本研究首先學習自行燒製玻璃圓珠，在研究二.中經實驗及光學理論得知，圓珠具有聚光、放大的效果。球徑等於厚度，屬於厚凸透鏡。由研究三利用測量裝置及造鏡者公式，取得焦距 f，發現，球徑越大，焦距越大。在研究四.五中根據焦距 f 值，製作七個放大鏡頭，再組合成一台玻璃圓珠顯微鏡。依序觀察水綿標本，再列印於紙上，實際測量水綿管束放大尺寸，發現，球徑越小，放大倍率越大。並與複式顯微鏡觀察倍數互相對照，驗證了自製圓珠顯微鏡具有接近 19 倍至 208 倍的放大效果。最後連接數位攝影機及電腦，可以即時觀看微生物活潑、生動的影像，並作畫面擷取、影片儲存。

在利用電腦螢幕來瀏覽圖形式資訊的時候，常常受限於螢幕的空間，沒有辦法在顯示\r 資訊整體結構的同時顯現細節部分的資料，目前的使用者介面所採用的方法有放大（zoom\r in）、捲動（scrolling）、開啟多個視窗（multiple view）等方法，這些方法雖然可以呈現出資\r 料的細節部分，但是仍有其個別的缺點存在，放大的方式會有遮蔽的情形；捲動的方式無\r 法同時地呈現整體結構；開啟多個視窗的方法使得使用者的眼睛必須在這些視窗間來回的\r 移動，造成麻煩。\r 魚眼鏡頭是一種短焦距、大視角的相機鏡頭，鏡頭成像的時候，越接近鏡頭中心的物\r 體會越放大而越遠的部分會越縮小，藉著發掘魚眼鏡頭的成像函數，我們發展出了一種新\r 的使用者介面，在瀏覽圖形式資訊的時候，能夠顯示整體的結構，並隨著滑鼠游標的移動，\r 以不開啟新視窗及無遮蔽的方式，即時地將想要觀察的部分局部放大以展現細部的資料，\r 這種使用者介面將具備現有方法的優點而無其缺點。\r Browsing the global structure of a large graph in limited screen space has the drawback that details\r are often too small to be seen. The most common solution provides a scrollable view. This shows full\r details at the region currently visible through the view, but hides the rest of the global structure.\r Alternatively, zooming into a part of the graph does show local details but misses the overall structure of\r the graph. The multiple views approach, one view of the entire graph and the other of a zoomed portion,\r has the advantage of seeing both local details and overall structure, but has the drawback that parts of the\r graph adjacent to the enlarged area are not visible at all in the enlarged views.\r A fisheye camera lens is a very wide angle lens that magnifies nearby objects while shrinking distant\r objects. It seems to be a tool for seeing local detail and global structure simultaneously. By means of\r exploring fisheye camera lens, we develop a user interface for browsing graphs using program analog of\r fisheye lens. Thus, our method seems to have all the advantages of the other approaches without suffering\r from any of the drawbacks.\r \r

NO.59-05 2020 OCT | 科學研習期刊目錄 本期專題 電池與化學 鋰離子電池的發展、應用與未來 | 洪為民 微型熔融鹽電解模組的設計與應用、應用與未來 | 廖旭茂 教學現場 動感自然課—體感式學習融入自然科教學 | 柯孟昌 會呼吸的瓶子 | 許良榮、辜家偉、楊家茜 火柴化學家：一根火柴的故事 | 江淑芳、陳坤龍 科學新知 自主性學習地圖規劃與研發歷程--以國立臺灣科學教育館常設展為範疇 | 于曉平 特約專欄 在繪本中發現漁船的構造與功能－像科學家一般的閱讀 | 劉淑雯、顧翠琴 音樂摩天輪STEAM創意課程 | 李易澄、黃琴扉 冬去春來高溫依舊 | 盧孟明 森棚教官數學題－信號發射臺 | 游森棚 科普活動報導 盲符TipFeel創作過程分享 | 張敏娟、楊夢萍、江皓全 大手拉小手 親子共學趣 | 黃真瑱、蘇萬生 全國高中探究實作競賽的三部曲 | 余進忠、蘇萬生 總召集人的話 化學電池是利用氧化還原反應將化學能轉變成電能的裝置；電解電池則是利用電能產生化學反應的裝置。所以，電池與化學關係緊密，本期特別以「電池與化學」為專題。 「本期專題」單元共有兩篇文章，〈鋰離子電池的發展、應用與未來〉介紹廣用在手機和筆記型電腦等無線電子產品的可充電電池—鋰離子電池—的發展、應用與未來。〈微型熔融鹽電解模組的設計與應用〉分享透過新開發的微型電解裝置，探討電解槽中陰、陽離子之移動與變化的實驗設計。 「教學現場」單元刊登三篇文章，〈動感自然課—體感式學習融入自然科教學〉分享在國小五年級自然課程中挑選三個單元導入體感式肢體活動與科學遊戲的經驗。〈會呼吸的瓶子〉分享利用寶特瓶、瓶蓋和吸管等簡易器材，讓瓶子很規律冒出空氣泡的「科學探究」實驗。〈火柴化學家：一根火柴的故事〉分享科工館以小五至國二學生為對象，辦理「元素殿堂的奇幻旅程」冬令營活動中，所規劃及實施的「一支火柴的故事/自製火柴，浴火磁生」活動課程。 「科學新知」單元刊登一篇文章，〈自主性學習地圖規劃與研發歷程--以國立臺灣科學教育館常設展為範疇〉介紹科教館透過「常設展區自主性學習地圖建置與運用」計畫以「人體的奧秘」、「探索物理世界」與「探索化學世界」三大展示區為範疇所建立的科學概念圖，以及依概念發展的邏輯順序串連各個展品，所連結形成的不同路線學習地圖。 「特約專欄」單元刊登四篇文章，〈在繪本中發現漁船的構造與功能--像科學家一般的閱讀〉分享如何教導國小學生透過閱讀三本繪本和以線畫方式創作漁船，關注漁船的結構與功能。〈音樂摩天輪STEAM創意課程〉分享透過團隊開發的STEAM動手做教具，以音樂摩天輪為主題，能建構學生多面向概念達到多元學習目標的教學策略。〈冬去春來高溫依舊〉針對今(2020)年上半年西伯利亞高溫更勝以往的現象，介紹相關數據和提出歸因分析。〈森棚教官數學題--信號發射臺〉拋出如何在兩個發射台之間, 等距增設三個發射台的問題。 「科普活動報導」單元刊登三篇文章，〈盲符TipFeel創作過程分享〉分享為視障者創作盲符TipFeel的過程和展望。〈大手拉小手 親子共學趣〉分享科教館於2019年度透過「女性科技人才」培育計畫之推動，增加設計多元的假日親子課程，增加孩子的學習機會、學習廣度以及營造良好的親子互動的經驗。〈全國高中探究實作競賽的三部曲〉則介紹物理教育學會所規劃含括「初試－素養命題筆試、複試－物理探究實作、決賽－物理辯論競賽」等三階段的「全國高中物理探究實作競賽」。 總召編輯委員 - 李隆盛 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：李隆盛 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：陳敬予 網頁設計編輯：施曉恬 投稿規範請來信詢問：article@mail.ntsec.gov.tw

本組結合暗箱及光度計組成自製光度實驗儀器，並利用廢棄電腦風扇及強力磁鐵製成自製攪拌器，探討影響活性碳吸附能力的因素，本組測量紫藥水透光度，求得透光度與其成份龍膽紫濃度的函數關係；並利用過量的NaOH(aq)與銅離子發生沉澱，算出一克活性碳可吸附龍膽紫及銅離子的個數。結果顯示增加紫藥水濃度或減少活性碳質量，甚至升溫，活性碳吸附龍膽紫效果均增加。但溫度對其吸附能力影響較小，若將紫藥水溫度從30℃加熱至90℃，活性碳吸附龍膽紫的個數只增加百分之十，攪拌時間則並無規律影響；而一克活性碳可吸附的龍膽紫與銅離子個數比約2：1。本組也取了竹炭及木炭，比較其吸附色素的能力，結果活性碳吸附能力最佳，竹炭及木炭無明顯吸附能力。

Early physicists such as Newton thought that all objects have definite positions. For example, they thought that an apple is either inside a fruit bowl, or outside of it. The advent of quantum physics in the early 20th century proved this viewpoint wrong. There is an uncertainty in the position of any object; we can find a set of possible locations where the object might be. This concept was termed superposition. Quantum tic-tac-toe (QT3) elegantly extends the popular game of tic-tac-toe by adding this quantum physics concept of superposition. Each turn, 1 piece is simultaneously played into 2 distinct squares of a 3-by-3 grid. Eventually, however, every piece will occupy exactly one square, like in tic-tac-toe. Yet, despite this intriguing addition, not much research has been done on the game. Hence in this paper we explore the game in terms of extension, analysis and solution. Firstly, we note that the quantum extension proposed by Alan Goff in QT3 is incomplete. In reality, there can be more than 2 possible locations for any object. Unfortunately, the QT3 game rules do not allow for this extension. Thus we non-trivially generalize the game (GQT3) by proposing a new set of rules. We show that the original QT3 is a subset of GQT3 and prove that our generalized game can always be successfully played from start to finish in a finite number of moves. Then, we begin our analysis of GQT3. Firstly, we investigate the game tree complexity, state space complexity and computational complexity of the game; indicators of how complicated the game is. Notably, we find here that QT3 has a total of about 18 trillion possible games, which is substantially higher than tic-tac-toe’s 400 thousand. Then we examine the Nash Equilibrium of the game; the result if two ‘Gods’ play the game against each other. We find that in this scenario, the first player will win by 0.5 points. To make the game fairer, we suggest minor variations on the scoring, which make the Nash Equilibrium a draw. Note that standard methods to analyze all of these would take at least a year, but we bring down the time to about a minute using symmetry considerations and other optimizations. Finally, we extend our programs into an artificial intelligence that is a perfect solution to the game. We then supplement this with a utility function to make the run-time performance pragmatic for more time-consuming versions of GQT3. Ultimately, GQT3 is a challenging and unique game with myriads of exploration possibilities; we have only scratched the surface here.

Starting from the problem in AMC competition of Australia, we try to find out the locus and its length when a point in a regular polygon rolls in a circle. The result is that the locus has a wonderful and regular cycle.Next, we discuss the regularity of the cycle when a regular polygon（n sides） rolls in another regular polygon. Furthermore,we discuss the the equation of the locus by changing the radius and the angle of rolling. we find out the argument function of the locus of a point inside when a a regular polygon（n sides）rolls in another regular polygon （m sides）： ， Aj is the summits of the regular polygon（m sides）, Bjcorresponds Aj when a point inside the regular polygon (n sides) rolls, ) And then, we do some moving simulation with some computer math software, such as Cabri Geometry、Mupad, etc. We discuss the regularity of the locus and its equation of a point inside when some special cycloids, like asteroids, cardioids, etc, roll in a certain condition. Moreover, with the result of research 2, we create the “plate＂ and apply for a patent on it. We hope to study math by playing games. 從澳洲AMC 競賽題出發，嘗試探討一正n 邊形中的一點在單位圓內滾動軌跡及其軌跡長度，發現該軌跡均會產生奇妙的循環規律。 接下來，推廣探討正n 邊形在其他正多邊形中滾動時循環的規律，並利用旋轉半徑及角度之間的變化深入探討其滾動軌跡方程式，發現正n 邊形繞正m 邊形滾動時其內部一點軌跡參數式為，其中， Aj 為 正m 邊形之各頂點、Bj 為正n 邊形中內部一點旋轉時對應 Aj 之點，。 進一步想嘗試使用數學電腦軟體如：Cabri Geometry、Mupad 等對以上研究去做一些動態模擬，並再探討一些特殊擺線如：星狀線、心臟線…等，在條件下相切滾動時，圖中某一點的軌跡規律性及其方程式。另外，應用研究二中的結果，創造出寓數學於遊戲的「圖形板」，並申請了新型專利。

當要抄寫文章的時候，光是看到很多字就會讓人覺得厭煩，其中還會發現很多字重複出現（例如：的、都、會…等）；不只如此，同偏旁或是部首的部分也重複出現頗多。因此想藉由這次的研究，把手寫的文字，藉由電腦程式將其拆解成多個部份，再和其他部份重新結合，即可組成更多不同的字，若計劃一下輸入之文字，便可簡便的組成一句話甚至一篇文章，再者，這些字都是由自己手寫出來的，因此，創造出來的字便如同一組自己的手寫字體，不但使用上具有個人特徵，而且列印出來之後，就如同一個一個我的個人化手寫字。

The Boolean Satisfiability problem, called SAT for short, is the problem of determining if a set of constraints involving Boolean (True/False) variables can be simultaneously satisfied. SAT solvers have become an integral part in many computations that involve making choices subject to constraints, such as scheduling software, chip design, decision making for robots (and even Sudoku!). Given their practical applications, one question is when SAT problems become hard to solve. The problem difficulty depends on the constrainedness of the SAT instance, which is defined as the ratio of the number of constraints to the number of variables. Research in the early 90’s showed that SAT problems are easy to solve both when the constrainedness is low and when it is high, abruptly transitioning (“boiling over” ) from easy to hard in a very narrow region in the middle. My project is aimed at verifying this surprising finding. I wrote a basic SAT solver in Python and used it to solve a large number of randomly generated 3SAT problems with given level of constrainedness. My experimental results showed that the percentage of problems with satisfying assignment transitions sharply from 100% to 0% as constrainedness varies between 4 and 5. Right at this point, the time taken to solve the problems peaks sharply. Similar behavior also holds for 2SAT and 4SAT. Thus, SAT problems do seem to exhibit phase transition behavior; my experimental data supported my hypothesis.

台灣通史「婆娑之洋，美麗之島」，身為台灣人，應知台灣事，本研究本維 基百科（Wikipedia）所揭示的「海納百川，有容乃大」精神，以Apache 網頁伺 服器為平台，MySQL 為資料庫，利用AJAX、PHP 網頁技術，並使用Google Maps 提供之服務，建立符合Web 2.0 精神的的b04地理資訊共享系統。在此系統下， 我們允許教師(編輯者)以合作方式上網提供與課程相關的地理資訊，並可進行資 訊修改或刪除，希望集合所有教師之力，提供給學生最豐富、最正確的b04地理 資訊系統。 In this paper, we propose a new map-based collaboration environment “MyGIS” for geographical information distribution. In MyGIS, the publishers/teachers can easily collaborate to annotate a spot with contents such as messages and links. The annotations of a spot are updated on the map in real-time which enables the receivers/students to correctly study at anywhere and anytime. To ensure the trustfulness of the content, the publishers are authenticated using login mechanism. In this study, several technologies inc lu ding Apache, PHP, MySQL, Ajax are involved. Finally, We implemented MyGIS on Google Maps and evaluated its feasibility and usefulness.

在學校上課時每當下課鐘響要休息或看書時，學校各處室突然連續地廣播`某某某`到指定地方集合，害我總是被廣播聲吵到無法休息和自習。在現今科技發達的時代，有很多你從未想到過的生活用品，但在使用的過程中，始終會帶來一些副作用，我們的作品就是針對學校廣播所產生的噪音問題來進行改善，成品名稱為「校園B.B.Call廣播系統」，此系統主要是讓教師或行政人員能透過電腦輸入廣播訊息和班級代碼，藉由RS-232傳送至無線電傳輸模組，並將訊息發送至「校園B.B. Call廣播系統」顯示傳輸的訊息。雖然市面上有些產品可以取代我們所設計的廣播系統，例如：電視牆、LED跑馬燈字幕機等，只不過相對成本考量來講比我們的「校園B.B. Call廣播系統」還要來的高很多，而且它們只能固定在某些顯眼的地方使用，但是我們的「校園B.B. Call廣播系統」卻能隨身攜帶著走。這就是我們「校園B.B. Call廣播系統」與電視牆、LED跑馬字幕機主要差異，成本低且使用便利，相信能有效地改善廣播所造成的噪音污染。