Optical fibre

A classwork passage xd" Topic: Talk about optical fibre (10 mins) Optical fibre is a tube-like devices which can transmit light. It's made by glass and some other material, layer by layer. Since total internal reflection always occur inside the tube, and the tube can be bent into a certain angle, it can transmit light in the curved path(though the light is running in stright line inside the tube). There are various application of optical fibre. The most important use is the usage on telecommunication services. Comparing with the traditional wire, it's much cheaper since the traditional wire uses a lot of copper. Even the material cost is more expensive than the production cost of optical fibre considering the same voume. Optical fibre also transmit information at a higher speed, since the signal medium is light. It gives different signals through different strengths of light, and it's signal is continuous. (The signal of copper wire is transmit by electricity and it's not continuous.) Most of the overseas cable were made by optical fibre now, and major communication network usually uses optical fibre. Centainly there is still is big room for optical fibre to development, following with the globalization, communcations between conutries and countries become more important. This require a high speed and capacity(band width) devices. Optical fibre is the best that we've ever known. In the future, optical fibre will be a major wired devices which can transmit information. It will not be replaced by other devices unless there's a breakthrough in wireless communication techlonogy which is more cheap or able to transmit more information at the same time in a far distance. Optical fibre may be able to transmit more information at the same time by using a more complicated system of signals. In the future, optical fibre may be applicated very frequently in our daily life. And at the moment, there're still some researchs on optics, nano techlonogy, information techlonogy and quantum physics, which will improves optical fibre. This passage was finished by me this morning, within 15 minutes. It's good to create one like this because optical fibre is a broad and intresting topic. =] P.S. This passage talks too much. I don't think that it's all "related to exam". Only the structure and the basic usage is enough although I write this out without any reference... Bold letters are main point that adviced to remember.

26-03-09

580天前。同樣是3:40~5:00。課室。 那時我在英國。一個叫David的professor教了我玩modular origami, 摺Sonobe unit。 從此，書櫃盡是Sonobe unit和PhiZZ unit，用了一盒又一盒的紙； 做了Maths project，並因為自己領導無方被獎溜走了； 580天後的今天可以把Sonobe unit教給同學，有機會係Maths Fiesta/Open day展示 實在係我榮幸呢！ 我或許不懂教大家砌好Octahedron 我或許教不好你們摺得又快又準 我也可能把個人心得飛掉了 但，還是那一句，practice makes perfect 暑假時我用了幾百張紙先弄明白icosahedron的砌法 將archmedian solids的duality特性算進Sonobe solid當中 心得其實不難，但一定要有數學底子。 「對於一階(f1-f2...-fn)立體，其close ring之組合為f1...fn。 對於N階(f1-f2...fn)'(k)立體，其close ring之組合為(f1,6...(k 6's), f2,6... fn,6...6)」 為甚麼？因為一個truangular ring of Sonobe unit係等邊三角形，因此6個triangular ring成為closed ring的angle sum 為360度，即zero curvature。 (抱歉……我讀這部分的3-D Geometry and theirems是用英文學的) 這是Sonobe unit的特別之處，不比Rhombus unit(限定3個為curved ring), Icos Triangle unit (要做equilateral trianglular ring還要算一大堆)，所以Sonobe unit又稱為最易的modular origami, 原因不是它易砌，而是易construct一個Sonobe unit的大概圖出來。 關於這部分，我並沒有打進Maths project中，因為摺的進階心法不太可能適合於口味奇怪的評審員……不過把它放這裡，卻可以讓大家更容易理解Sonobe unit的摺法，還有明白為甚麼我可以對住一個archmedian solid(甚至再次一等的regular/4 solid)就可以幾下砌出來。這正是Modular origami的精髓：不是砌已有的Solids，而是從理論中的無限組合中變化。 *順帶一提，2-cube(9)這個的原型是兩個tetrahedron，而不是一個長長的立體。還有，我所講過的「拼長方體法」，只可以做實心的立體，不可以做Spongy model(3D碎形)那些，我試過砌spongy model的話會因奇偶性問題不能完整砌好，不過也可以試一下(72 units)。

22-03-09

史無前例最短日記…… 我實在不知道要怎樣寫下去； 我實在不知道怎樣寫"偶像"； 我也不知道為啥現在寫日記； 明天有Bio test， 打Osu!後面又有Makubex， 誰可以幫我？

Carol的一萬字－之八

抱歉有一段時間沒寫了

單車於七十年代風靡全港，但到底何時開始有「單車」這種概念，則無從考究了。 據說溥儀在1922年(民國11年)結婚時，其表哥送了架單車給他，溥儀更因為要練車將皇宮的門檻拆功去(溥儀--我的前半生)，直至1924年馮玉祥砲轟紫禁城，驅溥儀出宮為止，踩單車一直都是其嗜好。另外，香港傳入單車的時間無疑也是七十年代頭，當然也以發展中的新市鎮為甚，因為英政府發展新市鎮時幾乎沿路炮製單車路。因此現在於沙田，特別是城門河一帶，一定會見到路旁有一條單車徑，並且曲折蜿蜒地覆蓋整個沙田。另外，港島南區一帶也曾出現過單車熱潮，但該區實在太多山路，對初學者而言實在太難了。不過，今時今日我們仍然可以看見山頂道、淺水灣道一帶看見專業車手的蹤影。 到底這個熱潮是何時消失的呢？大概就在90年代中。在97金融風暴前，彭定康成功地繼承七十年代影響甚大的決策，帶領香港高飛。幾乎每個成年香港人也必定聽過當年香港人有錢到怎樣：「魚翅撈飯」、一席席的鮑參翅肚……那時，幾乎每個稍為有錢的家庭都會有一部車－－單車就自然會被淘汰了。後來隨著交通網絡日益發達，單車也很難再掀起熱潮。 =========== 就這樣，我被那個多事的同學推去找神祕人。 根據他說，這個車神艦隊裡的人都有兩個共同特質－－自然是單車高手，而且都一定夠帥氣、漂亮。這個到底是增加名氣的噱頭還是真有其事？他自己也說不清楚……不過，那天我看見的神祕人看上去還蠻有氣質的。 到底這車隊看上我的原因是甚麼？ 我自己從來不認為自己是好看那一類，也不覺得自己踩單車很好……那我有資格考進去嗎？…… 帶著一肚子疑問，我還是跟他來到約定的地點。 「雅，你還留在這裡幹嘛？」 我的同學，陳俊雅，一副理所當然的樣子回答說：「當然在這裡看戲囉。」 我等了好一會，才發現那個可惡的神祕人從來沒有說過時間！ 現在是兩點三十分，我到底等不等他們呢？我又沒有帶書本或遊戲機，呆等的話會比寫作業痛苦吧……我不知不覺地走到幾架單車前。在郊區，在交叉路口看見單車是很正常的事。 這幾架單車很新淨，看起來也不像原廠生產的。正當我把手放到車上時，一名少女跑出來喝住了我：「喂！那可是我的車，不要亂碰！」 面前的這位少女有著一副白皙臉蛋，長而柔軟的黑髮披在肩上，她用著奇怪的目光打量著我，道：「你……是簡大哥邀請的人吧？有帶著他給你的指環嗎？」 原來那個神祕人叫「簡大哥」啊…… 「嗯。」我把戒指拿出來。 「那，有興趣來比一局嗎？」 「比甚麼？」我苦笑著，難道一個業餘也稱不上的車隊可以跟車隊的人對量嗎？ 她幽幽地道：「不如我們大家在單車上數一下從這裡到下個街口的電線杆數目吧！這裡附近的電線杆是用木造的，數起來也不難……」 「甚麼？！？」 ……

(1067字，怎麼越寫越長？)

Waltz...

絕對好聽~ Itou Konako - Waltz [Normal] +hardrock mod 2,647,098 , S , 98.19% acc 有段Bubbles - F [Hard] 不過影得好差 想睇自己去search

08-03-09

拆散了4x4的扭計骰，試了無數次終於弄好了

(1)一開始的爛樣

(2)整理好的零件，留意紙上的字同有個=Pge樣！！

(3)即將完成

(4)Yeah~

============

Osu! 突破4億分，上到#480

十萬個多謝Saturio幫我打左成3千萬分

十萬個多starrokirby86幫我mod好OblivioN

=]

Carol的一萬字－之七

「……」這句話仿如一把尖刀插進我的心裡。因為如果不是他，我也不會選爛車。 他沒有等我反應過來，繼續道：「呵呵，不想跟陌生人說話喔？」 「……」可惡！這個口臭兼多事的人好煩啊！我正想借隧道的斜坡甩開他，他卻比我加速得更快更瘋狂，就如脫疆的野馬一樣。 他依然不理我，說道「要知道新車不一定是好，舊車也不一定是壞；新車當然有它的好處，例如它能保證車胎夠新，還有零件也不會有磨蝕。然而，不到一半的新車可以用到幾年以上，當中有被初學者不小心騎壞的，也有因為品質不夠好而報廢。因此舊車大部分都不會被騎壞──因為它們鮮有被初學者選中，自己也有一定的質素。當然啦，太舊的就如你那一部就很難說了，大概真的會隨時掉零件吧！」 我漸漸留意他的說話，不知不覺間也過了好大段路，竟然沒有撞到障礙物。 「另外，近年單車租賃店的服務也很完善，很多時候會把原廠買來的車輛改裝。由於原廠的車輛是設計給職業車手用用的，他們不會坐著，因此坐板很窄，單車店就會換一些比較闊的。此外，他們也會換一些適合附近路段用的車胎。這些改裝又以舊車為先，所以選舊車也不給呢！」 「嗯……」正在整理思緒的我隨便應了一聲。 「另外……」他忽然露出了個詭異的微笑，「你的駕車技術也不錯啊，望著我踩也不會扭錯方向，一跆的汽水罐也避開了。有興趣加入我們車隊嗎？」 天啊！我沒扭錯方向也就罷了，我連路有汽水罐也有不知道啊！ 「不用那麼快決定啊。兩星期後你想來的話我自然會在這裡等你。」說完就逕自往旁邊的村屋小路駛去，消失的無影無蹤。剩下的只有他交給我的一只銀色戒指，上面有一些不知名的圖案。 …… 當他們追上我的時候，其中一位注意到我手上的戒指並驚訝道：「這是車神艦隊？楠你也太酷了吧！」 (700字)

03-03-09

100%失望 第一次Maths咁差 點解會諗唔到ga？！？ ..... --------------- 放學係三聯KO暮蝶了 超級好看 而且係我第一次猜中主謀+幫兇係邊個 (細聲)(慕昱薇+佢細路) 不過估錯動機 我原本估係呀薇佢自己知關於琉璃蝶的資料俾人知道左 真正動機自己睇 感覺上好似閉鎖3咁，不過呢本更好睇 XD chouchou真係勁= =點解只係人地「巧合」佢都知？ Zenky解釋唔到……(笑) 顏色鮮艷的植物有毒，七彩繽紛的蟲也有毒，不過靚ge女仔更毒。 呢個係推理小說的鐵律也。 憑住呢點係地下室兇案後就唔難估到，畢竟佢留低太多破綻啦 xD 另外似乎係Zenky手下姊弟對都一樣咁靚.... 【M.S.Zenky‧望宸-趕稿子】先來寫開心的故事～言小版12634是在推我耶～真不好意思XDDDD大家都想要一隻愛德華～～ 說： 這個很顯然是受到橫溝正史推理小說的影響啊...........（笨蛋） 另外，Zenky填左首靚詞，suit落每一章到，勁！不過第一句放落title...怪 :P <<蝶戀花>> by M.S. Zenky 故友十年終一會。暮城初臨，山下謠言沸。夕日流光天漸逝，晨時村口懸殘翅。 深鎖幽房聞血繪。狂雨霏霏，似夢仍無畏。坐看曙光雲漸退，翩翩蝶舞霞紅淚。

Red sign (O2 Jam)

2段片，第一段係piano版，第二段係original，原本係O2 勁歌，移植到Osu!

Outline of solution, Ch.9 WS 1 Part Two

That's the remining part of worksheet. I only give one solution here, simple and fast(maybe). Please don't copy the solution of no.4 bacause it's just a alternative way, without step and just for refrence. ==== 3. In the figure, ACDE is a sq. B is the mid point of CA, DE is produced to F such that CG=GF, and G is also lying on BE. GF and BE are stright lines. ai) Prove that triangle ABE congruent to EFA Solution: Seems a stright forward question, but actually not. Note that BA =EF has NOT BEEN GIVEN yet. CA//DF can only give you a pair of (equal) right angle, which is stated also by prop. of sq. .BE // AF also has not been given yet. Therefore, the only thing you can do is prove BA=EF. Focus on triangle CBG, which is congruent to FEG, then CB=EF=BA (corr. sides; given), since you prove that, it's not hard at all, you'll got two sides plu one right angle, and the reason is S.A.S. aii) Prove triangle ACH similar to EFH. Not hard. two times of alt. angles (or one time with prop. of sq.) plus a pair of vert. opp. angles give you A.A.A. for this. b) Hence, find area of triangle AHF: area of triangle of HEF Note that both triangle have diff. base but the same height, so that this questions is same as AH:HE. Apply 2 sides prop. on the similar triangle, and got 2:1. Summary: sometimes (a) is the most difficult part because something likely given (and true) hasn't been given to you. You should look carefully about the given information. 4. ABCD is a //gram, with E is a (free) point lying on AB, EC and BD intersect at F., find area of triangle DEF : area of triangle CBF. (HKCEE 2007 MC) Solution: Teacher said that it's all about primary knowledge, but I have no idea about the way to solve it. Let's take another way, just sensing and not a standard solution. Since E is a free point on AB, Let's let E is at the same position as A. By prop. of //gram, diag. bisect each other, and so that the two triangles are congruent! Well, 1:1 and this is a MC and don't too care the step. *xd* Summary: When there's some free point in the figure, try to move these point and get solution, but never try to do this when steps are required. 5.ABCD and ADEF is 2 identical rhombuses(shares the side AD), G is a point on AD such that BGE is a stright line. a)prove AG=GD. Once you finish reading the question, mose probably triangle ADE will be concerned, but remember this' an rhombus, and "identical rhombuses" give you a pair of equal sides, and prop. of rhombus gives you two pair of equal angle by parallel lines, and triangle DGE is congruent to triangle AGE, by corr. sides, AG=DG. b)Hence, if AD is perpendicular to BE, prove AEF is an equilateral triangle. In fact, "if" is rubbish because once you proved (a), AD is already perpendicular to BE (prop. of icos. triangle). You can find that triangle DGE is congruent to AGE, so that DE=AE(corr. sides), and it's not hard to get that AF=FE=DE=AE, so AEF is equilateral (by defination) Summary: Still, beware of the information that you had, never apply thing that you haven't got. 6.ABFE, BCGF and CEHG are 3 identical sq.s, (sharing lines BF and CG) Let angle DEF = a, angle DFG=b, and angle DGH=c. Show that a+b+c is an right angle. Just a verrrrry classical question. You will see this every year whatever in exam, competitions,... But let's follow the steps of worksheet. a)Show that triangle DFG is similar to triangle DEB. A.A.A. is useless here, but there's lot of right angle here, which means Pyth. thm. is useful here. Let AB=x, and calculate those sides and apply 3 sides prop.. b)show that angle BEF = a+b Not hard. Apply corr. angles and prop. of sq. and got it. c)Show a+b+c = 90 degrees. since angle BEF=angle DGH=45 degrees (prop. of sq.) their sum if 90 degrees. Warning: DON'T think that ext. angle of triangle is useful here. Infinite prople has dumbly tried this and got a beautiful zero mark without the above steps. Ext. angle can only tell you pretty a lot of rubbish and return to the original problem for this type of question. .Summary: This is a claaical question of sum of degrees. You know nothing about the angles (c is 45, but a and b is irrational no.), and nothing can be applied. Maybe similar triangle can tell you some more pairs of equal angle and help you to find out the answer. That's all about the question, and welcome to ask me or provide more way to do it (esspecially no.4). Back to part one: http://allmaths.blogspot.com/2009/02/outline-of-solution-ch9-ws-1-part-one.html

28-02-09

Time : 2:30~5:30 Venue: 港島民生 3"年"不見未必要刮目相看…… 依然係果堆人：盧Andy, 賴Zenky, 喇沙肥仔，陳某人.... 實力也不差很遠 40名我也還是1X 要好似小學時出7隊當然OK 出2隊就未夠班了 小學ge題目唔難，要的係狠+準 初中ge國際奧數級要的係快+狠 用Osu! darrihuka的歌打個比喻，小學係Fiesta[relaxing]，只有100%F.C.才有排名 所以個international邀請賽岩左14out of 15只有Third class prize，相當於Fiesta[relaxing] top 40係98.5%(no mod) 咁初中就係Red sign[darri Mix]，那怕唔夠準，只要夠快，岩一半多D就足以登上殿堂。就好似Red sign[darri miX]的Top 40只要670 combo(out of 1010) IMO級應該係OblivioN[darri MiX]，對普通人來說已是遙不可及，高手的快狠準以外還需要一些板斧，當然就是Number theorey……OblivioN[darri mix]一樣唔係常人可以打，cyclone F.C. 佢時同樣係LRZX混打…… TEST永遠是可怕，可惡的 吳老頭子玩扣分 可惡 其實一份卷我應該做到10 out of 13~14 只能怪自己唔小心，2分卷一份5一份6 10分係代表隊passing line 我要+++++倍努力 (Now typing the rest of solution of WS...)