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#huygens — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #huygens, aggregated by home.social.

  1. Gottfried Wilhelm Leibniz's (1646–1716) first great mathematical achievement was the ‘arithmetic quadrature’ of the circle through his alternating series: π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...

    He communicated the result to his mathematical mentor Christiaan Huygens (1629–95), who thought it ‘very beautiful and very pleasing’. Isaac Newton (1642–1726) welcomed Leibniz’s work as ‘very elegant’. Leibniz himself wrote that there was no simpler or more beautiful way of expressing the area of a circle using rational numbers.

    In a short note concerning the beauty of theorems, Leibniz wrote:

    ‘Theorems are not intelligible except by their signs or characters. […] The beauty of theorems consists in the beautiful arrangement of their characters.’

    To illustrate ‘beautiful arrangement of characters’, Leibniz gave the example of a theorem concerning Berthet’s curve (shown in red in 1st attached image). The detail of its definition is not important here, but it is defined with reference to an arc AC centred at B.

    Leibniz's result was a way of finding the tangent to the curve at E: take the tangent to the arc at its intersection with BE (i.e., at D), and find the point F such that FD ∶ DE ∶∶ EB ∶ BD. Then EF is the desired tangent (see 1st attached image).

    Why is there a ‘beautiful arrangement of characters’? Because the proportion FD ∶ DE ∶∶ EB ∶ BD is easily remembered via a mnemonic: one can draw the path FD ⋅ DE ⋅ EB ⋅ BD without raising one's pen (2nd attached image).

    1/2

    #geometry #Leibniz #Huygens #Newton #MathematicalBeauty #aesthetics #HistMath

  2. Gottfried Wilhelm Leibniz's (1646–1716) first great mathematical achievement was the ‘arithmetic quadrature’ of the circle through his alternating series: π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...

    He communicated the result to his mathematical mentor Christiaan Huygens (1629–95), who thought it ‘very beautiful and very pleasing’. Isaac Newton (1642–1726) welcomed Leibniz’s work as ‘very elegant’. Leibniz himself wrote that there was no simpler or more beautiful way of expressing the area of a circle using rational numbers.

    In a short note concerning the beauty of theorems, Leibniz wrote:

    ‘Theorems are not intelligible except by their signs or characters. […] The beauty of theorems consists in the beautiful arrangement of their characters.’

    To illustrate ‘beautiful arrangement of characters’, Leibniz gave the example of a theorem concerning Berthet’s curve (shown in red in 1st attached image). The detail of its definition is not important here, but it is defined with reference to an arc AC centred at B.

    Leibniz's result was a way of finding the tangent to the curve at E: take the tangent to the arc at its intersection with BE (i.e., at D), and find the point F such that FD ∶ DE ∶∶ EB ∶ BD. Then EF is the desired tangent (see 1st attached image).

    Why is there a ‘beautiful arrangement of characters’? Because the proportion FD ∶ DE ∶∶ EB ∶ BD is easily remembered via a mnemonic: one can draw the path FD ⋅ DE ⋅ EB ⋅ BD without raising one's pen (2nd attached image).

    1/2

    #geometry #Leibniz #Huygens #Newton #MathematicalBeauty #aesthetics #HistMath

  3. Gottfried Wilhelm Leibniz's (1646–1716) first great mathematical achievement was the ‘arithmetic quadrature’ of the circle through his alternating series: π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...

    He communicated the result to his mathematical mentor Christiaan Huygens (1629–95), who thought it ‘very beautiful and very pleasing’. Isaac Newton (1642–1726) welcomed Leibniz’s work as ‘very elegant’. Leibniz himself wrote that there was no simpler or more beautiful way of expressing the area of a circle using rational numbers.

    In a short note concerning the beauty of theorems, Leibniz wrote:

    ‘Theorems are not intelligible except by their signs or characters. […] The beauty of theorems consists in the beautiful arrangement of their characters.’

    To illustrate ‘beautiful arrangement of characters’, Leibniz gave the example of a theorem concerning Berthet’s curve (shown in red in 1st attached image). The detail of its definition is not important here, but it is defined with reference to an arc AC centred at B.

    Leibniz's result was a way of finding the tangent to the curve at E: take the tangent to the arc at its intersection with BE (i.e., at D), and find the point F such that FD ∶ DE ∶∶ EB ∶ BD. Then EF is the desired tangent (see 1st attached image).

    Why is there a ‘beautiful arrangement of characters’? Because the proportion FD ∶ DE ∶∶ EB ∶ BD is easily remembered via a mnemonic: one can draw the path FD ⋅ DE ⋅ EB ⋅ BD without raising one's pen (2nd attached image).

    1/2

    #geometry #Leibniz #Huygens #Newton #MathematicalBeauty #aesthetics #HistMath

  4. Gottfried Wilhelm Leibniz's (1646–1716) first great mathematical achievement was the ‘arithmetic quadrature’ of the circle through his alternating series: π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...

    He communicated the result to his mathematical mentor Christiaan Huygens (1629–95), who thought it ‘very beautiful and very pleasing’. Isaac Newton (1642–1726) welcomed Leibniz’s work as ‘very elegant’. Leibniz himself wrote that there was no simpler or more beautiful way of expressing the area of a circle using rational numbers.

    In a short note concerning the beauty of theorems, Leibniz wrote:

    ‘Theorems are not intelligible except by their signs or characters. […] The beauty of theorems consists in the beautiful arrangement of their characters.’

    To illustrate ‘beautiful arrangement of characters’, Leibniz gave the example of a theorem concerning Berthet’s curve (shown in red in 1st attached image). The detail of its definition is not important here, but it is defined with reference to an arc AC centred at B.

    Leibniz's result was a way of finding the tangent to the curve at E: take the tangent to the arc at its intersection with BE (i.e., at D), and find the point F such that FD ∶ DE ∶∶ EB ∶ BD. Then EF is the desired tangent (see 1st attached image).

    Why is there a ‘beautiful arrangement of characters’? Because the proportion FD ∶ DE ∶∶ EB ∶ BD is easily remembered via a mnemonic: one can draw the path FD ⋅ DE ⋅ EB ⋅ BD without raising one's pen (2nd attached image).

    1/2

    #geometry #Leibniz #Huygens #Newton #MathematicalBeauty #aesthetics #HistMath

  5. Gottfried Wilhelm Leibniz's (1646–1716) first great mathematical achievement was the ‘arithmetic quadrature’ of the circle through his alternating series: π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...

    He communicated the result to his mathematical mentor Christiaan Huygens (1629–95), who thought it ‘very beautiful and very pleasing’. Isaac Newton (1642–1726) welcomed Leibniz’s work as ‘very elegant’. Leibniz himself wrote that there was no simpler or more beautiful way of expressing the area of a circle using rational numbers.

    In a short note concerning the beauty of theorems, Leibniz wrote:

    ‘Theorems are not intelligible except by their signs or characters. […] The beauty of theorems consists in the beautiful arrangement of their characters.’

    To illustrate ‘beautiful arrangement of characters’, Leibniz gave the example of a theorem concerning Berthet’s curve (shown in red in 1st attached image). The detail of its definition is not important here, but it is defined with reference to an arc AC centred at B.

    Leibniz's result was a way of finding the tangent to the curve at E: take the tangent to the arc at its intersection with BE (i.e., at D), and find the point F such that FD ∶ DE ∶∶ EB ∶ BD. Then EF is the desired tangent (see 1st attached image).

    Why is there a ‘beautiful arrangement of characters’? Because the proportion FD ∶ DE ∶∶ EB ∶ BD is easily remembered via a mnemonic: one can draw the path FD ⋅ DE ⋅ EB ⋅ BD without raising one's pen (2nd attached image).

    1/2

    #geometry #Leibniz #Huygens #Newton #MathematicalBeauty #aesthetics #HistMath

  6. An enduring locus of mathematical beauty in the seventeenth century concerned curves like the cycloid and the catenary.

    A cycloid is the path followed by a point on the circumference of a circle rolling along a straight line (see attached image).

    Christopher Wren (1632–1723) proved that the arc length of the cycloid is four times the diameter of its generating circle.

    Christiaan Huygens (1629–95) thought Wren's work ‘really beautiful’. Blaise Pascal (1623–62) also called it ‘beautiful’ (even though he also seemed to repudiate any true notion of mathematical beauty in his ‘Pensées’.

    Huygens proved that an inverted cycloid was the ‘tautochrone’: the curve along which a body starting from rest and freely accelerated by uniform gravity reaches the lowest point in the same time, independently of its starting point.

    1/3

    #cycloid #tautochrone #Huygens #HistMath #MathematicalBeauty #Pascal

  7. An enduring locus of mathematical beauty in the seventeenth century concerned curves like the cycloid and the catenary.

    A cycloid is the path followed by a point on the circumference of a circle rolling along a straight line (see attached image).

    Christopher Wren (1632–1723) proved that the arc length of the cycloid is four times the diameter of its generating circle.

    Christiaan Huygens (1629–95) thought Wren's work ‘really beautiful’. Blaise Pascal (1623–62) also called it ‘beautiful’ (even though he also seemed to repudiate any true notion of mathematical beauty in his ‘Pensées’.

    Huygens proved that an inverted cycloid was the ‘tautochrone’: the curve along which a body starting from rest and freely accelerated by uniform gravity reaches the lowest point in the same time, independently of its starting point.

    1/3

    #cycloid #tautochrone #Huygens #HistMath #MathematicalBeauty #Pascal

  8. An enduring locus of mathematical beauty in the seventeenth century concerned curves like the cycloid and the catenary.

    A cycloid is the path followed by a point on the circumference of a circle rolling along a straight line (see attached image).

    Christopher Wren (1632–1723) proved that the arc length of the cycloid is four times the diameter of its generating circle.

    Christiaan Huygens (1629–95) thought Wren's work ‘really beautiful’. Blaise Pascal (1623–62) also called it ‘beautiful’ (even though he also seemed to repudiate any true notion of mathematical beauty in his ‘Pensées’.

    Huygens proved that an inverted cycloid was the ‘tautochrone’: the curve along which a body starting from rest and freely accelerated by uniform gravity reaches the lowest point in the same time, independently of its starting point.

    1/3

    #cycloid #tautochrone #Huygens #HistMath #MathematicalBeauty #Pascal

  9. An enduring locus of mathematical beauty in the seventeenth century concerned curves like the cycloid and the catenary.

    A cycloid is the path followed by a point on the circumference of a circle rolling along a straight line (see attached image).

    Christopher Wren (1632–1723) proved that the arc length of the cycloid is four times the diameter of its generating circle.

    Christiaan Huygens (1629–95) thought Wren's work ‘really beautiful’. Blaise Pascal (1623–62) also called it ‘beautiful’ (even though he also seemed to repudiate any true notion of mathematical beauty in his ‘Pensées’.

    Huygens proved that an inverted cycloid was the ‘tautochrone’: the curve along which a body starting from rest and freely accelerated by uniform gravity reaches the lowest point in the same time, independently of its starting point.

    1/3

    #cycloid #tautochrone #Huygens #HistMath #MathematicalBeauty #Pascal

  10. An enduring locus of mathematical beauty in the seventeenth century concerned curves like the cycloid and the catenary.

    A cycloid is the path followed by a point on the circumference of a circle rolling along a straight line (see attached image).

    Christopher Wren (1632–1723) proved that the arc length of the cycloid is four times the diameter of its generating circle.

    Christiaan Huygens (1629–95) thought Wren's work ‘really beautiful’. Blaise Pascal (1623–62) also called it ‘beautiful’ (even though he also seemed to repudiate any true notion of mathematical beauty in his ‘Pensées’.

    Huygens proved that an inverted cycloid was the ‘tautochrone’: the curve along which a body starting from rest and freely accelerated by uniform gravity reaches the lowest point in the same time, independently of its starting point.

    1/3

    #cycloid #tautochrone #Huygens #HistMath #MathematicalBeauty #Pascal

  11. Nicht zuletzt wegen der Lichtverschmutzung im RheinNeckarGebiet ist es oft schwierig, Saturn am Himmel zu entdecken, und Titan lässt sich nur mit einem Teleskop finden. Um so erstaunlicher, dass von Darmstadt aus die kleine Sonde Huygens erfolgreich auf dem Saturnmond abgesetzt wurde. Wirf heute Abend einen Blick in den Himmel und staune über das Universum!

    #Lichtverschmutzung #RheinNeckarGebiet #Titan #Darmstadt #Huygens #Universum
    #Buerstadt #Kalender2026

  12. Corre l'anno 2005. Sotto cieli densi di metano e azoto, la sonda Huygens tocca finalmente il suolo di Titano, la luna più grande di Saturno.

    La discesa, durata due ore e mezza, apre una finestra su un mondo che apparentemente non ci appartiene: rocce composte da acqua e idrocarburi, illuminate da una luce spettrale color arancio. Cosa ha a che fare con noi?

    La superficie, morbida come sabbia bagnata, ha accolto il lander che si è infilato appena sotto la crosta. Le batterie hanno resistito per novanta minuti, più che abbastanza per raccontarci un paesaggio che somiglia a un sogno congelato.

    A –179 °C, Titano racchiude un ambiente chimico - questa è la cosa notevole - che potrebbe ricordare la Terra prima della vita. Ben più che semplice scienza, questo è un invito a immaginare. Forse, in quelle rocce e in quell’aria densa, si nasconde un’eco del nostro stesso passato. Credo sia così: a volte si deve andare lontano, per capire davvero la propria storia.

    Crediti immagine : ESA, NASA, JPL, U. Arizona, Huygens Lander

    #astrocaffe #huygens #terra #titano #NASA

  13. 🌍🌑☀️ Quando la Terra e la Luna eclissarono il Sole viste da Saturno!

    La sonda #Huygens ha assistito a un evento che capita una volta ogni millennio: Terra e Luna sono passate esattamente davanti al Sole, viste da Saturno!
    Un allineamento rarissimo, che si verifica solo due volte ogni mille anni.

    Un allineamento straordinario, a oltre 1,2 miliardi di chilometri di distanza, una vera e propria prospettiva cosmica sul nostro pianeta.

    🌌 Seguici nel gruppo: @[email protected]

    youtube.com/shorts/XHw4Y_1lHss

  14. Zero expansion materials have the interesting property that as they heat up, their crystal structure changes, without changing volume. #Huygens #origami (bistable) #polyhedron

  15. Zero expansion materials have the interesting property that as they heat up, their crystal structure changes, without changing volume. #CTE #Huygens

  16. 14 January 2005, ESA’s #Huygens probe made history as it touched down on Titan, Saturn’s largest moon. This was humankind's first successful landing on a world in the outer Solar System. Relive those moments with this narrated video made with Huygens data youtube.com/watch?v=svmGxFaGIL

  17. 🎂 Le 14 janvier 2005, la mission #Huygens de l'ESA atterrit sur la lune #Titan de #Jupiter.
    Ces images stéréographiques (en fisheye) de la surface de Titan ont été prises pendant la descente de Huygens.

  18. CW: Youtube and Bluesky links inside

    #OTD 14 January 2005, ESA’s #Huygens probe made history as it touched down on Titan, Saturn’s largest moon

    youtube.com/watch?v=svmGxFaGIL

    via bsky.app/profile/esa.int/post/

    Onboard #Huygens, hardware from #MPSGoettingen made its way to the surface of #Titan. We contributed the CCD detector and associated operation electronics to the instrument #DISR – and thus helped to take the first pictures from the surface of an icy moon.

  19. Zo werkt licht met Huygens: golfjes maken golven!

    Hey lieve studenten! Vandaag ga ik jullie alles vertellen over hoe licht werkt met behulp van Huygens' principe. Het is echt super interessant en ik hoop dat jullie er net zo enthousiast van worden ...

    🌞 Leer verder: leeralles.nl/zo-werkt-licht-me

    #GOLFJES #GOLVEN #HUYGENS #LICHT #MAKEN #MET #WERKT

  20. Zo werkt licht met Huygens: golfjes maken golven!

    Hey lieve studenten! Vandaag ga ik jullie alles vertellen over hoe licht werkt met behulp van Huygens' principe. Het is echt super interessant en ik hoop dat jullie er net zo enthousiast van worden ...

    🌞 Leer verder: leeralles.nl/zo-werkt-licht-me

    #GOLFJES #GOLVEN #HUYGENS #LICHT #MAKEN #MET #WERKT

  21. Zo werkt licht met Huygens: golfjes maken golven!

    Hey lieve studenten! Vandaag ga ik jullie alles vertellen over hoe licht werkt met behulp van Huygens' principe. Het is echt super interessant en ik hoop dat jullie er net zo enthousiast van worden ...

    🌞 Leer verder: leeralles.nl/zo-werkt-licht-me

    #GOLFJES #GOLVEN #HUYGENS #LICHT #MAKEN #MET #WERKT

  22. Zo werkt licht met Huygens: golfjes maken golven!

    Hey lieve studenten! Vandaag ga ik jullie alles vertellen over hoe licht werkt met behulp van Huygens' principe. Het is echt super interessant en ik hoop dat jullie er net zo enthousiast van worden ...

    🌞 Leer verder: leeralles.nl/zo-werkt-licht-me

    #GOLFJES #GOLVEN #HUYGENS #LICHT #MAKEN #MET #WERKT

  23. Zo werkt het: Hoe licht zich als golf gedraagt met de truc van Huygens!

    Hallo allemaal! Vandaag ga ik jullie vertellen over hoe licht zich gedraagt als golf, met behulp van de truc van Huygens. 🌟

    Licht is een vorm van elektromagnetische straling en gedraagt zich als go...

    🌞 Leer verder: leeralles.nl/zo-werkt-het-hoe-

    #ALS #GEDRAAGT #GOLF #HET #HOE #HUYGENS #LICHT #MET #TRUC #VAN #WERKT #ZICH

  24. Zo werkt het: Hoe licht zich als golf gedraagt met de truc van Huygens!

    Hallo allemaal! Vandaag ga ik jullie vertellen over hoe licht zich gedraagt als golf, met behulp van de truc van Huygens. 🌟

    Licht is een vorm van elektromagnetische straling en gedraagt zich als go...

    🌞 Leer verder: leeralles.nl/zo-werkt-het-hoe-

    #ALS #GEDRAAGT #GOLF #HET #HOE #HUYGENS #LICHT #MET #TRUC #VAN #WERKT #ZICH

  25. On the 14th January 2003, ESA's Huygens mission landed on Titan becoming the world's first probe to land on a moon in the outer solar system.

    #ESA
    #Huygens
    #Cassini
    #Titan

  26. Toller Fund zu Interferenz von #Wasserwellen und #Huygens Prinzip

    Wasserwellen werden in einem See durch Füße erzeugt und konstruktive/destruktive #Interferenz mit einem Papierboot veranschaulicht

    Kann man womöglich als stummes Video auch durch Schüler vertonen lassen.

    #physikEdu #FediLZ

    yewtu.be/watch?v=4QO4C98ugHQ

  27. 350 Jahre altes Mechanik-Theorem klärt Lichtverhalten. Huygens' Pendel-Gleichungen zeigen Zusammenhang zwischen Polarisation und Verschränkung. #Licht #Huygens #Pendel #Mechanik #Physik
    scinexx.de/news/physik/350-jah

  28. Am 25. März 1655, heute vor 368 Jahren, entdeckte Christiaan Huygens den ersten Saturnmond: Titan.

    Mehr als 44 Jahren nach der Entdeckung der ersten Jupitermonde durch Galileo Galilei wurde damit bei einem weiteren Planeten ein Mond beobachtet.

    2005 landete eine Sonde auf dem Titan, womit erstmals auf einem anderen Mond als dem Erdmond ein Lander aufsetzte.

    #geschichte #historisch #heutevor #geschichtetoday #christiaanhuygens #huygens #astronomie #wissenschaftsgeschichte #saturn #mond #titan

  29. Maël Es-sayeh et collègues ont publié aujourd'hui un article dans le Planetary Science Journal : Nouvel modèle de transfert radiatif pour #Titan dans le proche infrarouge.

    Ils présentent un nouveau modèle qui tient compte des gaz atmosphériques et aérosols. Le modèle a été validé à l'aide de mesures effectuées par la sonde #Huygens et a ensuite été utilisé pour prédire les propriétés de la surface sur le futur site d'atterrissage de #Dragonfly.

    Lire l'article !

    iopscience.iop.org/article/10.

    #IPGP

  30. Maël Es-sayeh and coworkers published today an article in the Planetary Science Journal: "Updated Radiative Transfer Model for #Titan in the Near-infrared Wavelength Range".

    They present a new radiative transfer model that better accounts for atmospheric gases and aerosols. The model was validated using measurements made by the #Huygens probe and was then used to predict the surface properties at the future #Dragonfly landing site.

    Read the article!

    iopscience.iop.org/article/10.

    #IPGP

  31. "AIP: Brillenrezept für Christiaan Huygens nach 300 Jahren"

    "Huygens baute im 17. Jahrhundert hervorragende Linsen, aber seine Teleskope waren im Vergleich zu den damaligen Möglichkeiten nicht sehr scharf. Eine Pressemitteilung des Leibniz-Instituts für Astrophysik Potsdam (AIP).":

    raumfahrer.net/aip-brillenreze

    #AIP #Astronomie #Astronom #Brille #ChristiaanHuygens #Fernrohr #Geschichte #Huygens #Kurzsichtigkeit #Sehvermögen #Teleskop

    2.3.2023

  32. In 1657, Christiaan Huygens built the first clock regulated by a pendulum, and gave us the math to understand how it works. #Science #History #Poetry #Kinematics #Horology #Huygens #Pendulum (sharpgiving.com/thebookofscien)

  33. In 1656, Christiaan Huygens was the first to observe that Saturn had rings. In 1855, James Clerk Maxwell proved that they were composed of millions of tiny orbiting particles. #Science #History #Poetry #Astronomy #Saturn #RingsofSaturn #Galileo #Maxwell #Huygens (sharpgiving.com/thebookofscien)