Stereographic Projection 🗺

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point: the projection point. Where it is defined, the mapping is smooth and bijective. It is conformal, meaning that it preserves angles at which curves meet. It is neither isometric nor area-preserving: that is, it preserves neither distances nor the areas of figures.

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Dào Dé Jīng 📖

The Dào (道) that can be told of is not an Unvarying Way. The names that can be named are not unvarying names. It was from the Nameless that Heaven and Earth sprang; The named is but the mother that rears the ten thousand creatures, each after its kind. Truly, ‘Only he that rids himself forever of desire can see the Secret Essences’; He that has never rid himself of desire can see only the Outcomes. These two things issued from the same mould, but nevertheless are different in name. This same mould we can but call the Mystery, Or rather the Darker than any Mystery, The Doorway whence issued all Secret Essences.

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Logic Gate 🪫

A logic gate is an idealized model of computation or physical electronic device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has for instance zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device (see Ideal and real op-amps for comparison).

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Microservices 🔗

Microservice architecture – a variant of the service-oriented architecture (SOA) structural style – arranges an application as a collection of loosely coupled services. In a microservices architecture, services are fine-grained and the protocols are lightweight.

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CPU 💻

A central processing unit (CPU), also called a central processor,main processor or just processor, is the electronic circuitry within a computer that executes instructions that make up a computer program. The CPU performs basic arithmetic, logic, controlling, and input/output (I/O) operations specified by the instructions in the program. This contrasts with external components such as main memory and I/O circuitry, and specialized processors such as graphics processing units (GPUs).

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Gas Station ⛽

A gas station, also known as a filling station, fueling station, service station or petrol station is a facility which sells fuel and lubricants for motor vehicles. The most common fuels sold are gasoline (petrol) or diesel fuel. Many gas stations have a convenience store close to the pumps, to make extra earnings. Some have tunnel car washs.

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Formulas (1948-1994) 🧮

1948$$H(S) \leqslant m(S) \leqslant H(S) + 1$$ The mathematician Claude Shannon introduced the entropy in information theory in 1948. Entropy in information theory can be defined as the expected number of bits of information contained in an event. For instance, tossing a fair coin has the entropy of 1. It is because of the probability of having a head or tail is 0.5. The amount of information required to identify it’s head or tail is one by asking one, yes or no question — “is it head ? or is it tail?”. If the entropy is higher, that means we need more information to represent an event. Now, we can say that entropy increases with increases in uncertainty. Another example is that crossing the street has less number of information required to represent / store / communicate than playing a poker game.

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Formulas (1901-1927) 🧮

1901$$\begin{array}{c}P\left(\frac{X_{1}+X_{2}+\cdots+X_{n}-n_{\mu}}{\sigma \sqrt{n}} \leq x\right) \\rightarrow \\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{x} e^{-t^{2} / 2} d t\end{array}$$ Lyapunov’s theorem in probability theory is a theorem that establishes very general sufficient conditions for the convergence of the distributions of sums of independent random variables to the normal distribution. Lyapunov functions (also called the Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory. A similar concept appears in the theory of general state space Markov chains, usually under the name Foster–Lyapunov functions.

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Formulas (1825-1896) 🧮

1825$$\oint_{\gamma} f(z) d z=0$$ Cauchy’s integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk, and it provides integral formulas for all derivatives of a holomorphic function. Cauchy’s formula shows that, in complex analysis, “differentiation is equivalent to integration”: complex differentiation, like integration, behaves well under uniform limits – a result that does not hold in real analysis.

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Formulas (1500-1799) 🧮

1500$$\begin{aligned}&x^{3} + mx = n\&\Rightarrow\&x=\sqrt[3]{\sqrt{\frac{n^{2}}{4}+\frac{m^{3}}{27}}+\frac{n}{2}}-\sqrt[3]{\sqrt{\frac{n^{2}}{4}+\frac{m^{3}}{27}}-\frac{n}{2}}\end{aligned}$$ At some point in the early 1500’s, an Italian mathematician named Scipione del Ferro determined a general solution for what is known as the depressed cubic equation. This is cubic equation without any $x^{2}$ terms. The general form is : $x^{3} + mx = n$ . As it turns out, any cubic equation of the form $x^{3} + bx^{2} + cx + d = 0$ can be written as a depressed cubic, but that came later.

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