Basic Diagramming

"In mathematics, the Euclidean algorithm, or Euclid's algorithm, is a method for computing the greatest common divisor (GCD) of two (usually positive) integers, also known as the greatest common factor (GCF) or highest common factor (HCF). ...
The GCD of two positive integers is the largest integer that divides both of them without leaving a remainder (the GCD of two integers in general is defined in a more subtle way).
In its simplest form, Euclid's algorithm starts with a pair of positive integers, and forms a new pair that consists of the smaller number and the difference between the larger and smaller numbers. The process repeats until the numbers in the pair are equal. That number then is the greatest common divisor of the original pair of integers.
The main principle is that the GCD does not change if the smaller number is subtracted from the larger number. ... Since the larger of the two numbers is reduced, repeating this process gives successively smaller numbers, so this repetition will necessarily stop sooner or later - when the numbers are equal (if the process is attempted once more, one of the numbers will become 0)." [Euclidean algorithm. Wikipedia]
The flowchart example "Euclidean algorithm" was created using the ConceptDraw PRO diagramming and vector drawing software extended with the Mathematics solution from the Science and Education area of ConceptDraw Solution Park.

"In elementary algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form
ax^2+bx+c=0
where x represents an unknown, and a, b, and c are constants with a not equal to 0. If a = 0, then the equation is linear, not quadratic. The constants a, b, and c are called, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.
Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation, and in particular it is a second degree polynomial equation since the greatest power is two.
Quadratic equations can be solved by a process known in American English as factoring and in other varieties of English as factorising, by completing the square, by using the quadratic formula, or by graphing." [Quadratic equation. Wikipedia]
The flowchart example "Solving quadratic equation algorithm" was created using the ConceptDraw PRO diagramming and vector drawing software extended with the Mathematics solution from the Science and Education area of ConceptDraw Solution Park.

This work flow chart sample was redesigned from the picture "Weather Forecast" from the article "Simulation Workflows".
[iaas.uni-stuttgart.de/ forschung/ projects/ simtech/ sim-workflows.php]
"(1) The weather is predicted for a particular geological area. Hence, the workflow is fed with a model of the geophysical environment of ground, air and water for a requested area.
(2) Over a specified period of time (e.g. 6 hours) several different variables are measured and observed. Ground stations, ships, airplanes, weather balloons, satellites and buoys measure the air pressure, air/ water temperature, wind velocity, air humidity, vertical temperature profiles, cloud velocity, rain fall, and more.
(3) This data needs to be collected from the different sources and stored for later access.
(4) The collected data is analyzed and transformed into a common format (e.g. Fahrenheit to Celsius scale). The normalized values are used to create the current state of the atmosphere.
(5) Then, a numerical weather forecast is made based on mathematical-physical models (e.g. GFS - Global Forecast System, UKMO - United Kingdom MOdel, GME - global model of Deutscher Wetterdienst). The environmental area needs to be discretized beforehand using grid cells. The physical parameters measured in Step 2 are exposed in 3D space as timely function. This leads to a system of partial differential equations reflecting the physical relations that is solved numerically.
(6) The results of the numerical models are complemented with a statistical interpretation (e.g. with MOS - Model-Output-Statistics). That means the forecast result of the numerical models is compared to statistical weather data. Known forecast failures are corrected.
(7) The numerical post-processing is done with DMO (Direct Model Output): the numerical results are interpolated for specific geological locations.
(8) Additionally, a statistical post-processing step removes failures of measuring devices (e.g. using KALMAN filters).
(9) The statistical interpretation and the numerical results are then observed and interpreted by meteorologists based on their subjective experiences.
(10) Finally, the weather forecast is visualized and presented to interested people." [iaas.uni-stuttgart.de/ forschung/ projects/ simtech/ sim-workflows.php]
The example "Workflow diagram - Weather forecast" was drawn using the ConceptDraw PRO diagramming and vector drawing software extended with the Workflow Diagrams solution from the Business Processes area of ConceptDraw Solution Park.