#bernoulli — Public Fediverse posts

#LucioRusso (22 November 1944 – 12 July 2025) was an Italian physicist, mathematician and historian of science. Born in #Venice, he taught at the Mathematics Department of the #UniversityOfRomeTorVergata. He died in Bologna on 12 July 2025, at the age of 80. Among his main areas of interest were #GibbsMeasure of the #IsingModel, #percolationTheory, and finite #Bernoulli schemes, within which he proved an approximate version of the classical #KolmogorovsZerooneLaw. In the history of science.

Johann Bernoulli (= Jean; 1667–1748) posed the problem of finding the ‘brachistochrone’: the curve between two points along which a body starting from rest at the higher point and freely accelerated by uniform gravity would descend in minimum time to the lower.

Gottfried Wilhelm Leibniz (1646–1716) thought the problem beautiful; so did Guillaume de l’Hospital (1661–1704).

Bernoulli (and others) proved that the brachistochrone was again an inverted cycloid. He thought that the equality of the cycloid, tautochrone, and brachistochrone curve would leave his readers ‘petrified with astonishment’, and thought that it suggested some deep design in nature.

One of Bernoulli's proofs was what he considered a ‘very beautiful’ geometric demonstration that the cycloid was the brachistochrone.

But he did not publish it until 20 years later. Why? Apparently in part due to Leibniz, who had thought it so beautiful and extraordinary that he counselled against publication, with the aim of ‘so frustrating those who are not very grateful and who are accustomed to profiting from the inventions of others’.

**Here, mathematical beauty contributed to the suppression, albeit temporary, of mathematical knowledge.**

2/3

#Bernoulli #JohannBernoulli #JeanBernoulli #brachistochrone #Leibniz

Johann Bernoulli (= Jean; 1667–1748) posed the problem of finding the ‘brachistochrone’: the curve between two points along which a body starting from rest at the higher point and freely accelerated by uniform gravity would descend in minimum time to the lower.

Gottfried Wilhelm Leibniz (1646–1716) thought the problem beautiful; so did Guillaume de l’Hospital (1661–1704).

Bernoulli (and others) proved that the brachistochrone was again an inverted cycloid. He thought that the equality of the cycloid, tautochrone, and brachistochrone curve would leave his readers ‘petrified with astonishment’, and thought that it suggested some deep design in nature.

One of Bernoulli's proofs was what he considered a ‘very beautiful’ geometric demonstration that the cycloid was the brachistochrone.

But he did not publish it until 20 years later. Why? Apparently in part due to Leibniz, who had thought it so beautiful and extraordinary that he counselled against publication, with the aim of ‘so frustrating those who are not very grateful and who are accustomed to profiting from the inventions of others’.

**Here, mathematical beauty contributed to the suppression, albeit temporary, of mathematical knowledge.**

2/3

#Bernoulli #JohannBernoulli #JeanBernoulli #brachistochrone #Leibniz

Johann Bernoulli (= Jean; 1667–1748) posed the problem of finding the ‘brachistochrone’: the curve between two points along which a body starting from rest at the higher point and freely accelerated by uniform gravity would descend in minimum time to the lower.

Gottfried Wilhelm Leibniz (1646–1716) thought the problem beautiful; so did Guillaume de l’Hospital (1661–1704).

Bernoulli (and others) proved that the brachistochrone was again an inverted cycloid. He thought that the equality of the cycloid, tautochrone, and brachistochrone curve would leave his readers ‘petrified with astonishment’, and thought that it suggested some deep design in nature.

One of Bernoulli's proofs was what he considered a ‘very beautiful’ geometric demonstration that the cycloid was the brachistochrone.

But he did not publish it until 20 years later. Why? Apparently in part due to Leibniz, who had thought it so beautiful and extraordinary that he counselled against publication, with the aim of ‘so frustrating those who are not very grateful and who are accustomed to profiting from the inventions of others’.

**Here, mathematical beauty contributed to the suppression, albeit temporary, of mathematical knowledge.**

2/3

#Bernoulli #JohannBernoulli #JeanBernoulli #brachistochrone #Leibniz

Johann Bernoulli (= Jean; 1667–1748) posed the problem of finding the ‘brachistochrone’: the curve between two points along which a body starting from rest at the higher point and freely accelerated by uniform gravity would descend in minimum time to the lower.

Gottfried Wilhelm Leibniz (1646–1716) thought the problem beautiful; so did Guillaume de l’Hospital (1661–1704).

Bernoulli (and others) proved that the brachistochrone was again an inverted cycloid. He thought that the equality of the cycloid, tautochrone, and brachistochrone curve would leave his readers ‘petrified with astonishment’, and thought that it suggested some deep design in nature.

One of Bernoulli's proofs was what he considered a ‘very beautiful’ geometric demonstration that the cycloid was the brachistochrone.

But he did not publish it until 20 years later. Why? Apparently in part due to Leibniz, who had thought it so beautiful and extraordinary that he counselled against publication, with the aim of ‘so frustrating those who are not very grateful and who are accustomed to profiting from the inventions of others’.

**Here, mathematical beauty contributed to the suppression, albeit temporary, of mathematical knowledge.**

2/3

#Bernoulli #JohannBernoulli #JeanBernoulli #brachistochrone #Leibniz

Johann Bernoulli (= Jean; 1667–1748) posed the problem of finding the ‘brachistochrone’: the curve between two points along which a body starting from rest at the higher point and freely accelerated by uniform gravity would descend in minimum time to the lower.

Gottfried Wilhelm Leibniz (1646–1716) thought the problem beautiful; so did Guillaume de l’Hospital (1661–1704).

Bernoulli (and others) proved that the brachistochrone was again an inverted cycloid. He thought that the equality of the cycloid, tautochrone, and brachistochrone curve would leave his readers ‘petrified with astonishment’, and thought that it suggested some deep design in nature.

One of Bernoulli's proofs was what he considered a ‘very beautiful’ geometric demonstration that the cycloid was the brachistochrone.

But he did not publish it until 20 years later. Why? Apparently in part due to Leibniz, who had thought it so beautiful and extraordinary that he counselled against publication, with the aim of ‘so frustrating those who are not very grateful and who are accustomed to profiting from the inventions of others’.

**Here, mathematical beauty contributed to the suppression, albeit temporary, of mathematical knowledge.**

2/3

#Bernoulli #JohannBernoulli #JeanBernoulli #brachistochrone #Leibniz

🌊 La mecánica de fluidos estudia cómo se comportan líquidos y gases. Desde aviones hasta tuberías, sus principios están en todo. ¡Descubre sus fundamentos! 💡

Lee más 👉 https://www.soloingenieria.org/ingenieria-mecanica/mecanica-de-fluidos/

Imagen creada con IA.
#MecánicaDeFluidos #IngenieríaMecánica #Hidráulica #Hidrodinámica #Bernoulli #Ingeniería

Sin mecánica de fluidos no existirían aviones, sistemas de riego ni equipos médicos. Lo que parece teoría abstracta sostiene gran parte del mundo moderno. 🌊

#MecánicaDeFluidos #IngenieríaMecánica #Hidráulica #Hidrodinámica #Bernoulli #Ingeniería

Look what I found on a regional flea market. #iomega #bernoulli #vintagecomputing #retrocomputing

Look what I found on a regional flea market. #iomega #bernoulli #vintagecomputing #retrocomputing

Look what I found on a regional flea market. #iomega #bernoulli #vintagecomputing #retrocomputing

One day, one decomposition
A000928: Irregular primes: primes p such that at least one of the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) is divisible by p

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/Irregular_primes.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/Irregular_primes.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/Irregular_primes.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #Bernoulli #numbers #irregular #primes #PrimeNumbers #graph #threejs #webGL

One day, one decomposition
A249134: Numbers k such that Bernoulli number B_k has denominator 2730

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A249134.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A249134.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #Bernoulli #numbers #denominator #graph #threejs #webGL

One day, one decomposition
A249134: Numbers k such that Bernoulli number B_k has denominator 2730

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A249134.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A249134.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #Bernoulli #numbers #denominator #graph #threejs #webGL

One day, one decomposition
A249134: Numbers k such that Bernoulli number B_k has denominator 2730

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A249134.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A249134.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #Bernoulli #numbers #denominator #graph #threejs #webGL

One day, one decomposition
A249134: Numbers k such that Bernoulli number B_k has denominator 2730

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A249134.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A249134.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #Bernoulli #numbers #denominator #graph #threejs #webGL

One day, one decomposition
A249134: Numbers k such that Bernoulli number B_k has denominator 2730

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A249134.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A249134.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #Bernoulli #numbers #denominator #graph #threejs #webGL

I'll probably never own a drive to read those, but these are some very impressive floppy disk cartridges. Also, 20 megs in 1984 - that's more than a typical hard disk had at that time. 😲

#IOMEGA #Bernoulli #RetroComputing #ObsoleteMedia

I'll probably never own a drive to read those, but these are some very impressive floppy disk cartridges. Also, 20 megs in 1984 - that's more than a typical hard disk had at that time. 😲

#IOMEGA #Bernoulli #RetroComputing #ObsoleteMedia

I'll probably never own a drive to read those, but these are some very impressive floppy disk cartridges. Also, 20 megs in 1984 - that's more than a typical hard disk had at that time. 😲

#IOMEGA #Bernoulli #RetroComputing #ObsoleteMedia

I'll probably never own a drive to read those, but these are some very impressive floppy disk cartridges. Also, 20 megs in 1984 - that's more than a typical hard disk had at that time. 😲

#IOMEGA #Bernoulli #RetroComputing #ObsoleteMedia

I'll probably never own a drive to read those, but these are some very impressive floppy disk cartridges. Also, 20 megs in 1984 - that's more than a typical hard disk had at that time. 😲

#IOMEGA #Bernoulli #RetroComputing #ObsoleteMedia

Ok, nix explodiert und das Laufwerk meldet "ready", wenn die Disk eingelegt ist. 🙂 Richtig testen kann ich erst später, wenn das Laufwerk wieder in einem externen SCSI-Gehäuse verbaut ist und ich einen Mac mit SCSI aufgebaut habe.

#IOMEGA #Bernoulli #RetroComputing

Keine Ahnung, ob das eine gute Idee ist/war, aber da ich für das #Bernoulli-Laufwerk nur eine einzige, ziemlich verdreckte, 150 MB-Disk hatte, habe ich die mal zerlegt und gereinigt. Sehr interessanter Aufbau. Sind zwei Scheiben direkt übereinander. Dazwischen ist ein Flies. Vermute, die Köpfe werden zwischen die beiden Scheiben gefahren, da der Shutter nur die Oberseite freigibt.

In dem Video ist das Flies zwischen den Scheiben entfernt, daher sieht man nicht so gut, dass es zwei sind...

#RetroComputing

Zur Abwechselung etwas #SCSI-Zeugs: zwei 4/8 GB DAT-Streamer, der linke vom Design her definitiv für alte Macs gedacht.

Ein 150 MB #IOMEGA #Bernoulli-Laufwerk. Gehäuse ist leider aus Plastik und an etlichen Stellen gebrochen. Laufwerk scheint, zumindest mechanisch, aber ok zu sein.

Und noch ein schöner SCSI-Tower. 🥳

#RetroComputing

Let \(\varpi=\dfrac{\Gamma^2\left(\frac14\right)}{2\sqrt{2\pi}}=2.62205755\ldots\) be the lemniscate constant. Then,
\[\Large\displaystyle\sum_{n=1}^\infty\dfrac{1}{\sinh^4(\pi n)}=\dfrac{\varpi^4}{30\pi^4}+\dfrac{1}{3\pi}-\dfrac{11}{90}\]

#Series #Sum #InfiniteSum #LemniscateConstant #GammaFunction #Lemniscate #LemniscateOfBernoulli #Bernoulli #Math #Maths #InfiniteSeries #HyperbolicSines

Let \(\varpi=\dfrac{\Gamma^2\left(\frac14\right)}{2\sqrt{2\pi}}=2.62205755\ldots\) be the lemniscate constant. Then,
\[\Large\displaystyle\sum_{n=1}^\infty\dfrac{1}{\sinh^4(\pi n)}=\dfrac{\varpi^4}{30\pi^4}+\dfrac{1}{3\pi}-\dfrac{11}{90}\]

#Series #Sum #InfiniteSum #LemniscateConstant #GammaFunction #Lemniscate #LemniscateOfBernoulli #Bernoulli #Math #Maths #InfiniteSeries #HyperbolicSines

Buen día, miserables.

Hace trescientos veintiséis años don Isaac Newton tuvo un momento de someone is wrong on the Internet (https://en.wikipedia.org/wiki/Later_life_of_Isaac_Newton#Bernoulli's_mathematical_challenge) y gracias a eso tenemos no sólo un bello resultado matemático, sino una frase que le ha complicado la vida a los filólogos durante siglos:

https://www.nature.com/articles/333592c0.pdf

¡Sean vuestros conflictos por lo menos tan productivos como éste!

Variable-Nozzle Ducted Fan Provides Fluid Dynamics Lessons

#dronehacks #bernoulli #brushless #drone #ductedfan #fluiddynamics #jetengine #motor #remotecontrol #variablenozzle #venturi #hackaday

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Variable-Nozzle Ducted Fan Provides Fluid Dynamics Lessons

#dronehacks #bernoulli #brushless #drone #ductedfan #fluiddynamics #jetengine #motor #remotecontrol #variablenozzle #venturi #hackaday

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Variable-Nozzle Ducted Fan Provides Fluid Dynamics Lessons - Any student new to the principles of fluid dynamics will be familiar with Bernoull... - https://hackaday.com/2023/10/19/variable-nozzle-ducted-fan-provides-fluid-dynamics-lessons/ #variablenozzle #fluiddynamics #remotecontrol #dronehacks #bernoulli #brushless #ductedfan #jetengine #venturi #drone #motor

Variable-Nozzle Ducted Fan Provides Fluid Dynamics Lessons - Any student new to the principles of fluid dynamics will be familiar with Bernoull... - https://hackaday.com/2023/10/19/variable-nozzle-ducted-fan-provides-fluid-dynamics-lessons/ #variablenozzle #fluiddynamics #remotecontrol #dronehacks #bernoulli #brushless #ductedfan #jetengine #venturi #drone #motor

Variable-Nozzle Ducted Fan Provides Fluid Dynamics Lessons - Any student new to the principles of fluid dynamics will be familiar with Bernoull... - https://hackaday.com/2023/10/19/variable-nozzle-ducted-fan-provides-fluid-dynamics-lessons/ #variablenozzle #fluiddynamics #remotecontrol #dronehacks #bernoulli #brushless #ductedfan #jetengine #venturi #drone #motor

Variable-Nozzle Ducted Fan Provides Fluid Dynamics Lessons - Any student new to the principles of fluid dynamics will be familiar with Bernoull... - https://hackaday.com/2023/10/19/variable-nozzle-ducted-fan-provides-fluid-dynamics-lessons/ #variablenozzle #fluiddynamics #remotecontrol #dronehacks #bernoulli #brushless #ductedfan #jetengine #venturi #drone #motor

Variable-Nozzle Ducted Fan Provides Fluid Dynamics Lessons - Any student new to the principles of fluid dynamics will be familiar with Bernoull... - https://hackaday.com/2023/10/19/variable-nozzle-ducted-fan-provides-fluid-dynamics-lessons/ #variablenozzle #fluiddynamics #remotecontrol #dronehacks #bernoulli #brushless #ductedfan #jetengine #venturi #drone #motor

#OEIS #Bernoulli

In the mood to prove a conjecture about Bernoulli polynomials? This way:

a(n) is the positive integer k such that the k-th derivative of the n-th Bernoulli polynomial B(n, x) contains only integer coefficients but no lower derivative of B(n, x) has this property.

More generally:

The 'integral index' k of a rational polynomial p(x) is the smallest integer k such that p^[k](x) is an integer polynomial, where p^[k](x) denotes the k-th derivative of p. (Integer polynomials have integral index 0.)

Using this way of speaking, the a(n) are the integral indices of the Bernoulli polynomials.

Conjecture: Every integer appears in the sequence a only a finite number of times.

a(n) = https://oeis.org/A366189

To the attention of the #EDOC2023 and #CoopIS2023 Early Birds and Authors https://www.rug.nl/research/bernoulli/conf/edoc-2023/registration-form?lang=en


🗓️Authors' registration is open until September 3rd❗️❗️❗️

🗓️Early Bird registration until September 11th
📌Tutorial-only participants - use the tutorial-only option.


We are looking forward to welcoming you at the #Bernoulli Institute in #Groningen this year!

@academicchatter #conference #InformationSystems @edutooters

To the attention of the #EDOC2023 and #CoopIS2023 Early Birds and Authors
https://rug.nl/research/bernoulli/conf/edoc-2023/registration-form
🗓️Authors' registration is open until September 3rd❗️❗️❗️
🗓️Early Bird registration until September 11th
📌Tutorial-only participants - use the tutorial-only option
We are looking forward to welcoming you at the #Bernoulli Institute in #Groningen this year!
@academicchatter #conference #InformationSystems @edutooters

Spectral learning of Bernoulli linear dynamical systems models for decision-making

Iris R Stone, Yotam Sagiv, Il Memming Park, Jonathan W. Pillow

Action editor: Shinichi Nakajima.

https://openreview.net/forum?id=giw2vcAhiH

#stochastic #models #bernoulli

In 1738, Daniel Bernoulli discovered the principle that increasing the flow of a gas or liquid decreases its pressure. #Poetry #Science #History #Hydrodynamics #Bernoulli (https://sharpgiving.com/thebookofscience/items/p1738.html)

In 1683, Jacob Bernoulli discovered the third irrational constant, Euler’s number. #Poetry #Science #History #Mathematics #EulersNumber #Bernoulli (https://sharpgiving.com/thebookofscience/items/p1683.html)

In 1683, Jacob Bernoulli discovered the third irrational constant, Euler’s number. #Poetry #Science #History #Mathematics #EulersNumber #Bernoulli (https://sharpgiving.com/thebookofscience/items/p1683.html)

History of the Picard scheme by Steven L Kleiman
#lemniscate
#Bernoulli
#Fagnano
#Euler

https://arxiv.org/abs/math/0504020

Mathematical science shows what is. It is the language of unseen relations between things. But to use and apply that language, we must be able fully to appreciate, to feel, to seize the unseen, the unconscious.

- Augusta Ada King, Countess of Lovelace

#science #math #mathematics #mathematician #ada #lovelace #language #life #bernoulli

I've been thinking about implementing an algorithm for computing #Bernoulli numbers that Henri Cohen loosely describes in one of his books. Funnily enough, the first computer program intended to run on actual hardware was written by #AdaLovelace :lovelace: and was also intended for Bernoulli numbers.

Now I kind of want to understand her program and implement it too. I bet someone already has done it. Maybe I should go find what others have written on this.