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If you pick two points at random inside a regular dodecahedron and draw the line that contains them, that line can intersect three different kinds of pairs of faces, separated by angles of:

π, arcos(–1/√5), or arcos(1/√5)

The probabilities of these three events are:

1/4, (1+φ)/4, and (2–φ)/4

where φ is the golden ratio!

There is a general formula that applies to a d-dimensional regular polytope with f faces, for a single pair of faces separated by an angle θ:

P(d,f,θ) = 2d (cos(θ)–1)^2 / [(d+1) f^2]

That gives probabilities of:

1/24, (1+φ)/120, and (2–φ)/120

for the three possible angles, and there are:

6, 30 and 30

such pairs in total.

I give a proof of the general formula here:

gregegan.net/SCIENCE/PickTwoPo…

Greg Egan reshared this.

in reply to Greg Egan

You work on some fascinating and deep things. Very interesting, and mostly beyond me. Cool!


We're happy to announce three projects will be funded to contribute to the TALER secure electronic payment system based on open standards, free software, and advanced cryptography.

The three projects are:
Libre Payments in Ruby, a GNU Taler Integration for ethical trade.
Taler in Liberapay, an implementation of Taler as payment provider in Liberapay.
And Taler OpenAPI specification, a JSON/YAML OpenAPI for key GNU Taler API's.

nlnet.nl/news/2025/20250901-Ne…

@NGI_TALER

#NGI #FOSS #TALER

reshared this

in reply to Nicolas Vivier

Thank you very much for your message Nicolas! One of our core partners in the NGI TALER project is E-Seniors, based in France: eseniors.eu/

We would be delighted to stay in touch with you and more stakeholders in France who may be interested in connecting with our partners and following the progress of our mission.

Would you be interested in joining us on TALER ICH and introducing yourself there?
ich.taler.net/

@nicotentin @oec @Blort @nlnet

in reply to NGI TALER

i think one of the first people to join for adoption is lokavaluto.fr/ they make common tools for local communities who make local currencies. AFAIK they already made an app for payment but they could be interested for a more private solution
in reply to NGI TALER

I'm sorry to ask dumb questions but if GLSbank provide euros, fine but shouldn't the merchants have to make some adoption steps too? Or will the wallet allow to pay via nfc on any payment terminal?
in reply to Lutin Discret

Hello dear @lutindiscret

Thank you for informing us about lokavaluto.fr/ !

We suggest that you join us on TALER ICH and post your question there! We are building a vibrant community around GNU Taler, bringing together consortium members, grantees, allies, and other stakeholders interested in our work. Sharing and responding to important questions in the forum will also help future visitors who may have similar queries ich.taler.net/ 😀

@nicotentin @oec @Blort @nlnet

in reply to Lutin Discret

Not a dumb question at all. Yes, a merchant needs to be able to accept payments with Taler. Right now, there exist a couple of integrations with existing online shop systems such as Pretix, Drupal and WooCommerce, more to come, hopefully (if you have an idea, apply to our open calls! See nlnet.nl/taler/).

For physical shops, merchants can use our PoS software for Android tablets. We expect (well, hope) that at some point vendors of commercial PoS terminals will integrate the protocol.

In both (online and physical) cases, the merchant also needs to either run the GNU Taler merchant backend server themselve, or become a tenant at a service provider that runs that backend for multiple merchants.

F.e. POT (pot.ch), a cooperative of local food suppliers around Zurich, 🇨🇭, is doing the former: it runs a merchant instance for all members in the cooperative, and Swiss customers will soon be able to pay in Swiss Franc via GNU Taler, with taler-ops.ch as payment service provider.

Questa voce è stata modificata (2 settimane fa)
in reply to NGI TALER

I have already joined Taler Ich. I am curious to know if it will soon be available in France to exchange Taler with Euros as it is necessary for many real world usages.



Croatia hosts fourth open hot air balloon championship in Prelog
https://www.africanews.com/2025/09/01/croatia-hosts-fourth-open-hot-air-balloon-championship-in-prelog/?utm_source=flipboard&utm_medium=activitypub

Posted into Africanews @africanews-euronews



#GENOCIDIO #PULIZIAETNICA #GazaStarving

Ma sicuramente i grandi "pensatori" - esperti di nulla e perciò sempre in TV e sui giornali - del nostro Paese non saranno d'accordo.

#CeasefireNOW #GazaGenocide‌ #Gaza #WestBank #Israel #Peace #1settembre

ilfattoquotidiano.it/2025/09/0…



NEW WORLD ORDER!?!

Xi Jinping put forward the "global governance" initiative at the SCO summit.

"I would like to put forward the global governance initiative and work with all countries to jointly build a more just and equitable global governance system and a community with a shared future for mankind," Xi said.
#AureFreePress #News #press #headline #Ukraine #Russia #Putin #EU #NATO #China #Breaking #BreakingNews



Sportstreaming: Alles außer Fußball, dafür mit KI

Der Streaminganbieter Dyn geht sowohl in der Distribution als auch in der Produktion neue Wege. KI, Cloud und Glasfaser machen’s möglich.

heise.de/news/Sportstreaming-A…

#CloudComputing #Entertainment #KünstlicheIntelligenz #Streaming #news






When approval dips below 40%, manipulation becomes method.

Gerrymandered maps and election-denier placements are structural attempts to pre-rig 2028 before votes count.

Democracy deserves better.

#Brewminate #Democracy #Politics #2028

brewminate.com/rigging-the-fut…




Top 10 best Labor Day deals from $20: AirPods, Sony XM6, Find My card, Lectric, Legion Tab 3, more
https://9to5toys.com/2025/09/01/top-10-best-labor-day-deals/?utm_source=flipboard&utm_medium=activitypub

Posted into Apple Deals @apple-deals-9to5mac



Pope Leo meets LGBTQ+ Catholic advocate and vows continuity with Pope Francis’ legacy of welcome apnews.com/article/pope-leo-ja… #LGBTQIA




CNN: “250+ news outlets from over 70 countries will simultaneously black out their front pages and website homepages, and interrupt their broadcasting to condemn the murder of journalists by the Israeli army in the Gaza Strip.” www.cnn.com/2025/08/31/m...


Flags and graffiti on roundabouts and now even churches have made one West Midlands resident angry; when will it all cease? | Mark Cunliffe
centralbylines.co.uk/opinion/f…


The Evidence That AI Is Destroying Jobs For Young People Just Got Stronger


In a new paper, several Stanford economists studied payroll data from the private company ADP, which covers millions of workers, through mid-2025. They found that young workers aged 22–25 in “highly AI-exposed” jobs, such as software developers and customer service agents, experienced a 13 percent decline in employment since the advent of ChatGPT. Notably, the economists found that older workers and less-exposed jobs, such as home health aides, saw steady or rising employment. “There’s a clear, evident change when you specifically look at young workers who are highly exposed to AI,” Stanford economist Erik Brynjolfsson, who wrote the paper with Bharat Chandar and Ruyu Chen, told the Wall Street Journal.

In five months, the question of “Is AI reducing work for young Americans?” has its fourth answer: from possibly, to definitely, to almost certainly no, to plausibly yes. You might find this back-and-forth annoying. I think it’s fantastic. This is a model for what I want from public commentary on social and economic trends: Smart, quantitatively rich, and good-faith debate of issues of seismic consequence to American society.

Technology reshared this.

in reply to elephantium

Just wait all this is just a scam without any real revenue. That's why it's just investments right now into big companies. They're already starting to fail not really recognizing AI isn't supposed to be used in that way anyways.
in reply to DeathsEmbrace

Eh, I don't think it's an outright scam, rather "just" a bad investment / overhype. The language model programs do have some real uses, after all.




See, this crazy out of control medicine from Dr Crusher? Dis here is what our new HHS is afraid of from "medical science"! 🤦‍♂️😖

#AllStarTrek #StarTrek #StarTrekTNG #Genesis

Questa voce è stata modificata (3 settimane fa)
in reply to Kevin C 🎬

Dr. Crusher: If there’s nothing wrong with me, maybe there’s something wrong with the universe.

Us: No, Doctor, it’s you. Ya know, the one who unleashed a mutant virus on the Enterprise while treating Barclay for a simple condition. It’s you.

#AllStarTrek #StarTrek #RememberMe #Genesis

Also, for good measure #SubRosa 👻 🕯️

(I kid. I like Crusher. The entire #StarTrekTNG crew is like my TV family.)




Gute Nachrichten Freunde, in der #Milka ist jetzt weniger Scheiße drin 🤡



Military training of the Collective Security Treaty Organization (CSTO) started in Vitebsk, Belarus. They are called "Interaction-2025" and 2,000 troops from Russia, Kazakhstan, Kyrgyzstan, Tajikistan and Belarus will take part in them.

Among other things, the training will include planning to use nuclear weapons.

On September 12, "West-2025", a more large-scale training will begin in Belarus.
#AureFreePress #News #press #headline #Ukraine #Russia #Putin #EU #NATO



"There was no agreement on a meeting between Zelenskyy and Putin." - Russian representative Ushakov denies the previously announced arrangement between Trump and Putin on this matter. This makes Trump look even more weak and incapable.
#trump #putin #ushakov #zelensky #ukraine #geopolitics @geopolitics
in reply to Erik Jonker

⬆️ @ErikJonker @geopolitics

>> "There was no agreement on a meeting between #Zelenskyy and #Putin." - Russian representative Ushakov denies the previously announced arrangement between #Trump and Putin on this matter. This makes Trump look even more weak and incapable.

Same when #Modi denied Trump's role in #India-#Pakistan ceasefire.

#pattern



*Even Reagan*—who set this country on the course whose nihilistic end point is in sight—respected norms for which Trump has no regard.

Donald won’t take yes for an answer. He wants to destroy the Federal Reserve. I doubt even he really understands why. trib.al/wBaVS0T




Patricia joined Sisi Film Lab hoping to become an actress. There were no acting classes. Instead, she found herself behind the camera, learning cinematography, sound, editing, and set design. Along the way she discovered a new way to tell stories. Her journey is inspiring. Read her story here: sisifilmcollective.org/an-actr…

#blog #film #writing #art #sisi

ophiocephalic 🐍 reshared this.



As big techs são inimigas de classe. A estratégia de comunicação dos comunistas precisa ir além delas

Entender as big techs como inimigas de classe e suas mídias sociais como o terreno adversário nos impõe a tarefa de enfraquecer esse inimigo, de acumular forças em nosso terreno, e isso passa por direcionar as pessoas para fora dessas plataformas, o que está longe de ser uma tarefa fácil. É preciso resistir à tentação de afirmar que sites tradicionais, como o portal do partido ou o Vermelho sejam o bastante. A dinâmica da internet nos últimos vinte anos é dos usuários se restringirem cada vez mais às plataformas sociais, onde é mais difícil competir com as plataformas imperialistas, porque o valor delas depende principalmente do conjunto de seus usuários. Esse empecilho torna a proposta de criar uma “rede social de esquerda” quase um devaneio quixotesco. As pessoas não participam de plataformas sociais monotemáticas e podemos ver um exemplo prático com o relativo fracasso do ICL em lançar uma rede social recentemente.

pcdob.org.br/2025/08/as-big-te…

#vemprofediverso #politica #PCdoB



Comparing Web of Science and @OpenAlex at the scale of Grenoble University.

gates-data-shs.gricad-pages.un…

In the realm of bibliometrics, OpenAlex definitely paves a new path that is consistent with #OpenScience



🔗 Impact Research Letter (2022) thecakelin.notion.site/Impact-…

This is a Democratic campaign strategy letter from February 2022 with research about American's attitudes towards covid. It says Americans are tired of dealing with the pandemic. It recommends minimizing covid and emphasizing the personal responsibility of vaccines. A “we have the tools” and “covid is like the flu” messaging strategy.





"The President is always a controversial choice, always an infuriating but fascinating character. His job is not to wield power but to draw attention away from it." (Douglas Adams - Hitchkiker's Guide To The Galaxy)

#uspolitics #usa #trump #thiel #deepstate #fascism #idiocracy

in reply to 🇪🇺 Herr Vorragend 🌻

The image shows a man standing in a room with large windows, holding a large blank white board in front of him. He is wearing a dark suit, white shirt, and a bright yellow tie. Behind him, there are several flags, including the American flag, and a window with a view of greenery outside. The room appears to be an office or a formal setting, with a dark leather chair visible in the foreground. The man's expression is neutral, and he is looking slightly to his left. The blank white board he is holding is the central focus of the image, obscuring his face.

Provided by @altbot, generated privately and locally using Ovis2-8B

🌱 Energy used: 0.136 Wh



Mondiali 2026: l’onda anomala dei domini sospetti già pronta a colpire
#CyberSecurity
insicurezzadigitale.com/mondia…





Høljafossen, one of many waterfalls on the road through the Utladalen. Norway. Difficult to photograph. This is my try. Utladalen is the long beautiful valley in Øvre Årdal with the famous Vettisfossen waterfall at the end. Long hike. 6,5 kilometres one way, but worth it.
#utladalen #holjafossen #valley #hiking #landscape #nature #waterfall #photo #photography #norway #norge #longexposure #art #fineart #fjellphoto