Guess Solutions of Polynomials

For a given polynomial of $n$th degree

$$P_n(x)=\sum_{i=0}^n a_ix^i = a_nx^n+a_{n-1}x^{n-1}+…+a_1x+a_0$$

you can guess rational solutions $x$ for the corresponding problem $P_n(x)=0$ by applying the following two rules:

  1. $$x=\frac{p}{q}\text{, with } p \in \mathbb{Z} \land q \in \mathbb{N}\land p\mid a_0 \land q\mid a_n$$
  2. $$\lvert x\rvert\le2\cdot \max\left\lbrace \sqrt[k]{\frac{\lvert a_{n-k}\rvert}{\lvert a_n\rvert}}, k=1, …, n\right\rbrace$$

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Get into Orbit Without Lateral Acceleration

When I was about 6 years old, my dad explained to me that there was no possibility to shoot something right into orbit from the Earth’s surface. He said it was always necessary to accelerate sideways to reach orbit. At that time I did not really understand what he meant. However, later in physics class I did and I figured what he had told me was true. Now, 13 years later, I came up with a new thought: The Earth’s rotation adds lateral velocity to objects launched from its surface. This is also the reason why satellites, the ISS and pretty much every artificial object flying around Earth, orbits Earth counterclockwise and also, why most space flight organizations / companies launch their spacecrafts from locations as close to the equator as possible. Continue reading Get into Orbit Without Lateral Acceleration

Die drei ??? Telegram Bot

Since the publisher Europa uploads new Die drei ??? episodes on Spotify quite frequently, I have been wanting to get an update every time they upload something new. For me the most convenient way to be notified is to get a message on my smartphone. The free messenger Telegram is predestinated for that task because of its open API and bot capabilities. Continue reading Die drei ??? Telegram Bot

ABAP Objects Quick Reference

This is the second (and final) part of a quick reference for the programming language ABAP. Extending the first part, this one is primarily focusing on ABAP’s object oriented programming features, like classes, OOP-exceptions, and inheritance.

The first part can be found here: ABAP Quick Reference

Encapsulation using function groups
FUNCTION-POOL s_person.

* age is a global variable in the function-pool
DATA: age TYPE i.

FUNCTION inc_age.
  ADD 1 to age.
ENDFUNCTION.

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ABAP Quick Reference

This is the first of two posts, providing a quick reference for ABAP developers. It primarily consists of code examples and doesn’t include major object oriented programming features, introduced in newer language versions.

The second part of this series, targeting OOP related topics, can be found here: ABAP Objects Quick Reference

ABAP (Advanced Business Application Programming) is a high-level programming language created by the German software company SAP SE. It is currently positioned, alongside Java, as the language for programming the SAP Application Server, which is part of the NetWeaver platform for building business applications.
Wikipedia ABAP article

Basic program structure
PARAMETERS pa_num TYPE i.

* declare a variable
DATA gv_output TYPE i.

* assign value from pa_num to gv_output
MOVE pa_num TO gv_output.

WRITE: 'Input value', gv_output.

NEW-LINE. " this is an inline comment

WRITE 'Done'.

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Trigonometric Functions Formulary

This formulary has been created during the online onboarding process at Baden-Wuerttemberg Cooperative State University (DHBW). It is suitable for the related online tests and might be helpful for other people, seeking for formulas in this field of mathematics.

Basics

$$\begin{array}{l} \tan x = \frac{{\sin x}}{{\cos x}}\\ \cot x = {\tan ^{ – 1}}x = \frac{{\cos x}}{{\sin x}} \end{array}$$ Continue reading Trigonometric Functions Formulary

Node.js: Develop on Mac, Run on Raspberry Pi

For me the solution for productive Node.js development on Mac, with code execution on a Raspberry Pi was usage of Samba. After following the steps you will be able to develop Node.js applications right on your Mac, execute them on your Raspberry Pi (just by pressing cmd+S) and see the console output and errors on your Mac, without much hassle. This tutorial covers the entire setup. Continue reading Node.js: Develop on Mac, Run on Raspberry Pi

Periodic Table Trainer (Android Wear)

Memorize the Elements of the Periodic Table Right on Your Wrist

This Android Wear app shows the chemical elements of the periodic table. Starting with Hydrogen you can continue with a simple tap on the center of the screen. Before you do that, you should think of the name of the following element. What comes after Hydrogen (H)? Continue reading Periodic Table Trainer (Android Wear)