在傳統的解剖學分類上，台灣地區樹蛙科(Rhacopboridae) 共有台北樹蛙(Rhacophorus taipeionus)、莫氏樹蚌(R.multrechtis ) 、裴翠樹蛙(R.sp.)、白領樹蛙(Polypedates leuco leucomystax)、褐樹蛙（ R.robostus ）日本樹蛙 ( R.japonicus)、艾氏樹蛙 （ R . eifingeri ）等七種，其中除白頜樹蛙屬於 Polypedates 屬外，其餘六種均屬Rhacophorus 屬（呂， 1982 ）。這七種樹 蛙除裴翠樹蛙族群較小外，其餘六種在台灣都有不小的族群分佈，裴翠樹蛙是師大呂光洋老師實驗室民國七十年五月間新發現，依其外部形態與傳統解剖學分類，將其哲時歸屬於 RhacoPhorus 屬， 很可能是世界新種；本實驗目的之一，在研究裴翠樹蛙基本生化資料，進而對其在分類上位置之確定提供參考”國內關於無尾類(Anu-ra)的生化方面研究甚少，國外有關蟾蜍科（ Bufonidae ）、樹蟾科（ Hylidae ）、赤蛙科 ( Raniidae ）等的生化分析論文發表相當多，但卻很少看到樹蛙科（Rhacophoridae ）的文獻，內此樹蛙科的研究有共必要；本實驗目的之二，在研究台灣本區鄉土的樹蛙 生化資料。根據 Matthews ( 1975 )對蟾蛛( Bufo )的研究， Lew-ontin and Hubby ( 1966 )對果蠅（ Drosophila ）的研究 , He-dgecock and Ayala ( 1974 )對山椒魚（ Salamand ridae ）的研 究， Adest ( 1977 )對蜥蜴（ Iquanidae ）的研究都顯示酯酶（ Esterase ）是多型性現象（ Polymorphism ）最明顯的一種酶，因此取酯酶做此研究甚為適合。

我們試著尋找所需最小的城堡個數以看守整個a × b × c (a,b,c ? N) 的長方體。所謂城堡是一種棋子，當放置城堡的位置是(x, y, z) ，則(x, y,t)、(x,t, z)、(t, y, z) (t 是任何不超出邊界的正整數)是這個城堡可以看守的格子。我們用這些城堡來完全看守長方體，試著找出其最小值。在2005 年我們猜測了a = b = c 、a = b c 、a > b > c 的上界，而在2006 年時完成了a = b = c 、a = b c 的大部分情況的證明，少數不能解決的部份也提供了不錯的上界。目前我們在a = b = c 、a = b c 的情況幾乎完全解決，目前正在向a > b > c 的部份發展。A generalized searching method of finding the minimum number of castle which can oversee all over the rectangular box, defined as a × b× c (a,b,c ? N) , is presented. The castle here is defined as one kind of chess. The castle positioned as (x, y, z) can direct the lattice points of (x, y,t) 、(x,t, z) 、(t, y, z) (t is the positive integer and smaller than the box size). These castles we use here is to oversee the rectangular box and to help us to find the minimum number. In 2005, we got the upper bound of overseeing the rectangular box in the conditions of a = b = c、a = b c、a > b > c , while in 2006 we complete the proofs of the minimum number of castles based on the conditions of a = b = c 、a = b c . The further work we want to attain is to complete the case of a > b > c.

格子點上的三角形表示這個三角形三頂點的座標皆是整數。本研究先探討用平面格子點可以連出哪些三角形的相似形，再推廣到可以連出哪些多邊形的相似形；接著再研究空間中的格子點可以連出哪些三角形及多邊形的相似形，並用研究的結果討論空間中的格子點可以連出哪些正多面體。推廣到四次空間的格子點時，運用一條數論中的恆等式，發現可以做出來的三角形種類(所有相似形為同一種)居然與空間中的格子點一樣，這是個非常神奇的結果。另外，運用四平方和定理可導出，在五維空間中就能夠將所有可能用格子點連出的三角形種類連出來，這也是另一項收穫。When a triangle is formed with grid points, this means the coordinates of the vertices are all integers. This research aims to find out what type of triangles can develop into symmetries with vertices that fall right on 3 grid points on a plane. The same process is further applied to polygons. Based on the results obtained, the researcher moves on to explore what type of triangles can develop into symmetries that can be formed with spatial grid points. By using an equation in number theory to expand the study to a 4-dimension space, it is formed that the kinds of triangles—their symmetries included—which can be formed with 4-dimension grid points can also be formed in a 3-dimension space. In addition, all the possible kinds of triangles which can be formed in a 6-dimension space or up can also be formed in a 5-dimension space.

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.

液體中之球體運動與液體的黏滯性有關，本實驗找出球體半徑與終端速度之間的關係。利用攝錄機作為紀錄工具，拍攝三種材質（壓克力、玻璃、水晶）的球體在沙拉油中的自由落體過程。使用電腦影像處理軟體將影像分解成幅影像，時間的解析度為1/30秒。測量球體的高度與時間，分析高度與時間的變化情形，發現終端速度與球體半徑之間的關係。 流體中之運動方程Fdrag = -k1V，無法符合實驗結果。我們的實驗結果顯示油中的自由落體的運動方程應該是Fdrag = -（k1V+ k2V2）。由不同材質的壓克力球（~1.18g/cm3）、玻璃珠（~2.47g/cm3）與水晶球（~2.66g/cm3）所獲得的終端速度（Vt）與球體半徑（a）的關係為a3(ρ-ρ') = 0.00003（a Vt）2 + 0.00021（a Vt） + 0.00575，其中ρ與ρ'分別為球體密度與沙拉油密度（0.90 g/cm3）。 再者，在相同半徑的條件下，密度越大的球體終端速度越大，在靜止下落後，越久達到終端速度。 The motion of a sphere which is falling through a fluid is subject to the fluid viscosity. In this study, we find out the relation between the radius of a sphere and the terminal velocity. We used a digital camera to record the sphere's descent in the oil. The three kinds of sphere we choose are acrylic（~1.18g/cm3）, glass （~2.47g/cm3）and crystal （~2.66g/cm3）. Frame-by-frame analysis of the video footage yielded rough estimates of the sphere's location within 1/30 seconds accuracy for statistically consistent results. By measuring the location and time and analyzing them, we find out the relation between the radius of a sphere and the terminal velocity. The expression of the drag force,Fdrag = -k1V, is not cosistent with our results. The study indicates the expression of the drag force should be Fdrag = -（k1V+ k2V2）. The expression for the terminal velocities of the three kinds of sphere is of the form：a3(ρ-ρ') = 0.00003（a Vt）2 + 0.00021（a Vt）+ 0.00575, where a is the radius, ρ is the sphere density and ρ' is the oil density（0.90 g/cm3）. In addition, if the radius is the same, the terminal velocity of a denser sphere is higher and the time to approches the terminal velocity is longer.

NO.58-05 2019 OCT | 科學研習期刊目錄 本期專題 從臺灣邁向國際的機器人教育 FRC菜鳥教練的驚奇之旅 | 謝曜隆 機器人賽事分享 | 蘇鼎欽 淡江大學電機系機器人研發團隊 歷年參與國內外競賽心得分享 | 林怡仲、李世安、劉智誠、翁慶昌 人機合作模式的機器人教學設計 | 李文宏、陳璽宇 教學現場 生活科技競賽與108新課綱之結合 | 林坤誼 在成功國小和機器人相遇 | 鄭頌穎 機器人專題課程如何在高中階段實踐 | 汪殿杰 自製雷文霍克顯微鏡 | 陳其威 科學新知 熱浪洶湧的夏天 | 盧孟明 特約專欄 最快的小碎步 | 游森棚 STEAM機械摩天輪教具研發與教學 | 黃琴扉、葉凡愉 玩出繪本好味道－食育與動作發展 | 劉淑雯 科普活動報導 民間組織所舉辦的機器人競賽－台灣玉山機器人協會 | 謝宣而 培養科學的愛好者：「全國科學探究競賽－這樣教我就懂」 | 蔣振宇 氣象探究研習營－數位科技愛地球 | 楊玉蘭、黃嘉郁、蘇萬生 總召集人的話 機器人(robot)和教育的關連至少有三個面向：一是以機器人為學習內容(learning ABOUT robot)—將機器人當作學習科目或單元；二是以機器人為學習工具(learning WITH robot)—將機器人當作輔助、管理和/或支援學習的工具；三是以機器人為學習管道(learning THROUGH robot)—將主持教學的機器人當作學習管道。目前我國機器人教育在前兩個面向愈來愈普及，不但在學習者年齡層方面正持續向下扎根，在學習場域方面也正努力和國際接軌。本期特別以「從臺灣邁向國際的機器人教育」為專題。 「本期專題」單元共有四篇文章，〈FRC菜鳥教練的驚奇之旅〉一文介紹每年吸引世界各國對機器人製作有興趣的高中生，爭相投入的FRC機器競賽活動。〈機器人賽事分享〉一文介紹FIRST系列機器人競賽。〈淡江大學電機系機器人研發團隊歷年參與國內外競賽心得分享〉一文分享該研發團隊近幾年在國內外「輪型組」、「人形組」和「手臂組」機器人競賽中屢次獲獎的成果與心得。〈人機合作模式的機器人教學設計〉一文則以2019年「START!智慧小車競賽」的競賽試題為例，提出人機合作模式的機器人教學設計理念。 「教學現場」單元也刊登四篇文章，〈生活科技競賽與108新課綱之結合〉一文介紹當今的國、高中生活科技競賽，並說明其與108新課綱的結合。〈在成功國小和機器人相遇〉一文分享桃園市成功國小實施機器人課程與教學的經驗和心得。〈機器人專題課程如何在高中階段實踐〉一文分享臺北市立大同高中透過選修方式實施兩年機器人專題課程的經驗與成果。〈自製雷文霍克顯微鏡〉一文則介紹如何製作簡單的隨身單式顯微鏡。 「科學新知」單元刊登〈熱浪洶湧的夏天〉一文，指出全球暖化速度未減、各地愈來愈熱以及氣候行動新篇章。 「特約專欄」單元刊登三篇文章，〈最快的小碎步〉一文拋出隨便選一個正整數n再找出分母最小之有理數b/a使n、a和b構成特定關係式的問題。〈STEAM機械摩天輪教具研發與教學〉一文介紹運用STEAM整合式學習模式，結合布魯姆分類學概念，所發展之創新教案。〈玩出繪本好味道--食育與動作發展〉一文則分享可如何透過繪本導入烹飪活動，讓兒童學會飲食相關知識，並促進動作發展。 本期「科普活動報導」單元刊登三篇文章，〈民間組織所舉辦的機器人競賽--台灣玉山機器人協會〉一文，介紹該協會辦理機器人競賽的活動與心得。〈全國科學探究競賽--這樣教我就懂」〉一文介紹「這樣教我就懂」科學探究競賽的緣由、現況與展望。〈氣象探究研習營--數位科技愛地球 〉一文則是台北市國中、小學生「氣象探究研習營--數位科技愛地球」活動的回顧與展望。 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：陳雪玉 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 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/劉淑雯 策劃：曾聰邦 主編：錢康偉 本月專題特約主編：張玉山 編輯：吳郡怡 網頁設計編輯：施曉恬/廖憶慈/顏韶寬/蔡婉懿 投稿規範請來信詢問：article@mail.ntsec.gov.tw

溶液和溶劑置於同一容器中，當溶質向上擴散時，會形成濃度梯度及折射率梯度 dn/dy，且dn/dy 對高度y 的關係圖會呈現隨著高度改變的現象。 半徑r 的Ｄ形容器，下方置溶液，上方置溶劑，以雷射光照射容器的平面部份時， 雷射光沿著法線出射，受折射率梯度的作用而向下偏Ζ距離，a 為容器至屏的距離， 得到dn/dy=Z/ar 的關係式；改變雷射光的高度y 可得dn/dy 圖。 以硫代硫酸那作實驗，其dn/dy-y 圖為以原始界面為對稱軸，因其擴散係數不隨濃 度改變；甘游水溶液的dn/dy-y 圖呈現不對稱，圖形的極大值往甘油方偏，主要係因 為甘油的擴散係數隨濃度的增大而減少。 我們成功第把不同時間對同一溶液的實驗結果予以模型化，得到的dn/dy-y 曲線隨 時間改變，並發現該曲線所涵蓋的面積為定值。 雷射光經光柵再照射半圓筒，可直接測出各高度的折射率，量出y、 dn/dy、n、及濃度可算出擴散係數。The mixing between a pure liquid and a solutionin a vertical column produced a concentration gradient , which in turn produced the refractive index gradient . As the solute particles diffused upward into the pure liquid , a gradient was generated because of the varying solute concentration . The plot of the refractive index gradient versus vertical position y (dn/dy vs y) is found to vary with time . A D-shape container of radius r is partly filled with a dense solution , and partly filled with solvent which is on the top of the solution. When laser beam pendicularly enters the flat surface of the container, the outgoing beam strikes the container at a normal incidence , and is deflected down a vertical distance Z by the refractive index gradient . We can get dn/dy=Z/ar , where a is the distance between the container and the screen . By changing the vertical position (y)of laser beam , we can get the plot of dn/dy vs y . We have successfully modeled the time dependent experimental gradient curves on the same solution . The area beneath the trace of dn/dy vs y at different time is found to be constant . Additionally, with a grating at the center of the semicircle, we can measure the index of refraction n and get the plot of n vs y. The diffusion coefficient D of the solute can be calculated using the plot of dn/dy,y,and time t.

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.

這個研究起源於一個平分圓的問題：平面上有2n+1個點，任三點不共線、任四點不共圓(這個情況下的點稱為正常位置上的點)，任取三點可決定一圓，若圓內外都各有n-1個點，則此圓為一個平分圓。在[1]論文The Number of Halving Circles中，Federico Ardila教授證明了平分圓的個數為一定值n2。以此為基礎，我們探討了平分圓分割平面的區塊數、交點數、圓弧段數，發現雖然在正常位置的條件下這些個數會不定，但只要再多一項限制──若任三個平分圓共點，其所共的點必為原來2n+1個點中的一個(我們稱滿足這樣條件的點在「絕對正常位置」上)，這些個數均為定值。以下為本研究的結果：一、平面上任意2n+1個絕對正常位置上的點構成的平分圓，所分割的區塊數(N[2n+1])、交點數(N﹛2n+1﹜)、圓弧段數(N(2n+1))均為定值

The experiment was primarily focused on studying whether the enzymes from different bacterial species collected in various hot spring areas still exhibited activities at high temperatures. A further study would be conducted on analyzing the unique characteristics universally found in the genes of selected bacteria. First, hot spring samples were collected form Peitou and Wulai, and then cultured on the PY, PTG, MFB, and TS media in the laboratory. After the broth media growing with thermophilic bacteria, a series of continuous dilution method and solid-plate spreading were applied to separate these bacterial clones. The genomic DNA of the selected bacteria was extracted and used to analyze subtilisin-like gene by polymerase chain reaction (PCR) and electrophoresis. Finally, we examined the six selected thermophilic bacteria with the enzymatic activities of fibrin- and milk-protein degradation. We successfully concluded the experiment by proving that these thermophilic bacteria still exhibited significant enzymatic activitives in the high-temperature environments. The results of this experiment can be applied in numerous fields, for example, thrombus treatment and food processing, and a more in-depth study shall warrant the due consideration. 這次的實驗，主要是研究在不同的溫泉區中所採集不同種類細菌，是否酵素在高溫下仍具活性，如果有，再進而研究它們的基因有何特別的共同之處。首先，我分別自北投和烏來採集水樣，到實驗室後再以PY、PTG、MFB 和TS 四種培養基做細菌的培養，接著再利用連續稀釋和固態塗抹來做細菌的分離。經過挑選和培養之高溫菌直接進行DNA 的抽取，並利用「聚合?鏈反應」和「電泳跑膠」技術分析其類似蛋白質分解酵素subtilisin 基因。另外，本研究同時針對所選定之6 株高溫細菌利用血栓和牛奶蛋白來測試其蛋白質分解酵素的活性。由以上實驗結果可以證明某些細菌在高溫的環境下酵素仍具活性。這次在高溫菌的實驗結論，可應用在很多地方，例如：血栓的治療、在高溫下食品處理‧‧‧等，應用相當廣泛。

Many people in South Africa still use open fires for cooking. There is a\r large amount of wasted heat lost by four methods of heat transfer:-\r radiation, convection, conduction and evaporation.\r I constructed a vessel that would reduce heat loss, and focus the heat\r emitted from a fire onto the bottom of a pot. I used materials that were\r cheap and easy to obtain, so that those using open fires would be able to\r construct similar vessels to save energy and reduce pollution.\r The vessels were made up of a standard wire mesh frame that was\r surround by trial coverings, namely tin foil, asbestos rope, industrial foil,\r papier mache, ceramic, and 2 ceiling insulators.\r 5 mls of methylated spirits was burned in each vessel. The temperature\r gain of 100mls of water in a standard pot was recorded. 5 trials on each\r vessel were performed. 2 groups of vessel were found. Those that\r produced high temperature gains, burned quickly, and produced a large\r amount of soot deposits on the pot, and a second group that did the\r opposite.\r I compared the rate of heating from my best vessel to that of a stove as\r well as a microwave oven. Heating from the vessel was faster than that of\r the stove, and slightly slower than the microwave.\r I measured the heat emitted from a fire in a three-dimensional pattern and\r found that the maximal heat was some distance above the flame.\r From these results I devised 12 guidelines that would minimize the\r energy need, and pollution produced, when cooking on an open fire

本研究目的主要在瞭解昆蟲的複眼(compound eyes)結構，比較晝行性與夜行性昆蟲複眼之差異，探討其視覺遠近和複眼結構的關連，及進一步觀察其對不同波長光源反應的差異。本實驗使用反射式及倒立式顯微鏡來觀察複眼及其小眼的結構，及觀察其成像情形，並使用攝影式接觸分析儀與放大管來探討視覺遠近和小眼表面曲率之關連，另外在暗室利用不同波長的光源照射蝴蝶以觀察其反應。實驗結果顯示複眼是由數千至數萬個小眼組成，小眼表面曲率半徑隨選用物種在25.3μm 至117.6μm 之間，蜻蜓複眼上半部和下半部小眼曲率半徑分別為30.6μm、117.6μm，印證了蜻蜓複眼上看遠下看近的說法，也發現蝦子小眼是正方形，其他實驗物種則皆為六邊形，而蝴蝶對光的反應程度則是隨波長漸增而遞減。The main purpose of this study is to understand the structure of the compound eye of insects, to compare the difference between the diurnal insect’s compound eye (apposition eye) and that of the nocturnal insect (superposition eye), to explore the relationship between the vision and the structure of the compound eye, and to observe the eye’s reaction to the different light wave length. In this study, a microscope (OLYMPUS BX51M) and an inverted microscope (OLYMPUS 1X71) were used to observe the structure of the compound eye and its ommatidia, as well as the resulting image. A contact angle measuring instrument (Dataphyscis OCA 20) and a microscope (Mitutoyo NAVITAR) were used to determine the connection between the vision distance and the facet curvature of ommatidia. The butterfly’s reaction to the light source with different wave length was also observed in a darkroom. It was observed that the compound eye of insects is composed of more than a thousand ommatidia. Among the subject insects, the facet curvature radius of their ommatidia ranged from 25.3μm to 117.6μm. The radius of the top and bottom half of a dragonfly is 30.6μm and 117.6μm. It confirms a scientific finding that dragonfly’s top compound eye focuses farther than the bottom half. The facet of each ommatidium observed is hexagonal in insects compared with the square shape found in the eye structure of shrimp. Regarding the reaction to light of the butterfly eye; the reaction decreased when the light wave length increased.