensive portable encyclopedia and is designed for the following disciplines: arithmetic, geometry, fortifications, chronology, gnomonics (sundials), astronomy, astrology, steganography (encoding) and music. The case contains tables for calculations without ‘tiring the mind’. Each of the nine disciplines contains 24 flat boards of different colours, with definitions and information.
This is Athanasius Kicher:
Of course, in the exhibition you can also find compasses, rules, abacus, slide rules, the Napier bones,…
…and calculators from the 20th century:
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:
There also are some interesting abacus like this one:
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.
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!
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…
or this other ivory set made from the 17th century:
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:
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:
Finally, a very curious mathematical object: this magic cube made by A. H. Frost in 1877:
Each row, each column and each diagonal have the same sum!
I must finished this wonderful walk for the calculating machines going downstairs to the groundfloor again and showing some instruments more. Number 41 is a calculating machine from c.1955 made by Bell Punch Company Limited and number 42 is the ‘Eckel dial rule’ from the same year. The calculator number 51 is from 1955-1965.
Among the instruments which made our life more confortable there is also space for the sundials, clocks and quadrants. For example, look at this Gunter’s quadrant from the beginning of the 19th century:
One example of sundial is this inclining sundiel from 1800:
Finally, we notice this universal ring dial from the mid-eighteenth century. Sundials were still needed to set the clocks and watches that had superceded them as timekeepers:
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:
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:
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:
The groundfloor of the Science Museum is full of technical and scientific objects which change our world in the last centuries and we find some mathematical objects (of course!). For example, we can see some slide rules: Fuller’s slide rule from 1890 (nr.25), Boucher circular rule from c.1885 (nr.26), a celluloid slide rule for triangle-mesh-reinforced concrete slabs from c.1912 (nr.27) and an engineer’s combination rule from c.1870 (nr.28).
We also find the calculating machines which became popular after 1850 among bookkeepers, astronomers and engineer like this Trinks Brunsviga (c.1908-1914):
In 1870 the General Register Office purchased a DeColmar arithmometer -an early mechanical calculator- of this type, to analyse the census. By the end of the century, staff were also using slide rules:
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:
And more wooden models in this mathematical box:
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:
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:
Unsigned, English, c. 1679
Unsigned, English, 17th century?
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).
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:
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: