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。

本研究藉由觀察實體桃花心木種子的飛行狀態，探討實體桃花心木種子的長度、寬度、長寬比以及重心位置，試驗分析種子飛行時間和旋轉圈數。結果顯示：蒐集到的實體桃花心木種子寬2.5公分為眾數、長分布8到11公分、長寬比約4~5。此結果與其他科展研究相符。而實體種子重心位置靠近種子長的1/5，靠近肋寬的1/3處，有較佳飛行時間與旋轉圈數。依此結果，發展紙長公式「 Lpaper= Lseed + a + W*(n+1)/2」作為裁紙參考，建立摺紙種子模型並實驗驗證。結果顯示：最佳的紙模型為寬2.5公分、長8公分(長寬比3.2)、13折，重心在靠近肋寬的1/3處的飛行最好，與實體種子實驗結果相似。

We understood the definition and meaning of spider number by reading〝Wonders of Numbers〞. It interested us so much. So, we took further step to study the situation of extreme value when the gap sometimes lie on the line and sometimes on the circle or even on both. That is to say, we explored the relation between spider number and the gap when the spider number is maximum or minimum. New research for the application of spider number involves several directions. First, we design a new game called〝Stepping Land Mine〞with the rule of spider number. Give you a net with several hidden gaps, trying to find the right positions of gaps. Second is the further result for a different type of net about regular n-polygon. Third is a tactic for a net with destroying of the strategy points. In this situation, the gaps amount on the circle and on the line are fixed. At the same time, consider the situation of circles and lines designing the tactic of placing the gaps to attain the maximum of the destructive effect. 在本文中我們定義一個蜘蛛網上的蜘蛛數，若在蜘蛛網中加入缺口後，會影響蜘蛛數的大小。我們探討蜘蛛網上的缺口，該如何分配才能夠得到蜘蛛數的極值(最大值及最小值)。先觀察一直線和圓上缺口如何放置蜘蛛數有極值，再探討許多條直線及圓上的情況，進而推展至許多同心圓及通過圓心的許多條放射線的缺口，該如何放置，蜘蛛數才會有極值發生。

能源之獲得為當今半導體科技要突破所必須克服的課題，尤其須顧及到環保之要求。所以太陽能之研究及使用已經越趨重要之地位。本實驗用天然的染色子（葉綠素 A 及亞甲藍）當作觸媒劑加在自行研製的太陽電池薄膜： Cul /光敏物質/TiO? P-N型結構。光敏物質／ CuI/ Cu plate P-型結構。 光敏物質TiO?/ SnO?/glaaa N-型結構。不同層次薄膜分別是以溶膠凝膠法及化學沉積法將 TIO?及CuI長在玻璃甚板、鋼基板及 TIO?薄膜上。本實驗的太陽電池薄膜生長速率極其穩定 ( Cul : 0 . 25um/hr , TIO? :2um/hr) ，薄膜照光電壓 0 .01~0 .1V ，照光電流 0 . 030~0 . 050 mA/cm2。

A novel technology for detection of trace concentration of ions at ppb level was developed. The detection limit of this method can be reached to 1ppb. The Wheatstone bridge usually be used for determination the concentration of metal ion, the major disadvantage of this technique is the precision too low. Atom absorption spectroscopy is better for monitoring trace metal ion, but the cost of instrument is too expensive. In this study, the oscilloscope was used to modify the Wheatstone bridge Circuit. The difference between the voltages of two connection points of Wheatstone bridge was used to estimate the concentration of ions. The amplification system was used in this method to improve the limit to detect ion from 10 ppm to 10ppb. The parameters of measurement including types of probe, match of Wheatstone bridge resistances, parameters of input signal and electrolysis in solution were also being studied. 本研究主要是發展一個富有創新且經濟的ppb ( parts per billion ; 10-9)級，微濃度金屬離子量策技術，目前本實驗設計已可以達到 ppb的偵測極限，尤其本方法不僅能夠應用於定量，尚可做定性偵測。簡易的溶液濃度技術常使用惠司通電橋的方法，但這個方法的缺點在於精確度較低，而另外常用的儀器是原子吸收光譜儀，卻價格高昂。因此，我們回頭對惠司通電橋的技術作改良和創新技術。首先，最重要的新技術是對示波器的改良。示波器被用來量測惠司通電橋的電位，我們比較電橋上兩特定點的電位來判斷濃度，當兩個點的電位相同時代表溶液電阻和控制電阻相同。但當輸入信號的電壓太強時，示波器上並無法判別細微的電位變化，因此造成量測的精度不高。本組設計新的電路用以放大在高強度訊號的波形細微變化，成功將測量極限由 10 ppm推進到 ppb。另外關於此設計中的各種參數，包括探針類型、惠司通電路的電阻匹配、輸入訊號之強度頻率、電極間電容效應及溶液中可能發生的電解效應等，都有精確的探討。最後的設計結果將是創新且有別於以往的設計概念。

聚丙烯酸(PAA)是尿布中吸水成份，我們利用其結構上的羧基螯合Ag＋，並成功以甲醛將Ag＋還原成奈米銀。但我們意外發現螯合Ag＋的PAA白色粉末在沒有其他還原劑存在下也會漸漸變成黃色，與「利用甲醛還原製得的奈米銀」顏色十分相似。本實驗即揭開此粉末變色真相，希望能在不使用額外還原劑下，直接以PAA將螯合的Ag＋製成奈米銀，不僅具環保與實用價值，更能使奈米銀製程朝向綠色化學。我們透過水溶性聚丙烯酸鈉(SPA)在均相中進行變色機制探討及影響變因的研究，找出有利的反應條件，再應用於PAA。研究證實PAA能將螯合的Ag＋同步還原成奈米銀，反應機制與檸檬酸鈉作用模式相似，而提升濃度、溫度或照光有利於反應，酸性條件則不利，照各種色光也有所差異。

高分子發光二極體乃是利用電子和電洞在發光工作層結合而形成激子，激子在形成後隨即以光的形式衰退，而發出光來。一般而言，高分子發光二極體是一種三明治的形式，電子注入層/發光工作層(高分子)/電動注入層，而通常我們會選擇加入電子傳遞層和電動傳遞層，來增加其發光效果。本研究係針對聚苯胺做為電洞傳遞層對發光二極體之影響，分別對有電洞傳遞曾和無電洞傳遞層之發光二極體作導電度測量、循環伏安法、電位-電流測量、亮度-電位測量。發光二極體中所須之高分子層，須利用旋轉塗佈機，將其均勻的披覆在載體上，由於本校並無此儀器，所以將離心機改造成簡易旋轉塗佈機，並觀察其披附之效果。另外，在封裝元件時，係因學校缺乏真空蒸鍍的儀器，所以將利用電鍍法把鋅鍍在ITO玻璃上，或將鋁片和ITO玻璃緊靠在一起，針對此二替代方法，本研究將探討其所製出原件成效。Polymer light emitting diode (PLED) utilizes the energy gap between the layer of electron and electric hole that emits the light due to the decay of solitron. PLED is always in the sandwich from, that means the conducting polymer is contained between metal as an cathode and indium tin oxide as an anode. It is used the addition of another electric transfer layer and electric hole transfer layer to improve the lighting efficiency of PLED. The purposes of this study are to discuss the effect of polyaniline as the electric hole transfer layer. The study methods are conductivity measure, the cyclic voltametry, the luminance-voltage curve. The simplified spin coating machine was designed to coat the polymer onto the ITO. The zinc was electroplated onto the graphite as an cathode.

由於結網性蜘蛛視覺不靈敏，如何在網上藉振動進行獵捕，這是長久以來頗令科學家困惑的難題，當周遭環境各種振源觸網時，首先會產生不同振盪，蜘蛛是否藉由這些振盪得知獵物資訊？如何迅速準確的定位？又有那些決策條件影響蜘蛛的捕獵行為？更特別的，為何蜘蛛在捕獵過程中會“扯網”？本研究以台灣最大型結網性蜘蛛－人面蜘蛛為研究對象，並設計出一套非接觸式的測量方法，就上述謎題作深入的探討後，成功的解開人面蜘蛛的捕獵機制。簡單來說，其機制分為兩大系統：(1)當獵物擾動不明顯，人面蜘蛛會立即扯網，藉有無產生阻尼振盪，以判斷有無獵物存在；在阻尼振盪產生時，蜘蛛將感知其中具有最大阻尼振盪之放射絲為獵物所在方向，而振盪週期長短，係蜘蛛用以判斷獵物遠近之有效因素。(2)當振源明顯時，蜘蛛直接判斷各種擾動的振幅大小、頻率高低、波形模式、振源質量輕重，決定是否啟動捕獵或逃離反應，並在反應前先行定位，亦即以步足腳勾偵測並比較各放射絲之振盪大小，以振盪最大之放射絲為獵物方向，其次藉由第二對步足之位移所產生之準光角，判斷獵物之遠近。蜘蛛正確的將獵物定位後，會以適當的速度往前衝，一口咬住獵物，以蛛絲重重包裹後，拖往網中央並進行吸食。 Giant wood spider, Nephila pilipes, is the biggest orb web spider in Taiwan. The mature N. pilipes may even grow to exceed 5 cm body length. While waiting for the prey, its giant body hangs quietly on the hub of the web. Owing to its ineffective vision and sense of smell, the spider depends almost on detecting the vibration signal of the struggling of web cause by the struggling prey. When various kinds of sources from the environment contact the web, they will generate various types of vibrations which cause the spider to judge whether they represent danger, prey, or irrelevant signals. Our results suggest that if the disturbance is obvious, through discriminating the amplitude and frequency of the vibration, the spider will make a decision whether to attack or escape immediately. Yet, before any decision is made, it will need to locate the source of vibration. For example, it will locate prey correctly by comparing the vibration transmitted from the radiating strings. The radiating strings that transmitted the largest vibration are where the prey is entangled. The displacement of the second pair of legs will generate a quasi visual angle which enables it to comprehend the distance of prey. When the vibration signal is obscure, it will jerk the radiating string immediately. After jerking it, if there is damping oscillation on the web, then the spider can judge the location of the prey. When there is damping oscillation, the radiating string that transmitted the greatest damping oscillation is where the prey is entangled. Furthermore, the frequency of damping oscillation helps the spider to judge the distance of the prey. After locating the prey correctly, N. pilipes approaches the prey fast, wraps it with silk then drags the prey to the hub to feed.\r

通常使用隔熱材料可以降低熱量傳遞，而使用風扇、散熱片、熱導管等用來單向散熱。但如何在一個系統上同時滿足隔熱和雙向傳熱的需求呢？因此我研究設計了仿生智慧型熱控制系統，能隨環境改變而快速轉變成隔熱或轉變成雙向傳熱並控制熱傳遞的方向及大小，這可以應用在房屋、汽車、恆溫系統等。我先自製了自動傳熱量測系統，測試並找出好的隔熱和傳熱材料及構造。為了能快速控制熱的方向及大小，我又發展了第一代替換式、第二代熱柵式和第三代熱管式熱控制系統；經過多次實驗，利用低沸點有機溶劑和控制系統，我成功地完成仿生智慧型熱控制系統，讓熱隔絕或快速流進流出，比傳統的方法改進很多，也達到節約能源的目的。Insulation materials are usually used to reduce heat transfer rate, while fans, radiators and heat pipes are applied to increase heat transfer rate and bring heat away. But is it possible to have both functions of insulation and heat transfer together in a single system? This research is to design and develop an intelligent heat control system, with both function of insulation and function of transferring heat together. Besides, this system can control the direction and amount of heat transferred. Such a system can be applied in house walls, cars, thermostatic system, etc. I developed an automatic heat measurement system which was used to test the properties of heat transfer for different materials and structures. Three generations of intelligent bi-directional automatic heat control system were then developed to get fast heat transfer and function of heat control. They were phase 1 replacing-type system, phase 2 heat-grating system, and phase 3 heat-pipe system. After tens of experiments, I successfully control the amount and rate of heat transfer via low-boiling-point organic solutions and controller. The designed system is bi-directional, and is more innovative and efficient than conventional uni-directional heat control methods. Besides, this system also has huge contribution in reducing energy consumption.