在實驗中學2007 年校內科展，參展作品《三角形中的切圓》的研究中，研究三角形內的切圓時，發現連續切圓的圓心與拋物線的軌跡有關。於是去查資料，在偶然的情況下，翻閱《平面幾何中的小花》時，接觸了「六圓定理」。因為覺得這問題非常有趣，於是便著手證明（見報告內文）。 又發現，當移動六個圓中的起始圓時，總是在某種情況下，六個圓會重合成三個圓。繼續研究其重合的狀況，發現了馬爾法蒂問題（Malfatti's Problem）的一種代數解法。 當我試著推廣六圓定理至多邊形時，發現奇數邊的多邊形似乎也有如六圓定理般圓循環的狀況，於是著手證明，但目前尚未證明成功。而偶數邊的多邊形則無類似的結果。 ;In 2007 National Experimental High School Science Exhibition, one of the exhibit works, "Inscribed Circles in Triangles", shows that the centers of the consecutive inscribed circles has something to do with the parabola's trajectory. To learn more about inscribed circles and parabolas, I referred to literature. By accident, I am faced with the problem on six circles theorem, in the book The Small Flower of Plane Geometry(平面幾何中的小花). Out of my interest in this problem, I tried to prove it. The other results are as follows: With the initial circle of six circles moved, in certain circumstances, the six circles merge into three. Further in studying this coincidence leads to an algebraic method to solve the Malfatti's Problem. Applying six circles theorem to the odd-number-sided polygons exists the same characteristic. It indicates that the inscribed circles will form a cycle. However, it hasn’t been successfully proven. The even-number-sided polygons show no similar results.

當我們在風光明媚的北部海岸旅行時，常可撿到許多五光十色的貝殼。美麗的外殼，柔軟的軀體，引起我們莫大的興趣。究竟這些缺乏捕食利器而又不善於行動的小動物是如何生存的？它們吃些什麼？我們向老師請教之後，老師告訴我們研究它們齒舌的構造，也許可以知道它的食性，又說目前貝類養殖業正方興未艾，說不定我們的研究對漁民有所幫助，於是更加強我們研究的慾望，首先我們要蒐集貝類；貝類是軟體動物，它們有由外套膜所分泌的堅硬貝殼，所以稱這些動物為貝類。

Light diffraction and interference are two of most basic experiments, but they’re the most powerful evident of wave properties of light. Due to the lack of high-quality and fairly accurate equipment, these important experiments are limited to the simple demonstration of the phenomena. Especially, the spatial intensity variations of diffraction and interference patterns are, however, completely not drawn to scale. In order to precisely measure the diffraction and interference patterns intensity, we consult lots of reference, search for suitable materials and reuse waste old and useless laser printers. Finally, overcoming disadvantages of time consumption and poor spatial resolution, we develop two accurate, practical and delicate methods. We use optical power control circuit created on our own to steady the brightness emitting of laser diode. Then the high linear photoelectric detector is stored on XYZ axis micro movement control platform. Next high degree of reflection rotating polygon mirror employing optical lever is collocated with low vibration blushless motor. Thus, a self-scanning intensity pattern plotter is accomplished. At the same time, it overcome difficulties like time wasting and low reliability during doing these kind of optical experiments. In this article these two dependable and worth popularizing measurements of light diffraction and interference is going to be introduced. 光的繞射與干涉實驗是光學中最基本的實驗之一，也是證明光的波動性質之最主要的依據。在一般的高中物理實驗室中受限於器材的等級與精度，只能對光的繞射與干涉做近似定性的實驗，尤其是繞射、干涉圖形上的光能量分佈，完全無法以現有的器材做精準的測量。 在這一年的專題研究中，我們小組針對測量光的繞射、干涉能量分佈為目標，參閱許多相關文獻，四處尋找適用的材料及零件，發揮廢物利用的精神，克服萬難，發展出兩種精巧、實用又準確的測量方法，我們以自行發展的光功率控制電路使雷射二極體的光度穩定，並且以高線性度的光感測元件裝載在自行設計的X.Y.Z微動機台上，同時利用光槓桿原理所構成的高反射度的旋轉六面鏡，配合低震動的無刷馬達，完成了一套能自動掃瞄繞射能量分佈曲線的測試儀，經實際使用相當地穩定可靠，可以快速而精確地獲得大量的實驗數據，比對這些數據不僅能驗證繞射理論，並能更深入地延伸理論的探討。

有一天，同學教我下棋，覺得馬走的方法很奇妙：它是走日字型的；但是也產生了一些問題：馬是不是能走到棋盤上的每一點？如果可以的話，那又要怎麼走呢？於是帶著棋盤，和老師一起研究。

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，本實驗以滑軌、彈珠最好。樓頂加裝消能設施亦能減震，但設計極其不易。

(一)雪豆的睡眠運動乃因葉枕上下細胞膨壓之改變所致，而 k＋之進出於細胞內外，引起細胞膨壓產生變化。(二)根據食療法知：雪豆可治療神經衰弱，又可作為緩瀉劑。(三)動物神經突觸間產生乙醯胆胺，傳導神經衝動，而衝動的傳導乃k ＋由神經細胞中轉移到細胞外；乙醯胆胺又可促進消化道的蠕動。(四)雪豆能日出而醒日落而睡，光照與黑暗似可控制其睡眠運動。

隨著全球石油能源短缺，世界各國無不積極尋求永續開發且無公害污染之能源方案，而利用海洋能量發電的形式已成為世界諸國積極研究之重要課題。本研究利用近海岸浮體式波浪發電設計，並利用波浪理論推導與波浪實境測試之方式，創作出在波浪中之發電系統。發電過程為波浪推動浮體，浮體拉動水下的掛重移動，透過掛重上的橡膠管經由摩擦力效應拉動波浪發電機模型的旋轉輪，此刻旋轉輪的轉動與波浪的波高、週期產生連動效應，進而轉換擷取波浪能量，並利用此波浪發電方式，設計研發出『危險水域波浪警示燈』模型，且能在海中真實運作良好成功。

利用川燙地瓜葉可以誘捕螺類，這種自然捉螺方法讓我們感到新奇，於是進行這一次科學研究。首先，透過實際觀察、閱讀資料和請教專家，才確認我們所研究的螺類是「紅扁蜷」。然後，從飼養觀察過程不斷發現問題，並進行實驗來印證我們的猜測。經過研究後，我們更加了解紅扁蜷的生活習性：紅扁蜷屬於腹足綱－有肺亞綱－基眼目，避光性喜歡在陰暗處活動、覓食；紅扁蜷在15℃以下的水溫活動力不佳，在20℃到30℃的水溫中活動力明顯較好；加入珊瑚礁石可以幫助紅扁蜷生長，但珊瑚礁石與紅扁蜷的聚集現象無關；紅扁蜷是腐食性動物，經川燙過的菜葉或切片在水中會加速腐爛，因此可以有效誘捕紅扁蜷。比較不同菜葉的誘捕效果，其中以油菜葉的效果最好。

很多人都有泡奶粉的習慣，卻偶爾會發現在舀完奶粉後，會有少許奶粉殘留於桌面上,仔細的觀察後發現~舀奶粉時塑膠匙上有叢狀奶粉聚集，且部分奶粉會噴射出去,若奶粉是一般的電偶，理應在排列好後維持穩定的位置，相反的，若奶粉有帶上與塑膠匙面同性的電荷，它應該不會沾附於匙面，而是被斥離。但我們的觀測結果卻同時包含以上兩種現象，我們對此感到好奇而展開研究。

課堂上介紹到彩虹形成的原理是透過水珠的色散、折射與反射，而我們平時可以看到的虹和霓分別是反射一次與兩次所造成，本研究便欲探討更高階的彩虹。我們開發出電腦模擬程式，由「光線追蹤法」繪出一到十階的彩虹，研究光在水珠內反射次數、光的入射角與總偏向角之關係，發現反射次數越多，入射角要越大才會產生總偏向角的最小極限。此外我們也計算出每一條光線在各階彩虹中的能量，以及各階射出光當中每單位角度的光線數目與每單位角度的能量，結果發現能量最大、光線數目最多及總偏向角最小這三者的方向相同。並由以上數據的分析，成功設計出能呈現第三道彩虹的實驗。推廣研究：電腦模擬圖形中高階彩虹內部反射線所形成的包絡線。

A research on how a solution mixed with two or more solutes affect the solubility of each solute was done. If different solutes are put in a solution with a specific concentration, the solubility of the single state solute increases, stays the same, or decreases. The difference in solubility caused by several solutes will give solutions on selectively collecting heavy metals from bodies of water polluted by these heavy metals even more effectively. To test the changes in the solubility of the solution with several solutes, sedimentation has been used; however, colorimetric analysis was also done to observe the changes in color of solutes that show color in the solution. Nitrate compounds of Sodium, Magnesium, Strontium and Potassium were used for the typical metals, and for the transition metals, nitrate compounds of Silver, Cadmium and Lead were used. Test results show that Sodium decreased the solubility of Lead, and as the concentration of Sodium increased, the solubility of Lead increased too. On the other hand, K increased the solubility of Pb, and as the concentration of K increased, the solubility of Pb decreased. We can use the radius of ions and the enthalpy of hydration to explain the changes in solubility. In the case of Cd, as the concentration of K, Mg and Sr increase, the solubility of Cd increased with it. This is because the difference between the ionic radii of Cd and the other ions (K, Mg, Sr) has a tendency to increase in solubility in the enthalpy of hydration. Also, as the concentration of Ca increased, there was a tendency in which the solubility of Cd decreased. This is because the ionic radii of Cd and Ca are similar to each other and there was a tendency that the solubility decreased in the enthalpy of hydration. Through this experiment, the study shows the tendency of the change in solubility of several solutes by comparing ionic radius and the enthalpy of hydration, and if this result is used, the processing of certain heavy metals in the bodies of water can be even more effectively used than the previous method.

同樣是茶，為什麼茶的顏色、味道、香氣皆異？為何茶水顏色會變？於是我們實地參觀台大茶園及凍頂工作站，採集、試驗、觀察、探討茶樹的栽培與製造技術，認識茶葉種類與發現其成分，透過實驗了解不同溫度茶水變化；又將泡好的茶水置於不同溫度之恆溫箱，比較茶水顏色，並用光電比色計測得吸光值數據，探尋茶水變色因素與原理；最後試製紅茶菇，老師試飲、敷臉，黑斑略減，我們覺得好玩又有趣，對「茶」也有一番新認識。