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.

Pressure is directly tied to the microscopic behavior pf matter. Gas molecules collide with one another continuously. The mass of any single molecule is extremely small, but they are so numerous that collisions with the walls exert a force that pushes on those walls.  Pressure is the expression of this force per unit of surface area.

The smaller the volume, the more numerous are these collisions, and the greater the resulting pressure is.

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.

Why does each musical instrument have its own timbre?

Why does the same musical note played on two different instruments result in different auditory sensations?

The electrical signal produced by the microphone is a faithful image of the sound emitted by the loudspeaker. The oscilloscope shows us this signal as it changes over time. The signal is is periodic and its frequency corresponds to the pitch of the note.

A study of the frequencies, with the aid of a spectrum analyzer, enables us to represent the same signal in a different way.  It is thanks to this frequency analysis that we can explain the differences in timbre among musical instruments.

The force of lift, which enables an aircraft to fly, depends directly on the density of the air. Performance levels are always established according to a reference called the standard atmosphere.  Flight conditions being rarely standard, one has recourse to the density altitude in order to estimate the standard altitude (ISA) that has the same value as the density of the air you are in.

Contrary to what its name might lead you to believe, an altimeter does not directly measure altitude. It is a pressure measuring instrument used to estimate an altitude.

Its utilization requires calibration.

This animation shows an altimeter used in aviation. It is graduated in feet (1000 feet = 304.8 meters), and the pressures are in mb (millibars) or in inches (in) of Mercury.

An adjustment enables one to make an altitude correction.  See the Student Sheet for a simulation of its utilization in navigation by an aircraft.

A balance is used to measure the mass of an object. This animation is a game where the player is asked to find the weight of an object.