#$16.42

[mtg-cards-hourly]

Praetor's Grasp

"Wake up, new Phyrexian Planeswalker! You will not be the last." —Jin-Gitaxias

Artist: Ryo Kamei TCG Player Link Scryfall Link EDHREC Link

[kalbinnefhasi]

Ya çığlık atmanın toplumda yargılanmaması lazım çünkü

Çünkü beni bu hale siz getirdiniz amk

[heckaroniandcheese]

this time yesterday i was nearly in tears on the toilet thinking at best i was going to have to call out of work to have a doctor. induce bowel movement. I'm pleased to announce that i had four truly perfect poops today and three of them were on the clock at work.

[yourninjasareajoke]

lots of track feat. potential adventure and misery monopoly

oregon relays music was buss

[merpmonde]

Sangaku Saturday #14 - the grand finale!

We are only a few steps of algebra away from solving the "three circles in a triangle" problem we set in episode 7. This method will also yield general formulas for the solutions (first with height 1 and base b; for any height h and half-base k, set b=k/h and multiply the results by h).

Before we do that, it's worth noting what the sangaku tablet says. Now I don't read classical Japanese (the tablet dates back to 1854 according to wasan.jp), but I can read numbers, and fishing for these in the text at least allows me to understand the result. The authors of the sangaku consider an equilateral triangle whose sides measure 60: boxed text on the right: 三角面六尺, sankaku-men roku shaku (probably rosshaku), in which 尺, shaku, is the ten marker. In their writing of numbers, each level has its own marker: 尺 shaku for ten, 寸 sun for units, 分 fun for tenths and 厘 rin for hundredths (毛 mô for thousandths also appear, which I will ignore for brevity). Their results are as follows:

甲径三尺八寸八分六厘: diameter of the top (甲 kou) circle 38.86

乙径一尺六寸四分二厘: diameter of the side (乙 otsu) circle 16.42

反径一尺二寸四分二厘: diameter of the bottom (反 han) circle 12.42

I repeat that I don't know classical Japanese (or much modern Japanese for that matter), so my readings may be off, not to mention that these are the only parts of the tablet that I understand, but the results seem clear enough. Let's see how they hold up to our final proof.

1: to prove the equality

simply expand the expression on the right, taking into account that

(s+b)(s-b) = s²-b² = 1+b²-b² = 1.

2: the equation 2x²-(s-b)x-1 = 0 can be solved via the discriminant

As this is positive (which isn't obvious as s>b, but it can be proved), the solutions of the equation are

x+ is clearly positive, while it can be proved the x- is negative. Given that x is defined as the square root of 2p in the set-up of the equation, x- is discarded. This yields the formulas for the solution of the geometry problem we've been looking for:

3: in the equilateral triangle, s=2b. Moreover, the height is fixed at 1, so b can be determined exactly: by Pythagoras's theorem in SON,

Replacing b with this value in the formulas for p, q and r, we get

Now we can compare our results with the tablet, all we need to do is multiply these by the height of the equilateral triangle whose sides measure 60. The height is obtained with the same Pythagoras's theorem as above, this time knowing SN = 60 and ON = 30, and we get h = SO = 30*sqrt(3). Bearing in mind that p, q and r are radii, while the tablet gives the diameters, here are our results:

diameter of the top circle: 2hp = 45*sqrt(3)/2 = 38.97 approx.

diameter of the side circle: 2hr = 10*sqrt(3) = 17.32 approx.

diameter of the bottom circle: 2hq = 15*sqrt(3)/2 = 12.99 approx.

We notice that the sangaku is off by up to nearly a whole unit. Whether they used the same geometric reasoning as us isn't clear (I can't read the rest of the tablet and I don't know if the method is even described), but if they did, the difference could be explained by some approximations they may have used, such as the square root of 3. Bear in mind they didn't have calculators in Edo period Japan.

With that, thank you very much for following the Sangaku Weekends series, hoping that you found at least some of it interesting.

[edeess]

Onu acıtmak için akıttığım zehir yine bana bulaşdı.

16.42

[plasticdreams]

25: 2021/07/31(土) 00:14:16.12 ID:5NKimQGx0 なんJ相談員ならこんなに優しいのに 174 風吹けば名無し 2019/07/30(火) 00:36:16.42 ID:m3gWn+010 ガルちゃんで女が輝くのは30代後半からだから結婚は焦っちゃだめってレスして回ってたの実はワイなんや… 許してクレメンス… 580 風吹けば名無し 2019/07/30(火) 01:03:44.24 ID:m3gWn+010 >>542 特に婚活トピでこのレスするとめっちゃ＋がついて気持ちよくてやめられん 悪いのは分かっとるんやけどワイが気持ちよければあのトピにいる女が行き遅れようとワイの知ったことではないからどうでもいい 29: 2021/07/31(土) 00:15:25.74 ID:nIUml1yW0 >>25 ひどくて草

38歳婚活女子「結婚相談所に行ったら42歳のおっさんを紹介されました。こんな人と道を歩けません(怒)」 : はーとログ

[amol-98]

The Road Ahead – Navigating the Future of the Automotive Industry

🌍 Market Overview

The Global automotive industry Market Size is evolving rapidly, driven by technological advancements, sustainability initiatives, and changing consumer preferences. Automakers are embracing electric vehicles (EVs), autonomous technology, and digital transformation to stay ahead.

Download a Free Sample : https://rb.gy/iwh4in

📈 Growth Drivers

✅ Electrification – Rise in EV adoption due to sustainability goals and government incentives. ✅ Autonomous Vehicles – Investments in self-driving technology from major players like Tesla, Waymo, and GM. ✅ Connectivity & IoT – Smart features, in-car AI, and enhanced safety tech. ✅ Urbanization & Mobility Services – Growth of ride-sharing and subscription-based vehicle models.

⚠️ Key Challenges & Factors

🚧 Chip Shortages – Semiconductor supply chain disruptions affecting production. 🚧 Regulatory Hurdles – Stricter emissions policies worldwide. 🚧 Consumer Preferences – Shift towards SUVs and electric mobility. 🚧 Raw Material Costs – Fluctuations in lithium, nickel, and other EV battery components.

🔥 Emerging Trends

🔹 EV Market Boom – Tesla, Rivian, and legacy automakers expanding electric fleets. 🔹 Hydrogen Fuel Cell Tech – Toyota & Hyundai leading innovations. 🔹 Sustainable Manufacturing – Recycling initiatives & carbon-neutral plants. 🔹 Software-Defined Vehicles – Over-the-air (OTA) updates & AI-driven enhancements.

Related Urls :

https://www.sphericalinsights.com/reports/automotive-blockchain-market https://www.sphericalinsights.com/reports/china-halal-logistics-market

[homestuckreplay]

February 7, 2010

Homestuck Day 244

New Pages: 1328 - 1335

% Completion (Pages): 16.42

% Completion (Time): 11.77

[mtg-cards-hourly]

Shadowy Backstreet

Artist: Sergey Glushakov TCG Player Link Scryfall Link EDHREC Link

[kalbinnefhasi]

BEN GERÇEKTEN KULLANILMIŞIM

[tulisanutin]

Hai Luthfi..apa kabar nak..

Mama masih harus belajar

Untuk :

Belajar bersabar pun berat

Belajar ikhlas pun terasa berat

Tapi harus di jalani semua nya

Rindu dan kangen hanya bisa

Memeluk bayangmu saja

Walaupun nanti nya kita bertemu

Di surganya Allah..

Cinere, 26. 12. 24 | 16.42

[uni-rie]

Jangan menyerah

Apa yang sudah engkau mulai, jangan lagi mudah tergoda untuk memberi kesempatan salah itu kembali datang, jangan pernah membuka pintu untuk seseorang yang memang tidak diperkenankan untuk masuk. Cukuplah masa lalu sebagai pelajaran untuk berjalan lebih hati-hati, agar tidak lagi tersandung dan mengalami luka yang sulit untuk kau obati sendiri.

Walaupun perlahan tapi pasti, tutup segala yang akan membuatmu kembali, terus berjalan dengan cahaya yang terus kau imani, jangan putus asa seluruh perjuangan tidak akan sia-sia selama engkau yakin pada satu petunjuk, yaitu Ilahi Rabbi.

Hari 1, untuk yang lagi berjuang berbenah diri...

Di tengah terik sore, 17 Juni 2023

16.42 |

[edeess]

Beni mahvediyorsun farkında değilsin.

16.42

[embundidaun]

Tidak ada tempat cerita selain mencoba bercerita ke diri sendiri, awalnya terlena akan seseorang yang bisa mendengarkan semua cerita kita tapi pada dasarnya mereka hanya kepo tidak bermaksud benar -benar perduli,

Lelah terkadang menghadapi orang-orang tidak benar-benar baik

Adil

Bandung, 30 Januari 2024 | 16.42

[jaguarmen99]

771 名無しさんにズームイン！ 2023/04/30(日) 14:20:16.42 9u6tGN5k0エジプトのピラミッドは結構ホワイト労働って説有り815 名無しさんにズームイン！ 2023/04/30(日) 14:22:32.09 RsYWBkt10>>771働いた後にビール飲んでる壁画がみつかったんだっけ846 名無しさんにズームイン！ sage 2023/04/30(日) 14:24:16.94 5EMUHi7s0>>815それどころか呑みすぎて二日酔いで休んだという記録まである858 名無しさんにズームイン！ sage 2023/04/30(日) 14:25:08.01 Mmb7VNQ50>>846俺、どんなに二日酔いひどくても仕事は休んだことねえわｗ795 名無しさんにズームイン！ 2023/04/30(日) 14:21:04.29 DOC9XINM0ピラミッドは奴隷じゃなくちゃんと報酬出てた労働者だったって最新の研究で明らかになってんぞ無知なオジキやなぁw804 名無しさんにズームイン！ sage 2023/04/30(日) 14:21:47.55 VzQetlc40>>795でも奴隷が存在しなかったらモーセのエジプト脱出はないのよ856 名無しさんにズームイン！ sage 2023/04/30(日) 14:24:59.04 XiEhYGzF0>>804エジプト側の記録では不潔な民族だから追い出したとか書かれてるそうな

続・妄想的日常