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invariant
invariant

No variable. A quantity or property is invariant in a transformation if it remains the same under the transformation. For example: the areas of flat shapes remain unchanged under certain transformations such as rotation, reflection, shear, and translation.

inverse
inverse m

Inverse. If a set with a binary operation defined on it has a neutral element i identity, then any element x that has another element 1- x that achieves i = -1 x*x is an inverse element. For example:

The inverse of +7 in the case of addition is 7-.

The inverse of 8 in the case of multiplication is 1/8.

The inverse of a matrix in the case of multiplication

And the inverse of a flat transformation "turn 90°. around (0,0)" is "turn -90° around (0,0)".

inversely
inversely

Inversely. Two quantities change in opposite ways if they are inversely proportional to each other.

involute
courbe ƒ développante

origin. The origin of the circle is a curve drawn by the end of a thread wound on a fixed coil when it is unwound at (keeping the thread taut all the time.
The distances d1, d2, d3, etc. equal 1/4, 1/2, 3/4, etc. circumference of the circle.

irrational number
nombre m irrationnel

Irrational number. An irrational number is a number that is not rational, i.e. it cannot be expressed as a fraction, or written in the correct form as a terminating decimal fraction.
For example: π, e, 2/, 3/, 1/7-.

All irrational numbers, together with all regional numbers, form the set of real numbers.
It can be shown that 2/ is an irrational number as follows:
We assume that 2/ is a rational number, i.e. a/b = 2 where this fraction has been completely reduced).

... 2=a2/b²

2=b2=a2 ..
Since 2ba is always even, a must be even, for example: a=2p.
.:. 2b2=4p2

b2=2p2 ..

Since 2p2 is always even, b must be even. Here we have shown that both a and b are even, which means that they have a common factor (divisor) of 2, and so the fraction alb is reduced to 2. This is a clear contradiction, and so the basic assumption that 2 can be expressed as a fraction must be incorrect.

isometric
isométrique

Scalar (trigonometric). Standard graph paper is paper lined with equilateral triangles instead of squares.

isometry
isométrie

Scalar. A scaling is a transformation in which all lengths remain invariant. For example, rotation, transformation, and reflection are all scalings. Shear and enlargement are not.

Scalings that maintain direction are also called direct scalings, while those that change direction are called "opposite".

Reflection (opposite)
Rotation (direct)
Translation (direct)