This research divides into two subjects. The first subject aims at single-hole-swirls, we use single-hole-swirls to discuss water volume to the eddy current influence. The experiment obtains the relations between the aperture and the bottom area of the vessel. It also produces difference between free vortexes and forced vortexes of the eddy current. Our another discussion subject is twin-hole-swirls, which is extremely complex but actually an interesting part. Twin-hole-swirls is easy to be disturbed by the external factors. The result is different from our supposition. But from the experiment we discovered twin-hole-swirls is a mini version of twin-typhoons. Twin-hole-swirls has the same phenomenon with Fujiwhara effect. 本研究探討分為兩個主題。首先是針對單孔，我們利用單孔漩渦探討水量對漩渦的影響，並實驗求得孔徑與容器底面積的關係，以及自由渦流與強制渦流所產生之漩渦的差異。我們另一個探討的主題是雙孔，也是實驗中非常複雜但卻有趣的一部份。雙孔漩渦極易受到外在因素干擾，產生的結果與我們在實驗前的假設出入頗大，但從實驗中我們發現雙孔漩渦其實是雙颱的縮小版，雙孔漩渦與雙颱效應有著許多相符的現象。

NO.60-05 2021 OCT | 科學研習期刊目錄 本期專題 綠色永續化學 讓化學陪著地球永續發展──淺談綠色化學 | 黃琴扉、林寬禮、施雪雯、陳盈瑗 菱殼炭循環經濟 | 林弘萍 廢物利用：生質物氣化技術的前世今生 | 吳耿東 親子時光：是藥，還是毒？淺談家庭中的化學物 | 潘愷 農漁村地方創生環境永續綠色化學應用實例 | 施君翰、曾宗德、呂友銘、高偉傑 社群媒體、傳統新聞在食安議題扮演的角色 | 黃佰璋 教學現場 酒精的創意科學活動 | 謝迺岳 國中自然「熱的傳導」單元延伸實驗 ——運用紙箱烤雞活動落實綠色化學精神，引導國中生探討降低空氣懸浮污染物排放之課程範例 | 謝昆宏 麗山火箭飛 | 鄒語騏、吳明德 科學新知 行星磁場的形成 | 龔慧貞 隱身大地的晶瑩寶藏 | 王郁軒 未來的冬春季鋒面會怎麼變化？ | 王嘉琪 特約專欄 跨領域科學閱讀之教學研究──以〈To The Stars! The First American Woman to Walk in Space〉為例 | 劉淑雯、游舒媛 STEAM課程融入中學探究實作的案發現場 | 王冠智、黃琴扉 森棚教官數學題—奇怪天秤 | 游森棚 科普活動報導 科教館女性科技人才培育課程綜論與教學現場延伸運用之實踐 | 黃真瑱、佟冠誼、蘇萬生 科教館GO好玩 疫情下的線上營隊實踐與挑戰：科學屋塔房 | 高淑惠、林怡萱、劉軒齊 後疫情時代的數位創新學習── 以國立臺灣科學教育館｢結合適性回饋機制之自主科學DIY數位創新學習｣為例 | 陳香微、賴秋琳、吳書豪、李致翔 總召集人的話 心裏常常想著什麼是好的科普文章？科學內涵是首要的，太淺顯易懂顯得沒有深度，立論堅實又顯得不夠平易近人；容易理解又有足夠深度的科普文章一定來自在該領域有深入耕耘的作者，因為深入耕耘，才有能力在文章裏信手捻來講得有味道又有畫面。科普從往常的匱乏模式、上對下的傳播，到近來的公眾理解科學甚至公眾參與科學，都可以廣義的稱之為科學傳播。科學傳播可以定義成運用適當的技術、媒介、活動及對話，以產生個人對科學的AEIOU回應：意識（Awareness）、樂趣（Enjoyment）、興趣（Interest）、意見（Opinion-forming）、了解（Understanding）。我們看到的許多科學節目、科學動畫或是科學影片，多少都有AEIOU的不同程度回應；不管在教室內的科學課程或是在教室外的科學活動或是不同通路的媒體傳遞具科學內涵的報導等等，都屬於科學傳播的一環；疫情期間大家也變成了自媒體的一員，跟科學傳播的關係更是密不可分。如何吸引受眾的目光、讓他知道要表達的科學意涵、也願意採取行動學習科學，這都是第一線教師一致努力的目標。 本期的專題主題是綠色永續化學，想到化學就想到連續劇《絕命毒師》（BreakingBad），這個節目跟《CSI犯罪現場》一樣，讓大家在休閒娛樂過程學習許多化學知識。有個不變的道理是：當我們想解決一個眼前的問題，在過程中會有很多的問題陸續出現，再來就是一個多變數耦合的問題；只有透過review歷史吸取前人經驗，才能宏觀的訂定目標策略，透過最大利益來解決長遠的問題。這個道理在綠色永續化學的各個子題中都期待大家檢驗，保有此思維的思考，常常問有這麼好嗎？會不會衍生更多的問題？ 我們與化學相遇總是在《絕命毒師》《CSI犯罪現場》這麼驚險的場合嗎？對於化學我們是無可迴避。從源頭的管控讓有害物質的釋放、以及環境遭受的衝擊降到最低，生產過程提升使用率、減低衍生物及減廢等都是黃琴霏老師所提綠色化學的理念。菱角產地台南官田區就為每年龐大的菱殼廢棄物所苦，成大化學系林弘萍教授在專業上透過碳化產出菱殼炭，成為吸附異味的官田烏金，以及造粒後吸附精油緩慢釋出氣味的產品；化學專業在循環經濟充分發揮。沒有二氧化碳淨排放的循環是生質能的典型特色，生質物氣化技術的前世今生既古老又充滿機會。所有的化學物在某種劑量以下都可能是安全的，零檢出是不可能的，這些一般的常識的不足也曾在國內的大新聞中如空氣般的日常；當我們發現很多昨是今非時，就該發現國民科學素養其實不差，反倒是政治問題凌駕科學議題；生活環境中避免不了化學，劑量及傳遞途徑的基本常識很重要，唯有知己知彼，才能免於恐懼並避免危險；日常面對及接觸的空氣清淨機、臭氧機、除草劑、戴奧辛等都需要我們認真的對待理解，把沒有不毒的化學物質變成劑量正確的仙丹。食物安全是大家的切身問題，絕對不會被忽視，三聚氰胺、瘦肉精、塑化劑等等都是重要的案例；資訊傳遞的途徑從傳統媒體的不夠即時性到現今的社群媒體及自媒體，在深度及廣度上傳統媒體更是節節敗退，但也因為真偽難辨，科學的基本常識以及處理事情的科學態度都是避開假新聞荼毒的墊腳石。 教學現場 「物體本身沒有善惡，它的價值要由人們決定」，YouTube上製作滿二百集「科學五分鐘」的謝迺月老師，透過九個以酒精為主題的科學動手做活動，為酒精平反，也讓我們透過動手操作對於酒精相關的許多化學知識更加有感理解。食物烹調過程中熱傳導相關的問題長久以來與人們密不可分，生活中的問題透過實作讓學生有感且理解綠色化學精神。麗山高中的化學老師跟物理老師合開課程，讓我們知道探究與實作從氣體主題轉變到火箭主題的過程，從課程規劃、課程實施以及加入軟體使用的疫情解決方案，化學&物理課程不是漂亮的水果拼盤，而是讓讀者有感真正融合的綜合果汁，都是第一線老師很棒的學習典範。 科學新知 我們熟悉地球的磁場，那太陽系其他行星也有磁場嗎？亞洲首位獲美國礦物學會會士女科學家龔慧貞老師透過地核發電機理論模型幫您解密行星磁場的形成機制。臺灣一年平均雨量接近全世界平均值的三倍，但是卻也是嚴重缺水區域，蓋水庫絕對不是唯一的解決方案；您喝過千年以上年紀的礦泉水嗎？〈隱身大地的晶瑩寶藏〉一文會讓您讀得很有畫面，地底下溫泉、伏流水、水中礦物質等的許多水資源秘密也將一一揭曉，讓我們知道師法自然是永續經營之道。預測一直是個迷人的問題，股市預測、推估產能、天氣預報等等，透過歷史資料的建模與及近期資料的觀測，融合觀測資料及模式模擬的資料，已經是近來氣象分析的重要工具；在極端氣候下及非線性氣候方程條件下的不確定性必然存在，數值模擬更具挑戰。 特約專欄 透過科學家繪本閱讀及延伸的探究活動，去連結學生生活與知識，也透過閱讀科學家典範的日常去理解其性格並喚醒讀者自身的科學家性格-「像科學家一樣思考、進行探究」，提升讀者對科學研究的興趣。STEAM課程融入探究實作現場會遇見的問題、阻力、解決方案以及可以獲得的回饋，都在第一線教師的反思表達中呈現於文章中。天平是個公正平等的象徵，被用在買賣交易也用在司法圖騰；現在有個不公平的天平，如何透過這個奇怪天秤找出五個硬幣中的唯一偽幣，如何找出十一個硬幣中的唯一偽幣？這是讓人黏著度很高的問題，花點時間，享受解題的樂趣。 科教館GO好玩 科教館〈女性科技人才培育課程綜論〉一文從教師面以及學生面的培訓角度呈現其實施流程及建議。科學活動的舉辦受限於疫情，科教館線上營隊建立的合作模式、教學內涵及教案都是重要參考資料。科教館透過執行「結合適性回顧機制之自主科學DIY數位創新學習」計畫的成果，來呈現透過科技突破時空限制，開創數位創新教學，也是後疫情時代下之教學改變契機。 總召編輯委員 - 李旺龍 關於本刊 出版單位：國立臺灣科學教育館 發行人：劉火欽 總召集人：李旺龍 編輯委員： 物理科吳仲卿/陳耀榮/李柏翰/盧玉玲 | 化學科古建國/許良榮/王伯昌/林如章/周金城 | 生物科王美芬/蕭世輝/陳建志/郭淑妙 | 地球科學許民陽/王郁軒/李文禮/謝隆欽 科技科張玉山/汪殿杰/林育沖/趙珩宇 | 數學科李源順/鄧家駿/溫世展/張宮明 | 跨領域學科李名揚/連信仲 | 特約專欄 游森棚/黃琴扉/陳正改/劉淑雯 策劃：曾聰邦 主編：吳中益 本月專題特約主編：古建國 編輯：佟冠誼 林博雅 網頁設計編輯：施曉恬 投稿規範請來信詢問：article@mail.ntsec.gov.tw

我們的研究包括兩部份，第一部份是實地調查訪問。瞭解地震成因、傷害及現有防震方法，並調查坊間各種建築物類型，及常見私自改變建築物結構現象，做為研究的基礎。第二部份為建築物抗震實驗。研究發現：牆面挖空、頂樓加蓋、樓層挑高，建築物會在該處產生弱點，由此斷裂。柱子數量相同下，散開時支撐力較弱。不對稱建築物遇震時會不自然扭轉且易倒。隔震素材恰當，能有效提高耐震力。滑軌、彈珠隔震效果很好，但位移太大，為實際建築所不容許。建物下加裝阻尼材料，能吸收部份地震能量，降低地震對建築物的危害，並有效控制位移問題，是良好的隔震素材。樓頂加裝消能設施亦能減震，但設計極其不易。 The research includes two parts. In the first part the work is concentrated on on-site visiting and investigation such as understanding the cause of earthquake, the damage and the preventive method currently available, investigating the different types of building and the phenomenon of altering the structure of an existing building without permission by government authorities which is popularly seen in Taiwan. These are considered as the basis of the research. The second part is the experimental study of earthquake resistance of a building. The test results showed that weak-point can be caused at the place where the existing wall is moved or an extra building is attached to the roof or the structure of building has extended space between floors, and fracture always occurs at the weak-point. If the number of columns of a building is the same, then the scattering arranged location of columns is weaker than concentrating type of arrangement of columns. The building having unsymmetrical structure will twist in uneven fashion that causes the building apt to collapse in case of earthquake. Employing proper vibration-absorption material can effectively increase earthquake resistance. Sliding rails and balls can provide satisfiable vibration-isolation effect, but can also cause too much displacement of building structure. Install damping material beneath the building can absorb part of the energy of earthquake, and decrease the damage, and can solve the problem of displacement of building, therefore, damping material can be considered as an ideal vibration-isolation material. Install energy-attenuation equipment can also reduce vibration but the design of the equipment is extremely difficult.

During the evolution of humankind, development of frontal cortex has played a critical role, where higher brain function like emotions, self-consciousness, decisions…etc, were all related to frontal cortex. On the other hand, thalamus is usually associated with relaying the sensory signals from peripheral receptors. In order to understand the functional role of frontal cortex, the signal processing mechanisms in the thalamo-frontal cortical pathway became an important research issue. The aim of this experiment was to find a method to dissect a brain slice that contains a connecting route in vitro between thalamus and frontal cortex with functional activity. Through nerve fibers tracking technique using fluorescent-dye (DiI), it was understood that the 3D-space connection between thalamus and frontal surface was an upward curve with a turn of about 110 degrees and bending inwards from the two sides. If a conventional horizontal section was performed, the route would be cut-off and its integrity lost regardless of the direction. To solve this problem, a novel section method was developed to retain the route. Based on the route direction shown by the fluorescent-dye, a piece of brain block was cut and flattened of about 110 degrees. Other sections were performed as control for studying the effectiveness of the sectioning on the plane of the route. Finally, electrophysiological methods were used to verify the connection route was complete and functional. Thalamus-evoked extracellular field potentials in the frontal cortex were observed by changing stimulation strength, adjusting slice temperature and prepared oxygen supply and administration of drugs like CNQX and picrotoxin in the 110 degree flattened slice but not the others. It was found that the reaction was essentially a neuronal response, indicating the pathway between thalamus and frontal surface was retained substantially. With this novel brain slice technique, we can assess the functional connection between thalamus and frontal cortex and investigate the cellular mechanisms of the signal processing in this connection pathway. It is anticipated that present technique provides an important step to further elucidate the functional role of the frontal cortex. 在人類的演化史上，前額葉的發展扮演了極為重要的角色，凡舉情緒、自我意識、決策等，皆與前額葉有關。而丘腦通常與視覺、聽覺及本體感受如痛覺、觸覺、溫度覺的訊息傳遞有關。要了解前額葉的功能，丘腦到前額葉的徑路及訊息處理機制，便成為一個很重要的研究課題。本實驗的目的是尋找一個方法能在離體的腦切片上維持具有丘腦到前額葉連結的徑路並且有功能的活性。經由螢光染料(DiI)神經束追蹤技術，了解從丘腦至前額葉路徑的三度空間連結為一先向下再向上約110度的角度轉折，並同時先由內向外再轉向內的曲線，若用一般水平之切片方法，無論何種方向，其路徑必定會被切斷，不能保持其完整性。為了解決此問題，發展出一種可以保存其路徑的腦切片方法。依照螢光染料所顯示出的的路徑走向，在腦塊的皮質上切一刻痕，將腦塊以110度的角度展平，使其路徑處在一個平面上再切片。最後利用電生理的方法來證明所切出的連結路徑是完整且具有活性。改變在丘腦的刺激強度、調整腦切片(腦脊髓液)溫度、氧氣的供給以及施予藥物CNQX、picrotoxin，觀察其前額葉之電位變化，發現其反應確實為神經反應，表示從丘腦至前額葉的路徑已在這種特殊的腦切片中被完整保存。藉由這個方法，將有助於研究丘腦至前額葉功能性連結，神經網路結構，及其訊息處理機制，並期待以這樣一個全新的方法將來有助於瞭解前額葉的功能。

所謂約瑟夫問題，就是有 n 個自然數排成一環狀，從頭開始，殺 1(個數)留 1(個數)，求最後留下的數會是多少？該問題在台灣的全國中小學科學展覽出現多次（如表二）。而資訊界演算法大師 Donlad E. Knuth 在其著作 The Art of Programing，CONCRETE MATHEMATICS（具體數學），針對該數列作詳細的說明；但是，不論是歷屆科學展覽或是大師著作，對於該問題，都只是談及殺 1 留β或是殺α留 1。筆者本研究中利用獨創α分類、n 及 k 分類、F 函數、b 函數及循環節，將約瑟夫問題探討範圍提升至殺α(個數)留β(個數)，求倒數第 k 個留下的數是多少？

Most neurological diseases are characterized by the presence of protein aggregates,\r suggesting that aberrations in protein homeostasis are associated with neuronal demise. In eukaryotic cells, protein homeostasis is maintained by the chaperone, ubiquitin proteasome (UPS) and autophagy systems. As age is a risk factor for several types of neurodegenerative diseases, the function of these various protein homeostatic systems could become compromised with age. To understand the events that occur during normal aging, we examined the expression of key markers associated with the aforementioned systems in mice aged 1, 3, and >18 months. We found that proteasome activity and the amount of proteasome-related structures remained unaffected with age. Interestingly though, an agerelated increase of a novel Hsp70 chaperone protein species (herein designated Hsp70*) was observed. The expression of Hsp70* is also increased markedly in cells treated with pharmacological agents that promote proteasome inhibition, suggesting a functional interaction between the chaperone system and the UPS. Taken together, our results suggest that there is some form of crosstalk between the chaperone system and the UPS involving the observed HSP70 species.

在這個研究當中，我們設計並製作完成一部手工機械車模型。實驗該車曲軸分別在 0.5、1、1.5、 2 、2.5、 3 公分，連桿在9、10、11、12、13 公分，後腳在 3、3.5、4、4.5、5 公分各種組合對速度及拉力所產生的影響。並用 GSP(The Geometer’s Sketchpad) 繪圖模擬來驗證其結果之可行性。在拉力部份，原始實驗（前後腳底加日式止滑墊）由於與底面積摩擦力不足，實驗數據無法忠實呈現拉力。於是我們決定在軌道上貼砂紙並用以下四種方式來做實驗(1)在四腳上各加一個電池 (2)在四腳上加電池，在後腳底貼上橢圓形橡膠軟墊 (3)四腳加電池，後腳做關節且加大腳底面積 (4)四腳加電池並鋸短四腳，且加大腳底面積。實驗數據顯示在曲軸、連桿、長度改變及後腳孔位置高低改變時，拉力會隨之增加或減少。本研究歸納出下列結論:曲軸越短，速度越慢，拉力越大。連桿越短，速度越快，拉力越小。後腳孔位置越高，速度越快，拉力越小。

複雜系統廣泛地存在每個人生活的周遭，儘管這些系統在表象上有明顯的差異，卻不約而同的都呈現出臨界現象。一個簡單的物理概念卻能廣泛地使用在許多不同的場合當中，這是令人始料未及的。這份報告在尋找，是什麼原因導致這許多似乎與物理沒什麼關聯的系統，都呈現出臨界現象？以及這類系統是如何演化的？臨界現象在系統的演化歷史中，又是扮演怎樣的一個角色？一開始，先介紹臨界現象在實際系統中表現的形式，在這以文字系統作為範例。接下來，進入思考的階段，猜測系統個體間存有的關聯性，提出如何影響的假設，並建立模型。從模型結果，可以了解複雜系統隨時間演化的趨勢改變，並發現臨界現象在系統中扮演的角色以及代表的意義。這份報告有三項結論：1. 臨界現象在複雜系統中呈現的形式 2. 模型結果與實際系統十分相似 3. 臨界現象代表著系統的穩定態。The theory of Scaling Law and Universality was originally used in researching Critical phenomena, and now we find it existing in our normal life. A simple physical concept can be used extensively in different courses. This study try to find out the relation between individuals which causes Critical phenomena appear in such different courses in our normal life, and figure out the effect time brings about. To begin with, we introduce the sights of Scaling Law and Universality by exploring the formation of complicated system. Facing a complicated word system as a real example, we observe an extraordinary phenomena, and find out the Universality and Scaling Law in different kinds of linguistics. In the main part, to think further, what’s the relation between the individuals that leads to Critical phenomena? We will give hypotheses and build a model to simulate complicated system from the view of Universality, trying to find out the cause of the interaction of complicated system. From this model, we could understand: When a complicated system evolves with time, the Critical phenomena will naturally occur in this system that could be considered as dynamic equilibrium. From this study we found out(1) The Universality and Scaling Law in complicated systems, here we use linguistics as an example.(2) Under the hypotheses, the simulation is almost as same as the real result of linguistics system.(3) Time plays an important part in the Critical phenomena which can be found in many different complicated systems, and Critical phenomena symbolize a stable state of such systems.

I made this jet engine to demonstrate how a pulse jet works and to show were the fundamentals of powered aviation all began. I also made this project to gain more knowledge, due to my interests in engineering and turbines. I would also like to measure the thrust of this model in the future. And hopefully this might inspire other people to use this type of engine in their model aircraft.

The definition of "Fermat Point" is that a dot, which lies in a triangle, has the minimum distance to the three apexes. In other words, "Fermat Point" has the minimum distance to three dots which are not on the same line. In the broad sense, then, in a N polygon, a dot which has the minimum distance to the N apexes could be named "Fermat Point." But what if we link up the N apexes and find out that they cannot make a convex polygon? The above is what we wish to fully discuss. Our inspiration comes from a paper on"Fermat Point." It just describes N convex polygon, so we think of putting the case to naturally polygon. The case may be that it is a concave polygon or part of the apexes which lies on the same line. We would not base our study on the conventional methods. Moreover, strictly defined, the repeated line segment will not be taken into account. That is, if the "Fermat Point" drops on the line with more than two dots on it, we just count the\r line segments except for the shorter line segments which were originally included in other studies. According to the theorem, our conclusions are as follows: 1. If N points lie on the same line segment, then the "Fermat Point"can be any point on the line segment. 2. If (N-1) points are on the same line segment, then the "Fermat Point" is on the point which two lines join together. One is that the line segment, and the other is the one which passes the remaining point and\r perpendicular to the first line segment. 3. Now there are (M+N) points. Among them, M points will make a M jog-polygon. The others all drop in the polygon. As the diagram shown beneath, we know that the "Fermat Point" drops on the point which two lines join together. The two lines must pass as many points as possible. 所謂的「費馬點」是指三角形內到三頂點距離和最小的點。換言之，「費馬點」就是到平面上不共線三點距離和最小的點。因此，我們可定義，廣義的「費馬點」即是n 多邊形內到各頂點距離和最小的點，亦即到平面上不共線n 點距離和最小的點，但若平面上n 點不能恰為n 多邊形的頂點呢？這就是我們所要討論的。由於我們的靈感來自一份關於「費馬點」的科展作品，所以我們想到，當平面上n 點不能恰為n 凸多邊形的頂點，甚或其中有一部分的點共線時，將不能以n邊形的方法來探討，但我們可以將之化為m 邊形內（n-m）個點來討論。而更重要的是，我\r 們增加了另一個限制，重複的線段將不被我們列入計算。亦即當所求點落在某一多點共線的線段上時，我們只計算該線段的總長，而不計其中重複的較短線段。根據這個原則，我們試行證明平面上三點、四點、五點及六點的可能情況，期望能從中找出足以推廣至平面上n 點的一般性。結果雖不完美，但我們總算差強人意的歸納出了下列結論：1.若n 點共線段，所求點可為所共線段上任一點。2.若（n-1）點共線段，則由該不共線點引一線與共線段垂直，其交點即為所求。3.若（n+m）個點中有m 個點為一m 多邊形的頂點，另外n 個點落在該m 多邊形內，則由兩個外頂點引直線盡可能通過最多點，該兩直線的交點即為所求。

本研究目的是探討大豆卵磷脂對於老化及學習記憶能力是否有改善之功能。以 24 隻 SAMP8 小白鼠，分為大豆卵磷脂組及對照組，飼養 8週。經由主動迴避試驗、單次被動迴避試驗，測其學習記憶能力；另測量其腦部丙二醛(MDA)之含量，評估其老化的程度。由實驗結果顯示，在主動迴避試驗中，大豆卵磷脂組被電擊次數有減少趨勢；在單次被動迴避試驗中，大豆卵磷脂組停留在明室的時間高於對照組。而在 MDA方面，大豆卵磷脂組腦中MDA含量低於對照組。由上結果推測大豆卵磷脂對於抗老化及學習記憶方面都有改善的功能。 The purpose of this research was to study the effects of soybean lecithin on improving the aging process and learning and memory abilities. The first part of the experiment is to raise 24 SAMP8 mice eight weeks, and divided them into group A and Group B. We tested them memory power by Active shuttle avoidance test and Single-trail passive avoidance test, and tested their degrees of the aging by the content of MDA. The result demonstrated that there was a decreasing tendency in times of being hitting in group A during Active shuttle avoidance test. The time which group A stayed in the bright room was higher than group B during Single-trail passive avoidance test, and the content of MDA in group A was apparently all less than group B in the experiment of MDA. So we can get the message that Soybean Lecithin has the improvement of ameliorating the speed of oxygenation and increasing memory power.

「外觀數列(The Look and Say sequence)」為依照外觀產生下一列的數列，第一列為「1」，第二列則描述第一列「1 個1」而為「11」，第三列「21」，第四列「1211」，依此類推。本研究針對外觀數列的各項數學性質作研究探討，並由此推導出外觀數列的一般式，即給定第n列就可知道該列的內容。