Загрузка видео...

Не удалось загрузить видео

На главную

Why sin²θ + cos²θ =1? A Geometric Proof.

stemexplor's profile picture

S.T.E.M Explorer

55,093 subscribers

35,879 просмотров • 3 месяцев назад •via X (Twitter)

ОбразованиеНаука и технологии
LIVE

Anya Rossi• Live Now

Private livecam show

Комментарии: 0

Нет доступных комментариев

Здесь появятся комментарии из оригинального поста

Похожие видео

Finally got to know the real use of Sin θ/Cos θ …!💀🔥🙌🏼
2:44

Finally got to know the real use of Sin θ/Cos θ …!💀🔥🙌🏼

Ravi Tiwari🇮🇳

40,396 просмотров • 2 месяцев назад

🎶🎸(❛▽❛)✨♪( ´θ｀)🥁🎶!!
0:23

🎶🎸(❛▽❛)✨♪( ´θ｀)🥁🎶!!

✨内田清輝・グ弍✨

113,801 просмотров • 2 лет назад

ブラジル人にウケる一発ギャグ(θヮθ) (ﾉﾉ_☆)ｗｗｗｗｗｗ
0:24

ブラジル人にウケる一発ギャグ(θヮθ) (ﾉﾉ_☆)ｗｗｗｗｗｗ

コ タ ツ ミ

91,724 просмотров • 5 месяцев назад

“٩ﾉ( ＾ᗜ＾)θ♬゜ #SDVX
0:33

“٩ﾉ( ＾ᗜ＾)θ♬゜ #SDVX

SOUND VOLTEX STAFF

698,389 просмотров • 1 год назад

This is points P_k at polar coords (radius = k·r, angle = k·θ) as θ spins. Connect sequentially: • small θ → smooth Archimedean spiral • θ = 2π·p/q → perfect n-gons & stars emerge!
0:20

This is points P_k at polar coords (radius = k·r, angle = k·θ) as θ spins. Connect sequentially: • small θ → smooth Archimedean spiral • θ = 2π·p/q → perfect n-gons & stars emerge!

Mathematica

23,350 просмотров • 2 месяцев назад

n₁ sin(θ₁) = n₂ sin(θ₂) This elegant equation describes how light bends at the boundary between two media. Here, n₁ and n₂ are the refractive indices, while θ₁ and θ₂ are the angles of incidence and refraction measured from the surface normal. As light rays obey this simple trigonometric relationship, beautiful caustic curves emerge and focal points shift with every change in geometry or material. It is pure geometric optics at its finest: the raw interaction of light and matter, reminding us that the universe is governed by beautiful, predictable symmetries. This is used while designing high-resolution camera lenses (correcting aberrations for sharp focus) and enabling fiber-optic communication through total internal reflection.
1:05

n₁ sin(θ₁) = n₂ sin(θ₂) This elegant equation describes how light bends at the boundary between two media. Here, n₁ and n₂ are the refractive indices, while θ₁ and θ₂ are the angles of incidence and refraction measured from the surface normal. As light rays obey this simple trigonometric relationship, beautiful caustic curves emerge and focal points shift with every change in geometry or material. It is pure geometric optics at its finest: the raw interaction of light and matter, reminding us that the universe is governed by beautiful, predictable symmetries. This is used while designing high-resolution camera lenses (correcting aberrations for sharp focus) and enabling fiber-optic communication through total internal reflection.

Mathematica

32,750 просмотров • 1 месяц назад

虽然有毛毯，可是一下一下的撞上去，还是疼的(ΘへΘ)
1:43

Sensitive content

虽然有毛毯，可是一下一下的撞上去，还是疼的(ΘへΘ)

凌小湿

19,990 просмотров • 2 лет назад

#ジャンボ文鳥 #茜音 ( ･θ･)ﾁｮｯﾁｮｯﾁｮｯﾁｮﾁﾁﾁﾁﾁﾋﾟｭｰｲ♪
0:54

#ジャンボ文鳥 #茜音 ( ･θ･)ﾁｮｯﾁｮｯﾁｮｯﾁｮﾁﾁﾁﾁﾁﾋﾟｭｰｲ♪

saeko

45,439 просмотров • 1 год назад

n₁ sin θ₁ = n₂ sin θ₂ Watch this laser hit the glass-air boundary. At first, it bends out (refraction). Then... boom. Angle exceeds the critical θ_c = arcsin(n₂/n₁) ≈ 42° for glass (n≈1.5), and every photon turns back inside. No leakage. Pure total internal reflection. This is why fiber optics carry the internet across oceans without losing signal. Why diamonds sparkle like crazy. Why light can get trapped in a stream of water.
0:28

n₁ sin θ₁ = n₂ sin θ₂ Watch this laser hit the glass-air boundary. At first, it bends out (refraction). Then... boom. Angle exceeds the critical θ_c = arcsin(n₂/n₁) ≈ 42° for glass (n≈1.5), and every photon turns back inside. No leakage. Pure total internal reflection. This is why fiber optics carry the internet across oceans without losing signal. Why diamonds sparkle like crazy. Why light can get trapped in a stream of water.

Mathematica

48,338 просмотров • 2 месяцев назад

Έλενα Χαραλαμπούδη Θ-Ε-Α ! Ως εδώ ακούστηκε η τάπα στο Φιπστερ
0:56

Έλενα Χαραλαμπούδη Θ-Ε-Α ! Ως εδώ ακούστηκε η τάπα στο Φιπστερ

Η Αβυσσαλέα 🎯🎲

43,002 просмотров • 1 год назад

Hmm? Something's weird? My smartphone is posting without my permission!📱♪( ´θ｀)ノ
0:55

Hmm? Something's weird? My smartphone is posting without my permission!📱♪( ´θ｀)ノ

beekeeper

30,476 просмотров • 11 месяцев назад

Δεν βάζω συχνά δηλώσεις του π/θ αλλά ήταν δυνατή η σφαλιάρα.⬇️
1:32

Δεν βάζω συχνά δηλώσεις του π/θ αλλά ήταν δυνατή η σφαλιάρα.⬇️

Aris ⚔️

29,251 просмотров • 3 месяцев назад

#ジャンボ文鳥 💢(•ө•)💢ｷﾞｬﾙﾙﾙﾙﾙ (｡･ө･｡)💢ｷｬﾙﾙﾙﾙｧｧﾙｶﾞﾗﾗﾗｧｧﾙﾙﾗｧ!!! ( ･θ･ )💢……!!……ｯｯｯ!!!ﾋﾟﾋﾟ!
0:29

#ジャンボ文鳥 💢(•ө•)💢ｷﾞｬﾙﾙﾙﾙﾙ (｡･ө･｡)💢ｷｬﾙﾙﾙﾙｧｧﾙｶﾞﾗﾗﾗｧｧﾙﾙﾗｧ!!! ( ･θ･ )💢……!!……ｯｯｯ!!!ﾋﾟﾋﾟ!

saeko

38,252 просмотров • 5 месяцев назад

In 1998, Japanese Mathematician, Engineer and Machine Learning pioneer Shun-ichi Amari published "Natural Gradient Works Efficiently in Learning (722 Cites in Papers and 9 Cites in Patents)" and made a point that still feels fresh even today If your loss is L(θ), then the usual update θ̇ = −∇ L(θ) quietly assumes your parameter space is flat. Amari asked what happens when the model itself has geometry, described by G(θ), the Fisher information. Then the more natural direction becomes θ̇ = −G(θ)⁻¹∇ L(θ). This is the same loss, but with a different notion of distance. As the animation shows, ordinary Gradient Descent follows the raw slope and gets dragged around by distortion, while the natural gradient moves in a way that respects the geometry of the statistical model itself.
0:20

In 1998, Japanese Mathematician, Engineer and Machine Learning pioneer Shun-ichi Amari published "Natural Gradient Works Efficiently in Learning (722 Cites in Papers and 9 Cites in Patents)" and made a point that still feels fresh even today If your loss is L(θ), then the usual update θ̇ = −∇ L(θ) quietly assumes your parameter space is flat. Amari asked what happens when the model itself has geometry, described by G(θ), the Fisher information. Then the more natural direction becomes θ̇ = −G(θ)⁻¹∇ L(θ). This is the same loss, but with a different notion of distance. As the animation shows, ordinary Gradient Descent follows the raw slope and gets dragged around by distortion, while the natural gradient moves in a way that respects the geometry of the statistical model itself.

Mathelirium

45,750 просмотров • 3 месяцев назад

"Αν δεν υπάρχει δρόμος, εμείς θ’ ανοίξουμε τον δρόμο." Μαζί σε όλα 🤘🏼☘️ #paobc
2:19

"Αν δεν υπάρχει δρόμος, εμείς θ’ ανοίξουμε τον δρόμο." Μαζί σε όλα 🤘🏼☘️ #paobc

Crash☘️

13,777 просмотров • 1 месяц назад

Got too turnt and got shut down LOL 🔥🔥🔥 📸: magnus θ∆
0:24

Sensitive content

Got too turnt and got shut down LOL 🔥🔥🔥 📸: magnus θ∆

Foster 🔜 AC

36,090 просмотров • 1 месяц назад

⋛⋋( ‘Θ’)⋌⋚宇宙味！ chocolate box 🍫※音が出ます Full 🛸 #オカモモ (Okamomo) #ダンダダン #Dandadan
0:43

⋛⋋( ‘Θ’)⋌⋚宇宙味！ chocolate box 🍫※音が出ます Full 🛸 #オカモモ (Okamomo) #ダンダダン #Dandadan

ひかり/(夏光)

78,038 просмотров • 1 год назад