D6 家 庭‧心肺科‧腸胃肝膽‧耳鼻喉 07.19.2024 星期五 在學校，我們都熟悉某些類型的數：平方數（1, 4, 9, 16, 25, ...）、立方數 （1, 8, 27, 64, 125, ...）、素數（只有兩個因數的數：1和它自己）、三角形數（1, 1 + 2 = 3, 1 + 2 + 3 = 6, ...）。然而，數種類型包羅萬有，以上舉例，只屬一 隅。有一些數特性顯著，個性鮮明，並且被賦予饒富趣味的名字。它們在我 們的日常生活中或許並不重要，但它們是美麗的，因此值得一看。 由比薩的意大利數學家萊昂納多 （又稱斐波那契）引入，以非常簡單的 數列方式建構。從兩個1開始相加以 得到下一個數字：1 + 1 = 2，然後再 將這個2添加到它前面的1中得到︰1 + 2 = 3，依此類推。這就完成了斐波 那契數的清單：1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...。 這個數列的迷人之處，在於它無 處不在。如果你計算一朵花的花瓣數 量，甚至是鳳梨上的螺旋數量，你通 常會發現總數是一個斐波那契數。據 統計，三片葉子的三葉草比較常見， 而3是斐波那契數；相反，四葉草出 現的機率可謂少之又少。由此可見， 斐波那契數實在與生活息息相關。 更值得注意的是，如果你將 數列中的一個數除以排列在前的 數，例如︰8 ÷ 5 = 1.6，89 ÷ 55 = 1.618...，你會發現你愈深入數列，答 案就愈接近1.618033...，這個數被稱 為黃金比例。以1：1.618的比例建造 或繪製的東西，無論是一幅畫、一棟 建築，甚至是一張人臉，看起來勻稱 協調，人們甚至稱譽黃金比例為「神 的比例」、「美的規範」。 幾乎可以肯定的是，你在學校沒 有接觸這種數類型！一個數的數位被 取出後，將這些數位重新排列成新數 字，相乘後可得到原來的數。例如 1260中的1、2、6和0，這四個數可以 重新排列成兩個兩位數：21和60，而 21 × 60 = 1260，因此1260是一個吸血 鬼數，而21和60被稱為它的「尖牙」。 下一個吸血鬼數是1395 = 15 × 93， 而有些更大的吸血鬼數，甚至可以有 多對尖牙：125460 = 204 × 615 = 246 × 510。 此外，我們亦有其他「變種」的吸 血鬼數，例如： 「偽吸血鬼數」（Pseudovamp i re Numbers）： 尖牙大小不同，例如︰ 1206 = 6 × 201 「吸血鬼素數」（Pr ime Vamp i re Numbers）： 一個吸血鬼數，其尖牙是其質因 數，例如︰ 117067 = 167 × 701 「雙吸血鬼數」（Double Vampi re Numbers）： 一個吸血鬼數，其尖牙也是吸血 鬼數，例如︰ 1047527295416280 = 25198740 × 41570622 = (2940 × 8571) × (5601 × 7422) 1. 你最喜歡這裏討論的哪個數類型呢？斐波那契數、完美數、吸 血鬼數，還是自戀數？ 2. 你喜歡「吸血鬼數」、「自戀數」這些名稱嗎？試替這些數類型另 擬一些更加貼切及動聽的名字。 3. 數學家認為超級電腦的運算結果，不可取代數學的嚴謹證明。 你的意見又如何？ 4. 請你試試定義一些其他新的、有趣的數類型，並且以一些貼切 的名稱命名。 自戀數乃取名自希臘神話， 一個愛上了自己倒影的英俊獵人 Narcissus。根據定義，若取一個有n 個數位的自戀數的每個數位，分別將 它們提高到n次方，然後將它們加在 一起，會得回原來的數。例如三位 數153，它有三個數位1、3和5，若把 它們每個數位的三次方加在一起， 便會得回153：13 + 53 + 33 = 153。一 個更大的自戀數是四位數9474，其四 個數位的四次方加在一起，便會得 回9474：94 + 44 + 74 + 44 = 9474。現 知存在的自戀數共88個，從最小的 0，到最大的115132219018763992565 095597973971522401，足足有39個數 位！ 就像吸血鬼的數字一 樣，自戀的數位也有一些有 趣的「變種」： 「杜德尼數」（Dudeney Numbers）： 在提高到三次方之 前先將數位相加，例 如︰5832 = (5 + 8 + 3 + 2)3。 「 孟 喬 森 數 」 （Munchausen Numbers）： 將每個數位提高到自身的次方， 然後相加可得回原來的數，例如︰ 3435 = 33 + 44 + 33 + 55。（但目前已知 的另一個孟喬森數只有1哩。） 「升序冪數」（Ascending Power Numbers）： 將每個數位的次方每次增加1， 然後相加，例如 2646798 = 21 + 62 + 43 + 64 + 75 + 96 + 87。（注意：此處每 個數位的次方為1、2、3、4、5、6和 7。） 數學中有「數論」（Numb e r Theory）這個範疇，主要研究整數的性 質，被譽為「最純」的數學領域。箇中 學問變化萬千，趣味盎然。若你對以 上這篇文章感興趣，不妨繼續鑽研， 發掘數學的魅力！ 完美數是一個等於其因數之和（不 包括自身）的正整數。以4為例，除了 自身的4外，其因數包括1和2，如果我 們將它們加在一起，我們得到1 + 2 = 3 ≠ 4，因此4稱不上是完美數。我們 再看看6，其因數除了自身的6，還有 1、2和3。這些因數的總和是1 + 2 + 3 = 6，因此6是完美數。事實上，最小 的完美數是6，下一個已是28：除了自 身的28，其因數為1、2、4、7和14， 而1 + 2 + 4 + 7 + 14 = 28。 完美數是非常罕見的，接着是496 和8128，第五個是3355033（6 超過3350 萬），數值龐大！數學家們使用超級計 算機發現了一些驚人的大完美數，迄 今為止最大的有近5000萬位的完美數。 到目前為止，找到的完美數都 是偶數（能被2除盡的整數）。有趣的 是，數學家們至今仍未解開謎團，到 底是否有無限個完美數，亦不知道 是否存在任何奇數（不是偶數）的完美 數。 1. 斐波那契數 （Fibonacci Numbers） 3. 吸血鬼數（Vampire Numbers） 小思考，大智慧 4. 自戀數（Narcissistic Numbers） 2. 完美數 （Perfect Numbers） 星島教室 數字類型 本欄由教育評議會邀請資深中小學老師、校長及大學講師撰稿，旨在為學生提供多元化的STEAM學習材料，引發學生探求知識的興趣，將學習融入生活，培養學生的世界觀、敏銳的觸覺、積極學習的態度。 嚴文迅博士 九龍真光中學 數學科科主任 作者介紹 讀社論學 英文 The High Court yesterday started hearing the earlier application for an injunction by the Department of Justice (DOJ) to ban people from using the song that incites Hong Kong independence "Glory to Hong Kong" in any way. However, the judge asked the DOJ to clarify issues such as the identity of the defendant and means of serving the injunction. He did not rush to reach a conclusion because the case has a wide impact and must be handled with care to ensure that the entire hearing is based on legal grounds, lest the West have any pretext to attack Hong Kong's judicial impartiality and independence. DOJ races with time "Glory to Hong Kong" is an iconic song of the anti-amendment movement with lyrics that incite Hong Kong independence. In several recent international sports events, the organizers mistakenly played this protest song as Hong Kong's national anthem, which drew criticism from the government. However, search results for "Hong Kong national anthem" on Google always put this song at the top. After many protests and negotiations, Google still ignored the issue. The DOJ thus filed an application for an injunction and a temporary injunction in the High Court last week, prohibiting four acts related to the protest song online: broadcasting, disseminating, publishing or reproducing in any forms or versions to prevent people with ulterior motives from inciting secession. The application came with a request to ban dissemination of the song by 32 YouTube sites. However, designated national security law judge Wilson Chan Ka-shun was concerned about only mentioning four types of behaviour without naming the defendant. The injunction should not cover the whole world either. So the DOJ was asked to specify the defendant and how to serve court papers. The case was adjourned to July 21. The DOJ representative emphasized that the injunction is not aimed at the whole world, but only at "a person who is conducting now and intending to conduct the prohibited acts" agreeing that it is difficult to specify the defendant and clarification will take time. In fact, the DOJ has seen troublemakers repeatedly disseminating or posting the Hong Kong independence song online. To safeguard national security and the dignity of the national anthem, it applied for an injunction to completely ban the "Glory to Hong Kong". Under a court order, internet companies must ban the song. The starting point is good, but without due consideration in the rush leaving the judge to point out deficiencies. The judge is not in a hurry to issue a temporary injunction, because it is a serious matter with all parties focused on the ruling. Therefore, the hearing was carried out in an orderly manner according to legal principles. He thus asked the DOJ to specify the defendant, allegations and means of serving court documents. The purpose is to clarify ambiguities before issuing an injunction. The judge needs to be careful and prudent when handling this case, so that the hearing is done in accordance with legal procedures. The injunction decision must also be based on legal grounds without involving political considerations, so as not to let the outside world question Hong Kong's judicial fairness and independence. Legal procedures to avoid western criticism Since the ban is politically charged, involving platforms such as Google, Facebook and Apple iTunes, once the High Court issues an injunction, they cannot sit back and do nothing. Otherwise, it will be regarded as contempt of court. But if they remove the song, they are bound to be questioned and severely criticized by the US Congress. Amid the SinoUS gaming, the latter will have even more excuses to criticize the Hong Kong government for being intent to expand internet and social media crackdown, which will affect freedom of speech. If not handled properly, it will not only affect Hong Kong's international image. If these platforms choose to withdraw from Hong Kong in line with Washington's policy of "containing China with Hong Kong", the impact will be hard to predict. Therefore, the DOJ must specify the defendant as soon as possible. The injunction application is reasonable and legal, so the court can make a decision, which upholds the rule of law without impairing freedom of speech. 翻譯自6月13日《星島日報》社論 （http://std.stheadline.com/） injunction (n) —— 禁制令 incite (v) —— 煽動 serve (v) —— 正式送達 pretext (n) —— 藉口 impartiality (n) —— 公正 iconic (adj) —— 標誌性的 secession (n) —— 分裂國家 adjourn (v) —— 延期 legal ground —— 法律依據 ulterior motive —— 不可告人的動機 legal principle —— 法律原則 contempt of court —— 蔑視法庭 A government statement published earlier noted that "Glory to Hong Kong" had been widely circulated since 2019, with the lyrics of the song containing slogans that the Court has ruled as constituting secession. It said, "Recently, the song has also been mistakenly presented as the 'national anthem of Hong Kong' instead of the correct one, 'March of the Volunteers' repeatedly." 1. The word _____ in the first paragraph is the opposite of "bias". 2. The DOJ wanted to ban people from broadcasting, _____, publishing or reproducing a protest song. 3. In the passage, the word ____ means "uncertainties". 4. Ignoring the High Court's injunction is _____ of court. 5. According to the last paragraph, the DOJ must first specify the _____ before further action. Answers 1. impartiality 2. disseminating 3. ambiguities 4. contempt 5. defendant & Q A Vocabulary Useful Terms Did you know? Protest song hearing safeguards national security, highlights justice 翻譯︰George
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