Mathmatical Objects of Mystery

(Above) DRAWING MADE FROM SPIROGRAPH, 1975:
A pattern drawn using a Spirograph, a popular graphic toy used to draw any combination of curves.


(Above) CONSUL THE EDUCATED MONKEY, 1916
Above is a mathematical toy calculator patented by William Robertson and made by the Educational Novelty Company of Dayton, Ohio, USA. This is an early example of a mathematical toy. When each of the monkey’s feet are moved to point at two numbers, the monkey’s hands move to indicate the product.


(Above) MAGIC BRAIN CALCULATOR, C. 1955:
“Magic Brain” calculator made by Chadwick in tin and plastic, with stylus and instructions. c. 1955. Very similar to the Exaxctus and other stylus calculators of the period, the Magic Brain could add, subtract, and multiply and divide by repeated addition and subtraction.


(Above) FACE-CENTERED CUBIC PACKING MODEL, 1975:
This model, made from ping-pong balls, represents an example of ‘face-centered cubic packing,’ a structural form which occurs in crystals.


(Above) CIRCULAR SLIDE RULE, 1660 - 1680:
A circular slide rule, made by John Brown in 166o, with two brass radial arms and an astronomical quadrant engraved on the back. A spiral slide rule affords a long and therefore accurate logarithmic line in a small amount of space. The potential of spiral rules was not really utilized until the Victorian period, when several spiral and helical designs appeared on the market.


(Above) ARITHMETICAL JEWEL, 1619
The ‘Arithmetical Jewel’ was invented and publicized by William Pratt in 1619. This instrument combines features of the abacus with pen reckoning. Numbers are put in by moving the flags to reveal dots. Sums are then worked out with a pen and paper.



(Above) LATE 19th CENTURY ‘CHUCKRUM BOARD’ FROM INDIA:
This item is called a Chuckrum board with 108 small coins. This board was used to count 100 small ‘chuckrum’ coins rapidly by spreading them over the surface to fill the holes.

(Above) ROBERTSON’S RAPID CALCULATOR:
This odd contraption was made by the Robertson Rapid Calculator Company of Glasgow, and was one of several large-scale ready reckoners to be developed in the first decade of the 20th century. This form of ready reckoner placed the tables of numbers on four rollers, each one of which was likened to ‘a book with 200 or 300 pages open at the one time’. It gave the cost of various quantities of goods at various prices per pound, hundredweight or ton.



(Above) NAPIER’S BONES:
John Napier (1550-1617), discoverer of logarithms, also created this popular calculating tool known as Napier’s bones or rods. Napier’s bones reduced muliplication to a sequence of simple additions; division and square roots could also be achieved. This example consists of a wooden box containing ten rotating cylinders each of which bears the numbers ‘0 times’ to ‘9 times’. The inside of the lid is inscribed; “This box was the identical property of the author of ye Logs, Napier 1824”. This type of Napier‘s bones was first published by Gaspard Schott in 1668, so it is unlikely that they were actually the property of the inventor.



(Above) PLASTER SURFACE MODEL:
Alexander Crum Brown (1838-1922), mathematician and chemist, was professor of mathematics at Edinburgh University and a prolific maker of mathematical models. This surface represents the equation: z=3a(x squared - y squared) - (x cubed + y cubed). Every section made by a plane passing through the blue line and cutting the surface is an ellipse.



I THINK I HAVE SPOKEN BEFORE AT HOW TERRIBLE I WAS AT MATH WHEN I WAS GROWING UP. Numbers both terrified me and intrigued me. When I found these images and descriptions of early calculating devices, I thought how interesting it would be to peer into the world of mathematics, my old arch enemy. All of the things you see above, some going back to the 1600’s, we invented to help figure out complicated and complex methods of counting, figuring out the abstract nature of the universe, and those things beyond the grasp of our mind alone.

I also look at these objects as things of wonder. Other than the more recent items, most of us would have a difficult time trying to figure out what one of these machines was used for if we came across it at an estate sale or antique store. We would probably guess it was for calculating, but that might be as far as we get. The passage of time can erase the previous understanding if it is not handed down or passed on. Today, there are many “things” in museums whose use or purpose is not fully understood.

All of these wonderful objects were found in the Science Museum located in the U.K.