#euler

One day, one decomposition
A179188: Numbers n such that phi(n) = phi(n+6), with Euler's totient function phi=A000010

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A179188.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A179188.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #Euler #totient #function #graph #threejs #webGL

One day, one decomposition
A179186: Numbers n such that phi(n) = phi(n+4), with Euler's totient function phi=A000010

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A179186.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A179186.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #Euler #totient #function #graph #threejs #webGL

Euler–Mascheroni constant!

In fact, the last one is:
\[\large\displaystyle\int_1^{+\infty}\mathrm dx\ \left(\frac{1}{\lfloor x\rfloor}-\frac1x\right)=\gamma\approx0.5772156649\]

Equivalently,
\[\large\displaystyle\lim_{n\to\infty}\left(\sum_{k=1}^n \frac1{k}-\ln n\right)=\gamma=0.5772156649\ldots\]
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Unsolved problem in mathematics:
Is Euler–Mascheroni constant irrational? If so, is it transcendental?

#Euler #Mascheroni #EulerMascheroni #Constant #gamma #EulerConstant #EulersConstant #EulerMascheroniConstant #Irrational #Irrationality #Transcendental #Transcendence #Unsolved #UnsolvedProblem #Maths #Mathematics #Indeterminate #IndeterminateForm #IndeterminateForms #Inf #Infinity #HarmonicNumber #HarmonicNumbers #HarmonicSeries #Logarithm #Log #Logarithms #NaturalLogarithm #Integral #ImproperIntegral

The #Euclid-#Euler #Theorem is a fundamental theorem in #NumberTheory that beautifully connects #PerfectNumbers with #Mersenne #Primes.

https://knowledgezone.co.in/kbits/679340ac379a5d09cb2d1a93

@Erklaerbaer
Im Ernst schau dir den Unterricht an der zbsp an der Schule (Gymnasium Eifel Kreis Euskirchen) unserer Kids abläuft. Da wundert es dich kaum noch, wenn die Lücken haben.
Es fehlen häufig so viele Lehrkräfte das es wundert dass der Schulbetrieb aufrecht erhalten werden kann.

#Fermat #Euler #Euklid

Ich musste letzte Woche meinen 4. Semester Informatik Studierenden den kleinen Satz von #Fermat, #Euler sche Phi-Funktion und den erweiterten Satz von #Euklid erklären. Was machen die denn in den Mathevorlesungen? Oder im Mathe-Abi?

One day, one decomposition
A145292: Composite numbers generated by the Euler polynomial x^2 + x + 41

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A145292.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A145292.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #composite #numbers #generated #Euler #polynomial #graph #threejs #webGL

> Euler’s work touched upon so many fields that he is often the earliest written reference on a given matter. In an effort to avoid naming everything after Euler, some discoveries and theorems are attributed to the first person to have proved them after Euler.

https://en.wikipedia.org/wiki/List_of_things_named_after_Leonhard_Euler

#euler #til

> .. the problem out of which the calculus took shape was therefore essentially practical.. to adjust the stakes in a game of chance.. with a rule which ensures success if applied consistently.. This is the theme song of the later treatise ( #ArsConjectandi, i.e. #ArtOfGuesswork) by #JamesBernoulli (1713) and it was the major pre-occupation of all the writers of what one may call the classical period, i.e. de Moivre, D. #Bernoulli, d’Alembert, and #Euler.
@bsmall2@mstdn.jp

Tomorrow, a small group of mathematicians realize that Euler's Identity has subtly changed. Scientific communities all over the world crack into factions, the majority believing that Euler's identity has not changed at all, others that the iconic proof was always incorrect, and a smaller yet very frightened faction left puzzled by how a mathematical invariant like the concept of 1 or an imaginary number can morph from one day to the next, and how the entirety of mathematics and physics must now be different. Yet, tragically, the world will refuse to change with it.

#microfiction #euler #mathematics https://en.m.wikipedia.org/wiki/Euler%27s_identity

Letters of Euler to a German princess, on different subjects in physics and philosophy

https://openlibrary.org/books/OL17328039M/Letters_of_Euler_to_a_German_princess_on_different_subjects_in_physics_and_philosophy

#math #euler

This is an interesting problem in #ClassicalMechanics and exercised luminaries like #Newton and #Euler. I think the latter's use of the #CalculusOfVariations is a stroke of genius.

#MyWork #CCBYSA #Mathematics #Maths #AppliedMathematics #Physics #Calculus

Came in during bedtime routine to hear Flip asking his dad what #Euler's totient function is. Dude. How high do grade levels on Twinkl go for maths?

Variation On The Euler Diagram-Map Of The British Isles
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https://commons.wikimedia.org/wiki/File:British_Isles_Euler_diagram_15.svg <-- wiki page
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https://en.wikipedia.org/wiki/Euler_diagram <-- wiki background to euler diagrams
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Helps in naming of certain groupings of islands, although it might be seen as a controversial groupings for some…
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“An Euler diagram is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining complex hierarchies and overlapping definitions. They are similar to another set diagramming technique, Venn diagrams. Unlike Venn diagrams, which show all possible relations between different sets, the Euler diagram shows only relevant relationships…”
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#GIS #spatial #mapping #euler #eulerdiagram #gischat #map #relationship #knowledgegraph #sets #relationships #venndiagram #UK #BritishIsles

How Euler Did It, by Ed Sandifer
http://eulerarchive.maa.org/hedi/index.html
#ycombinator #euler #works #euler_archive #opera_omnia #life #biography #mathematics

How Euler did it? (by Ed Sandifer)
http://eulerarchive.maa.org/hedi/index.html
#ycombinator #euler #works #euler_archive #opera_omnia #life #biography #mathematics

"Euler calculait sans aucun effort apparent, comme les hommes respirent, comme les aigles se soutiennent dans les airs." – François Arago (1786-1853)
#citation #mathématiques #maths #math #Euler

"Euler calculated without any apparent effort, as men breathe, as eagles sustain themselves in the air." – François Arago (1786-1853)
#quote #mathematics #maths #math #Euler