在這篇報告中，我們以貝斯曲線的做圖原理建立出一種新的曲線－環狀貝斯曲線，進而得到不少有趣的結果。我們發現有名的古典曲線－蚶線，也是屬於二次環狀貝斯曲線。軌跡方程式為：，此時，係數恰符合二項式定理。之後我們推廣至n次環狀貝斯曲線的軌跡方程式：，也符合二項式定理。 在複數平面上，給定z0、z1、z2三點，我們定義出一個二次變換 ，若，，可映射成蚶線的圖形；若z∈實數，則可映射成拋物線。利用此結果類推我們找到一個複數平面上由 z0、z1、...、zn 所決定的n次變換將以原點為圓心的單位圓，映射成n次環狀Bezier曲線。 In this essay, we use the method of forming a Bezier Curve to establish a new curve, circular Bezier Curve, and find a lot of interesting results. We discover the famous classical curve ＂limacon＂, which belongs to the Quadratic Circular Bezier Curve. The locus of Quadratic Circular Bezier Curve is, where. Its coefficients match the binomial theorem. Then we apply it to the locus of nth-circular Bezier Curve:, and it also matches the binomial theorem.On the complex plane, we define a quadratic transformation corresponding to three points—z0,z1 and z2 as .If , where , a limacon is mapped. If z is a real number, a parabola is mapped. With this result, we will find a nth transformation defined by z0、z1、...、zn on the complex plane. It will form a nth-circular Bezier Curve with unit circle centering on the origin.

隨著科技的發達，工業廢棄物應運而生，在地小人稠的台灣，每年就產生約6000 公噸的廢觸媒，為了讓環境免於遭受廢棄物的污染，本實驗著重於廢觸媒的再利用，探討廢觸媒作為混凝土中礦物摻料對水泥(砂)漿流動性的影響。 本實驗所採用的廢觸媒來自石油裂解廠的靜電集塵廢觸媒，主要由SiO2 及Al2O3 所組成且具有部份非結晶相和卜作嵐材料之特性，外觀為乳灰白色粉末、含水量2.8﹪，溶於水中有放熱現象，pH 值為3.85。廢觸媒對水的親和力大，添加至水泥(砂)漿中會使得漿體的流動性減小，因此必須藉由提昇強塑劑劑量才能提高工作度。 在水膠比(W/B)為0.42 時，隨著強塑劑HPC-1000 劑量的增加，水泥漿的流度明顯增加，而且適當量的廢觸媒取代水泥，能維持水泥漿一定的流度。當強塑劑HPC-1000 劑量為3.0﹪、砂/水泥＝2.75 時，隨著水灰比(W/C)的增加，水泥漿的流度也明顯增加，而同條件下，不論水膠比(W/B)0.485 或0.55 時，廢觸媒取代水泥之水泥砂漿的流度比飛灰、爐石、高嶺土好，與矽灰相當，其最佳取代水泥量為15﹪。 As technology continues to develop, a considerable amount of industrial wastes have been produced.In Taiwan, over 6,000 tons of spent catalysts were brought out yearly. If such wastes can be reused in some ways, it may be helpful to protect our environment from being polluted. This study was taken to determine the influence of spent catalysts on the flowability of mortar while the catalysts were used as mineral additives for concrete. Since the catalysts could reduce the flowability of cement pastes because of the affinity between the catalysts and water, it was necessary to have superplasticizers added to improve the fluidity of the mortar. The spent catalysts used in this study were spent electrostatic precipitator cracking catalysts, called Epcat, which were provided by petroleum refining companies. Comprising mainly silicon oxide and aluminum oxide, the off-white catalyst powder present water content of 2.8%, pH value of 3.85 and exothermic reaction with water. In this study, it was found that while the ratio of water to binder (W/B) was 0.42, the flowability of the cement pastes increased with the increasing addition of superplasticizers. Besides, the flowability of cement pastes kept steady while a proper amount of Epcat was used to replace cement.When the ratio of sand to cement (W/C) was 2.75, with 3.0% superplasticizers HPC-1000 added,the flowability of the mortars markedly increased while the W/C increased, and the replacement with spent catalysts made the mortars show similar flowability as silica fume but better flowability than fly ash, slag and kaolinite, no matter the W/B value of the cement pastes was 0.485 or 0.55. In fact, the best Epcat replacement for cement was 15%.

在生活的觀察中，我們注意到人們在轉動呼拉圈時似乎是行一種「以軸轉動一個半徑遠大於軸半徑的環」的運動，在查過相關資料後，並沒有發現比較完整的探討。本研究的目的，是要找出在圓環被轉軸所驅動的運動模式中，影響環轉動頻率的各個因素，諸如：環半徑、環質量、轉軸半徑與環轉速之間的關係。根據我們所做的實驗，對相同的一個環而言，以半徑較小的軸用固定轉速轉動時，即使環的轉速變快，但始終與轉軸的轉速相等。由此我們推斷：無論環與軸之間的半徑關係為何，在環能穩定轉動的情況下，兩者的轉動週期將會相等。另外，在實驗的過程中，「軸驅動環」所引起的軸晃動一直困擾著我們，但這也引發了一項應用：如果原本穩定轉動的環和軸振動，則振動將被放大，藉此設計可以作為地震感測器。亦可作為儀器的保護裝置或是指向裝置。While playing a hula-hoop, we noticed that it seems to be a motion that the axis rotates a circle whose radius is larger than axis’. By checking relative theses, we found that there is no better research having fully discussed about this topic. The purpose of this research is to find out the motion pattern that a circle is rotated by the foce of an axis and the factors affecting rotation, such as radius and mass of circles, the radius of axes, and the frequency of axes and circles. According to our experience, no matter which height the circle stay at, or how fast the frequency of axis is, the frequency of circle will be the same. As a result of this, we guess that if it can be a stable circle, the frequencies of the axis and the circle shall be the same. Another confusing fact is the vibration of the axis, but it enables a new application: if a vibration affects a circle-axis system, the vibration will be enlarged. By this application, we are able to design an earth-quack senor, or protecting or pointing instruments as well.

NO.59-06 2020 DEC | 科學研習期刊目錄 本期專題 透過STEM、STEAM提升科技素養與AI素養 工程設計與跨領域教學的課程分享 | 汪殿杰 從科技發展到Maker教育該如何實踐 | 黃信惠 影像AI在自駕車上的模型訓練實作 | 連宏城 教學現場 簡易ROV設計製作於108課綱 | 郭銘哲 從創意到實作-「跨領域的STEAM教育」點亮孩子的學習 | 詹羽菩 結合POE教學法與跨領域美感之小學科技教學活動設計與實施-旋轉舞者_螺旋斜面應用 | 何仁偉 特約專欄 從兒童文學的作品中探索「穩定與改變」的概念 | 劉淑雯 融合STEAM理念，創發「自製扭蛋機」課程 | 黃琴扉 極端天氣下的加州大火 | 吳育雅 森棚教官數學題 - 巧拼 | 游森棚 科普活動報導 2020高中生太空酬載研習營 | 趙吉光 深耕女力科學－「傑出女科學家」桌遊推廣成效初探 | 陳萱、黃真瑱、呂玉環、蘇萬生 能源教育議題課程的發展與實踐－科普素養的向下紮根 | 黃真瑱、陳世文、蘇萬生 總召集人的話 摩爾定律(Moore's law)說，積體電路上可容納的電晶體數目，約每隔兩年便會增加一倍。簡單地說，晶片效能約每18個月，就會成長一倍，接近指數型的成長。例如最近引起注意的「量子電腦」，以不同的邏輯運算，則可能更以雙指數(指數的指數)的倍數成長。屆時，量子電腦應用在各生活層面時，人工智慧(AI)將造就更不同以往的生活形式。跟上科學科技的腳步，發展AI時代的關鍵能力與跨域能力，便成為重要的課題。在尖端科技發展下，STEAM跨域的科學科技教學，成為國際矚目的教育趨勢。就如Georgette Yakman和史丹佛大學所強調，透過STEAM設計思考來引發探究和創新，在設計創新中應用知識，也在設計創新的需求下，探究新的知識，又應用回到設計任務中，STEAM知識在探究求知和設計應用中，相生相長，如同太極一般，如下圖。 圖一.STEAM知識的太極理念 因應科技發展的趨勢，本期聚焦在科技普及、科學探根的核心。本期從專題到教學現場，一脈相承，從AI影像辨識的技術與自駕車上面的應用，深入淺出地介紹AI影像模型的建立與演算法的發展。再把科技發展與科技實作(Maker)，進行教學觀點的解析，告訴科學與科技教師，如何將科技實體引介到課堂中，讓科學與科技教師掌握住科技，並且介紹給學生。然後是以高中的「高壓空氣競速車專題製作的STEAM融入教學」，介紹跨領域的STEAM科技教學實例。在教學現場，「遙控水下載具設計與製作」的教學實務整合工程設計與跨領域的知識，為新課綱科技領綱的工程設計教學提供很具體的實例。接下來在小學階段的結合POE教學與跨領域美感教育，以及跨領域STEAM創意實作的教學現場，透過教學實例的分享，呈現科學探究、科技創新設計、以及人文與美感的整合教學，讓有助於學生建立核心素養。 特約專欄中的繪本跨科以及扭蛋機兩篇文章，延伸STEAM跨科教學的推動經驗，讓科學科技更具人文的關懷。極端天氣的加州大火與森棚教官數學題，提醒我們對環境的關注，也動動數學腦。最後的太空人營隊、科學女力、和能源教育的科普素養扎根，讓我們看到了卓越的未來科學菁英與幼苗。 代理總召編輯委員 - 張玉山 關於本刊 出版單位：國立臺灣科學教育館 發行人：劉火欽 代理總召集人：張玉山 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：張玉山 編輯：佟冠誼 網頁設計編輯：施曉恬 投稿規範請來信詢問：article@mail.ntsec.gov.tw

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.

在高二學習複數時，我們由棣美佛定理： nεN(cosθ +isinθ ) n= cos nθ + isin nθ )導出 cos n θ與 sin n θ可用 cos θ及sinθ 之多項式表示。我們發覺他們的細數頗有規律，值得研討，因此就開始研究tan nθ與sin nθ+cos nθ展開式中，其係數間關係。

本研究的目的在利用LP 唱盤系統發聲原理，以鑽石唱針摩擦各種金屬表面所產生的頻譜圖，與金屬材質的相關性。除了LP 唱盤外，我們應用CoolEdit 軟體來分析聲音資料，並利用相似度統計理論，將頻譜圖用量化比較。實驗結果發現：Ⅰ、藉用LP 系統錄取各種金屬材質頻譜圖形，有相當高的穩定性，相同金屬聲音頻譜圖形重疊性高，以統計演算出的量化結果與圖形觀察相似。Ⅱ、同一金屬在不同摩擦速率時，所產生的頻譜圖略異，經由樣本相似度門檻t 值鑑定，顯示摩擦的速率會影響聲音頻譜的產生。本研究的結果可應用在材質的分析比較。The objective of this study is, based upon the principle how LP phonograph players generate sounds, to obtain sound spectrographs from rubbing diamond phonograph needles against surfaces of a variety of metal and thus to link the sound spectrograph to certain metal material. Besides the LP phonograph player, we also use the software, Cool Edit, for analysis of sound data and, according to theory of similarity statistics, quantity comparisons of spectrographs. The result of the study shows: I. A high stability exists when spectrographs of a variety of metal material are recorded by the LP system. There is high frequency that spectrographs of same metal material overlap. The quantification result from statistic calculation is similar to the graphs as they are observed. II. Spectrographs differ slightly when a certain metal is rubbed at different speeds. As appraised by sample similarity threshold t value, it shows that rubbing frequency will affect the formation of spectrographs. The result of this study can be employed to analyze and compare qualities of material.

The applications of digital image are rapidly growing with the developments in computer technology. This enforces digital image industry to produce devices with better quality. Despite the today’s advanced level of technology, it is known that input and output devices somewhat cause color distortions. International Color Consortium suggests that we can use ICC profile to overcome the problem mentioned above. But the related hardwares and softwares are too expensive for the general users. In this study, we base on the ICC profile’s mechanism to develop a color calibration method for low cost image acquisitions. From the theoretical and experimental results, it can be demonstrated that our method appears satisfactory.數位影像的應用隨著電腦資訊科技的快速成長而蓬勃發展，這也促使著數位影像工業的相關產品漸漸地普及與廣泛地使用，時至今日，雖然有著很好的製造技術，但是任何數位影像設備均無法完美無失真地將原有的色彩呈現出來或紀錄下來，或多或少都有色彩偏差的存在，尤其在價格越低廉的設備上更為明顯。雖然可以依據國際色彩協會的建議，使用每項設備的專屬色彩描述檔來克服色差的缺點，但是用來產生色彩描述檔的相關軟硬體均價格昂貴，實非一般使用者所能承受的負擔，本篇研究以色彩描述檔的色彩轉換機制為基礎，發展出針對廉價取像設備的色彩校正程序，無論從理論數據上的探討以及實際影像上的測試看來，我們的校正方法確實有效，讓原有的色彩能精準地重現。

In the future, energy supply is the most serious problem to our society due to the shortage of fossil fuel. We should try to save energy as much as we can in different aspects in order to maintain the sustainable development of our society. According to the statistic report of electrical end uses 2008, showing that Space conditioning and Lighting shared 27% and 12% of the total electricity supply respectively. We design this “Free-Dome” to provide the individual users unique spaces for their work or entertainment where the lighting and temperature are easily and freely controllable. As a result, we may save lots of energy by reducing the lighting and space conditioning to the unnecessary area or public area.

我們根據物理學的彈性體振動模型發現:主動脈硬化程度可由測量主動脈相對於心臟運動的延遲時間分析得知。我們除了由樣品之超音波影像分析驗證此一觀念之外，還用一自製模型進行實驗，模擬血管厚度對延遲時間的影響，實驗結果與理論相吻合，證實了彈性體模型之可靠性。在診斷方面，此方法可用目前臨床使用的心臟超音波儀直接進行測量，使得它具有方便、普遍的優點;而且可由體外的胸前超音波掃描(TTE)進行觀測，具有非侵入性、免除受測者的不適及避免副作用，此外，能定量分析、早期診斷、鑑別度高也是此方法重要的優點。According to the elastic oscillation model of physics, we found that the aorta stiffness could be obtained by measuring the delay time of the aorta relative to the cardiac motion. The idea was confirmed by an analysis of the echocardiograph images of several samples. A home-made mechanical model was also employed to simulate the effect of cardiovascular thickness. The experimental results fitted the theory very well, verifying the feasibility of the elastic oscillation model. This measurement could be carried out with the conventional echocardiography instruments, making it convenient and common. Furthermore, the delay time could be measured with TaransThoracic Echo (TTE) instead of TransEsophadeal Echo (TEE). This non-invasion can avoid patients’ discomfort and side effect during medical process. The quantitative measurement also enables that the diagnostics can be progressed in advance.

An orbital angular momentum (OAM) sorter concept was designed for high-speed data transfer. The OAM of a light beam known as an optical vortex can exist in one of an infinite number of states and may be used to carry information. The augmented alphabet of states carries the potential to increase date transfer speeds over conventional binary (0 and 1) methods. A vortex generator, or OAM encoder , was constructed from a slit cover slip functioning as an adjustable spiral phase plate, and a vortex analyzer, or OAM measurer, was created using a transparent print of a computer-generated hologram. The two components were then incorporated in an OAM sorter concept that that employs a novel combinatoric method for sorting data. The vortex generator and analyzer created were inexpensive simpli-fications of previous devices and have the potential to increase the alphabet of transmission states several thousand times over binary methods if implemented in the OAM sorter concept.

Every year more soluble and insoluble substances are added to the oceans by runoff. This process slowly increases the salinity of the oceans. As the salinity of the oceans increase, what effect will this have on our climate? The purpose of this investigation is to determine how an increase in salt concentration affects the evaporation of sea water. Four ten liter aquaria were filled with six liters of distilled water in each aquarium. One aquarium contained only water. The other three aquaria had different amounts of Kosher salt added as follows: 120. grams, 240.grams and 480.grams. Measurements of the level of water in each tank were taken over a period of two months. The tank with the highest concentration of salt had the smallest rate of evaporation. In the feature with less evaporation of sea water the atmosphere will receive less moisture. This could result in fewer clouds and less rain fall for the planet.