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Academia - Collins - Pocket Scientific Dictionaries - Mathematics - English - French - Arabic Letter 3_ S

sequence
suite f

Sequence. A set of quantities, usually ordered numbers ...,a1,a2,a3 such that each number in the sequence corresponds to a specific natural number. Sequences are sometimes specified by a formula such as 1 - 2n2=an which gives the sequence .....1.7.17. Sequences can also be specified inductively by linking each term to its predecessors such as n=3an-1+1 and a1=1
gives the sequence 1,4,13,40....
The number of terms in sequences can be finite or infinite.

series
série f

Series. The sum of finite or infinite numbers of
:terms, such as +a1+a2+a3...

The study of a series and the associated properties of sums and limits is an important branch of pure mathematics.

The sum of n terms of a series of terms in an arithmetic progression

a + ( a + d ) + ( a + 2d ) + ( a + 3d ) ...
is: n/2 ( 2a + [ n - 1 ] d )

And the sum of n terms of a series of terms in a geometric progression

a+ar+a2+ar...
is: r -1/a ( 1 - r n ) .

set
ensemble m

A set. A collection of distinct objects or things. The set contains members and elements, which can be finite or infinite in number.

The symbol { } means "set", while the symbol = means "member of" or "belongs to".

Sets can be identified by listing or describing their elements.
They are often indicated by a capital letter. For example:

Even numbers = E and 4EE.
iEv, v = { a, e, i, o, u }

sexagesimal
sexagésimal

sexagesimal. A system related to base 60. For example: the general system for measuring angle degrees is the sexagesimal system.

360 degrees = one revolution
60 minutes = one degree
60 seconds = one minute

shear
cisallement m

Cut. A transformation in which a line (two-dimensional) or a three-dimensional plane remains fixed while other points parallel to the fixed line or plane move to a distance proportional to their distance from the line or plane.

The area of ​​a closed figure in a plane remains invariant in shear. Likewise, the volume of a solid remains invariant in shear.

Shear with invariant lines or planes can be represented across the origin by matrices, for example:

represents a shear in an x-y plane with the y-axis fixed. Different geometric and spatial properties of shapes can be explored using shear information.

The area of ​​a parallelogram
is equal to the area of ​​a rectangle in shear.

side
coté m

side. A polygon side is a straight line segment that forms part of the boundary of a figure.

For example: A quadrilateral has four sides.

sieve (of Eratosthenes)
crible m

sieve (of Eratosthenes). An ancient process of finding prime numbers by extracting the natural numbers (multiples of 2...4,6,8) first, then extracting the multiples of 3, then the multiples of 5... and so on, leaving aside the prime numbers.

sigma
sigma

Sigma. A letter of the Greek alphabet. The capital letter is represented by Σ and the lower case by α.

The first of these two symbols is often used to mean addition. For example:

Σ ai = a1 + a2 + a3 + a4 + a5

Σ i2 = 12+22+ 32+42=30

The lower case letter α is often used to mean the standard deviation of a distribution in statistics.

sign
signe f

Sign. A notation used to indicate that a quantity is positive or negative. The positive sign is + and the negative is –.

The sign is also used in relation to symbols representing various operations and mathematical relationships. For example: the multiplication sign ×, the equal sign =, and the square root sign 1.