Vector Calculus :
This is a scalar field and its gradient.
The RED arrows represent the direction and intensity of change in the scalar field
The arrow points in the direction where the value (like temperature or height) increases the fastest

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In any triangle, the point where the perpendicular bisectors of the sides intersect is the center of the circumscribed circle

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When you apply the function z→z² to a grid in the complex plane, the grid lines transform into curves. The vertical and horizontal lines become parabolas or hyperbolas, depending on their orientation with respect to the real axis.

The NumPy module in Python facilitates manipulation of complex numbers

This illustration was created using Matplotlib

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A scalar field is a function that assigns a scalar value to each point in space. For example, temperature can be considered a scalar field, where every point in space is associated with a specific temperature value.
This scalar value can be represented using a color gradient.

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#physics

Let f be a function from a set A to a set B.
f is a :
- injection if and only if f(x)=f(y) implies x=y.
- surjection if and only if for every y in B, there exists an x in A such that f(x)=y.
- a bijection if and only if f is injective and surjective

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#sets
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Electromagnetism : a 2D electric field generated by two electric charges of the same sign .

Illustration created with python

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#python

Let f be a function from a set A to a set B.
f is a :
- injection if and only if f(x)=f(y) implies x=y.
- surjection if and only if for every y in B, there exists an x in A such that f(x)=y.
- a bijection if and only if f is injective and surjective

Identify the non injective surjection, the non surjective injection, the bijection, and the function that is neither surjective nor injective, in this illustration ( done with python )

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#function
#sets
#illustration
#python

Pascal's Theorem states that if a hexagon is inscribed in a conic section (such as an ellipse), then the three intersection points of the pairs of opposite sides of the hexagon are collinear (they lie on a straight line )

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#geometry
#illustration