This animation represents the Japanese abacus (soroban). Balls are strung along rods (columns). Each rod corresponds, going from right to left, to ones, tens, hundreds, thousands…

The upper balls have a value of 5. The lower ones have a value of 1. In other words, an upper ball on the third rod from the right has a value of 5 hundreds (500).

A lower ball on the second rod from the right has a value of ten (10).

A ball is only counted when it has been moved  down to the transverse (horizontal) bar.

The principle of the abacus has been known since the 3^rd millenium BCE (the Mesopotamians). It enables one to carry out simple operations like additions and subtractions, but, in expert hands, the abacus can also be used to carry out multiplications, divisions, and even the calculation of roots.

This animation represents the Japanese abacus (soroban). Balls are strung along rods (columns). Each rod corresponds, going from right to left, to ones, tens, hundreds, thousands…

The upper balls have a value of 5. The lower ones have a value of 1. In other words, an upper ball on the third rod from the right has a value of 5 hundreds (500).

A lower ball on the second rod from the right has a value of ten (10).

A ball is only counted when it has been moved  down to the transverse (horizontal) bar.

The principle of the abacus has been known since the 3^rd millenium BCE (the Mesopotamians). It enables one to carry out simple operations like additions and subtractions, but, in expert hands, the abacus can also be used to carry out multiplications, divisions, and even the calculation of roots.

The soroban is a descendant of the Chinese abacus (suanpan), but it has one less ball on both the upper and lower levels. The soroban is still in widespread use among the Japanese. It can be found in all of their schools, because it is very visual tool for illustrating the principles of the base ten (decimal) numeral  system.  Moreover, one frequently sees merchants verifying their calculations with a soroban,  placed just beneath the cash register.

On November 12,  1946, a competition was held  that set a soroban expert in opposition to someone using one of the first electronic calculators.  The soroban won, 4 trials to 1.

It is very impressive to watch the Japanese perform anzan (blind calculation). With a lot of training, a soroban expert can obtain a mental picture of his tool and perform complex calculations by running his fingers over an imaginary soroban.

Animation produced in collaboration with the Musée des Arts et Metiers - Paris.

The arithmetic machine created by Blaise Pascale (1623-1662) - the Pascaline - was one of the first mechanical calculating devices (first model 1642). It's a calculating machine because the carrying over across places occurs automatically.

It enables one to directly add and subtract.  It is also possible to multiply and divide using successive additions and subtractions.

"Consul - the educated monkey" was originally produced from 1916 - 1918 by the Educational Novelty Co, 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 hands move to indicate the product.

Brought to you in cooperation with the Musée des Arts et Metiers - Paris.

The principle of operation of all mechanical clocks rests  on the combination of the following three functions:

• A source of energy that can produce rotary motion (here, a driving weight)
• A regulator:  A pendulum measures time precisely and without variations. The escapement system , linked to the pendulum,  enables control of the rate of energy release.
• A display:  graduations and needles ("hands") provide access to the measured information.

Escapements generally use an anchor, as shown in this animation. For small angles (<5°) of oscillation of the pendulum, one approaches the condition of isochronism:  the pendulum's period depends practically exclusively on local gravitational conditions and the length of the pendulum (bit not on either the mass of the pendulum or the amplitudes of its oscillations).  For example, in Paris, a meter long pendulum has a period of two seconds. Lengthening the pendulum increases its period of oscillation.

The digitization of an analogue signal is carried out by taking several samples and translating them into binary code.  The series of codes thus obtained are then regrouped in a digital file. The advantage of such digitization lies in the ability of such file formats to undergo processing  by a computer.  In order to obtain a digitization that corresponds to the original analogue signal one must gain precision. To do this, it is sufficient to increase the sampling frequency and decrease the pace of quantization.

This animation illustrates the negative powers of ten. Starting with one meter, we delve successively  into matter until we reach  objects in the range of a nanometer.
A correspondence between exponential notation and units of measurement (millimeter, micrometer, nanometer, angstrom) is demonstrated.

The width of an image divided by its height is known as the aspect ratio of the image.
the aspect ratio of a traditional TV screen is 4:3 but some high definition movies prefer the 16:9 standard.

This is a simple vector construction animation. Click and draw three vectors then drag them around the plane. The distance between the two end points (norm) of each vector is automatically shown.