Joseph Bentrand
:
1 ê 圓形內底, 畫 1 ê 正 三角形, hit 三 ê 角 hē tī 圓ê 箍線 頂。問題： random 隨機 chhìn-chhài tī chit ê 圓形 線頂 2 點 牽 1 條 直線, án-ni-siⁿ chit 條 直線 長 ē 比 hit ê三角形 1 條 邊線 khah 長 ê 機率 有 jōa chōe ？
頭 1 ê 解：看 長度, 1：1 -- 1/2
第二 解：看 直線中間點 落 tī toh, 1/4
第三解： 看 角度, 1/3
Chit 3 種 解答 lóng 真有道理， án-ni, 到底 kám ē-tàng 回答 原本 ê 問題 leh？
ē-sái ê 理由 是 cháiⁿ-iūⁿ？ bōe-sái ê 理由 iū-koh 是 cháiⁿ-iūⁿ ？
Random chords, selection method 1; red = longer than triangle side, blue = shorter
Random chords, selection method 2
The "random endpoints" method: Choose two random points onthe circumference of the circle and draw the chord joining them. To calculate the probability in question imagine the triangle rotated so its vertex coincides with one of the chord endpoints. Observe that if the other chord endpoint lies on the arc between the endpoints of the triangle side opposite the first point, the chord is longer than a side of the triangle. The length of the arc is one third of the circumference of the circle, therefore the probability that a random chord is longer than a side of the inscribed triangle is 1/3.
The "random radius" method: Choose a radius of the circle, choose a point on the radius and construct the chord through this point and perpendicular to the radius. To calculate the probability in question imagine the triangle rotated so a side isperpendicular to the radius. The chord is longer than a side of the triangle if the chosen point is nearer the center of the circle than the point where the side of the triangle intersects the radius. The side of the triangle bisects the radius, therefore the probability a random chord is longer than a side of the inscribed triangle is 1/2.
Random chords, selection method 3
The "random midpoint" method: Choose a point anywhere within the circle and construct a chord with the chosen point as its midpoint. The chord is longer than a side of the inscribed triangle if the chosen point falls within a concentric circle of radius 1/2 the radius of the larger circle. The area of the smaller circle is one fourth the area of the larger circle, therefore the probability a random chord is longer than a side of the inscribed triangle is 1/4.
Our brother Hakkaian have been always longing for their root even faked or fictitious. Taiwanese have absurdly been homeless in Taiwan long. 客人迷思於原鄉； 台語人 卻 變成在地流浪者
[Apr. 16]
thàu-chá cheng-sîn m̄-goān lo̍h thô͘-kha, khiok siūⁿ-khí khak-si̍t Liāu Suibeng hiaⁿ chhiùⁿ chit tiâu koa lán thiaⁿ kòe. Lán sa bô i ê chhiò-sîn kap chit khoán koa chō-sêng ê 反差效果！ pi~
Jîn-seng bú-tâi i to-châi，Sūi-bêng thài ē chá lo̍h-tâi，lâng-lâng hán i lo̍k-thian pài，siàu-liām chhiò-sîn sim pi-ai
人生舞台伊多才，瑞銘汰會早落台，人人罕伊樂天派， 數念笑神心悲哀
His show was too short to present his talents and gifts. We could not help to miss his smiling optimistic faces.
It's painful to see our love departs. We close friends with relatives gether here like a family but him. This warm guy we're missing loved our mother language, however, departed so early.
Pò-thâu chi̍t-tia̍p bô saⁿ-tán，sian-siⁿ phiau-phiat hôe sian-san，tāi-hān saⁿ pek m̄-khéng ān，un-loán chhiò-sîn lâu jîn-kan。
報頭一霎無相等，先生飄撇回仙山，大限相迫毋肯限，溫暖笑神留人間。
Too late to caught the sign of his illness. He went to Elysium freely and easely. One's life is short and no way to postpone. His smile is keeping our heart warm.
Châi-chêng tú-thiⁿ pah-chhian pō͘，thun lo̍h pi-oàn kap kan-khó͘， chóng ūi bó-gí ê chiân-tô͘。
才情拄天百千步，心悶台灣天巢烏，吞落卑怨佮艱苦，總為母語的前途。
Splendid gift he was given, he can not help worrying the future of Taiwanese, then endure much hard time.
電視 kheng-á 內 火 燄 kah， in 有leh報 無 boeh hang 蕃薯， 辦胚Bar B Q chiah 是時行。Chit pái 卻是 chhèng 出人味。
