Educational blog

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Nouns, adjectives, and adverbs in Esperanto
Esperanto has an extremely simple system of nouns, adjectives, and adverbs. There are no grammatical genders (non-living things are not (...)
July 13, 2017 – Jakub MarianEsperanto
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Why not mij, vij, lij instead of ni, vi, ili in Esperanto?
Esperanto is a very logical language, with complex words derived from simple roots in a highly regular way. Why, then, is it not possible (...)
July 12, 2017 – Jakub MarianEsperanto
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‘Most everyone’ vs. ‘almost everyone’ in English
“Most everyone”, meaning “almost everyone”, is a colloquial phrase that became somewhat widespread in spoken American English, but the (...)
July 10, 2017 – Jakub MarianEnglish
How to calculate the factorial of 1/2
As I proved in my article on integration by parts (at the end), the factorial of a natural number $n$ can be calculated using the (...)
July 8, 2017 – Jakub MarianMathematics
Integral of $\log(x)$ (or $\ln(x)$)
The natural (base $e$) logarithm is usually denoted $\log(x)$ in mathematics, but for the sake of students of other disciplines, we will (...)
July 7, 2017 – Jakub MarianMathematics
Explanation of integration by parts
Integration by parts is one of the first methods people learn in calculus courses. Together with integration by substitution, it will (...)
July 6, 2017 – Jakub MarianMathematics
‘July’ in European languages
July, the seventh month of the year, was named iūlius by the Roman Senate in honour of the Julius Caesar, and the Latin name spread to (...)
July 5, 2017 – Jakub MarianMaps
A simple way to create “radiating waves” in Photoshop
There’s a technique I found about recently that I wanted to share with my readers. There is a simple way to create an impression of (...)
July 4, 2017 – Jakub MarianVisual arts
Integral of $\sin^3(x)$
Integrating the third power of $\sin(x)$ (or any odd power, for that matter), is an easy task (unlike $∫ \sin^2(x)\,dx$, which requires (...)
July 4, 2017 – Jakub MarianMathematics
Integral of $\sin^2(x)$
The integral can be calculated using integration by parts (remember that $∫u’(x)v(x)\,dx = u(x)v(x) - ∫ u(x)v’(x)\,dx$): $$ ∫ (...)
July 3, 2017 – Jakub MarianMathematics