問題與想法：邊長1的正三角鏡ABC中，光由原點B射到CA上一點P(圖一)，再依反射定律繼續反射下去，我們想探討：是否能回到原點B？而若回到原點B，所走路徑及反射次數可找到通式？考慮圖二探討此問題。圖二中的每一頂點都對應△ABC中每一頂點。主要結論：我們算出每一反射點在圖二中的座標得以下結論： (1)CP為有理數時，CP=b/a,(a,b)=1,a,b∈N，導出第一個相交頂點在展開圖的座標為(a-b,b)。再利用展開圖中，同名點構成的直線特徵(如圖三)得：由B射出光時，會返回原點B。並知反射後回到B所需的次數與路徑可由a、b決定，公式如下：若a+b≡0(mod3)，次數為2(a-1)次，路徑為B→B 若a+b≡1(mod3)，次數為6(a-1)次，路徑為B→C→A→B 若a+b≡2(mod3)，次數為6(a-1)次，路徑為B→A→C→B (2)當CP為無理數時，我們得到由B射出的光線不會返回B。且所有無窮多的反射點，在邊上的分布具有稠密性。

聽說窗簾可能有吸音及隔音效果，但真的嗎？ 研究顯示：(1)窗簾材料：吸+隔音效果為棉質>麻質>塑膠質>厚棉>紗質>海報紙>雙面質 (2)窗簾厚度與吸音呈正相關與隔音呈負相關 (3)窗簾孔隙面積與吸、隔音都呈負相關 (4)牆面的窗簾數與吸、隔音都呈正相關 (5)對稱H型擺設雙牆窗簾吸、隔音都比連續L型好 (6)窗簾波折高度與吸、隔音都呈正相關，波折高度≥10cm吸音效果好 (7)窗簾波折間距6~7cm吸+隔音效果好 (8)窗簾到牆距離與吸音呈正相關與隔音呈負相關；到牆距離3cm處有最佳吸音效果 (9)多層窗簾有吸、隔音效果，以2層為最佳 (10)窗簾含水量與吸、隔音量折減率呈正相關，棉質窗簾含水量168％為最佳吸音含水量。 窗簾改善噪音是有效，理想吸音可減42 dBA及隔音可減139 dBA。

世界上最美的比例－黃金比例為1.6180988…，像是希臘雅典的古廟、美術、雕塑、音樂……等等，生活上有許多實際的例子都應用了黃金比例，鸚鵡螺的殼形也是自然界黃金比例的實例之一。經由日常中實際觀察，發現每個蝸牛殼形大多都是螺旋狀－與鸚鵡螺形狀大致相符。然而日常生活中常見的蝸牛殼形是否就存在著黃金比例呢？經過運用畢氏定理、尺規作圖以及特奧多魯斯螺旋描繪出蝸牛殼的形狀、再用電腦製圖做更精細的確認之後，說明了蝸牛殼形中藏著黃金比例，證明「自然就是美」。

This Project is inspired by the situation incurred by pedestrians, which for the most part are students who need a crossway in order to obtain public transportation or to get to the school; the difficulties that are faced by the personnel to exit the parking lot as well as the students who have a vehicle and to help those parents who drop and pick up their children at the school. At the same time, we would like to reduce the amount of contaminated gas emissions that are emanated into our environment. As consequence of the emission of toxic substances, the air contamination can cause side effects such as the burning of eyes or ears, throat irritation and itching and or respiratory problems. Under determined circumstances, some chemical substances that are found in the contaminated air can produce cancer, congenital malformation, brain damage and disorders to the nervous system, as well as, pulmonary damage and harm to the respiratory tract. For the present investigation it has been suggested as a primary goal: The development of a device, in this case a traffic light, which has the objective to reduce the previously mentioned traffic/security problems that arise upon entering and exiting the institution. The secondary goal is to have a friendly ecological impact within our community. This device was built and tested during a month to obtain figures and demonstrate benefits reported. The device should be low maintenance, it should have a long lifetime and, be simple enough to be operated by those who use it. Among the benefits found, the safety of the students, the prevention of accidents such as: car crashes and run overs, etc. Our studies indicate that per week it is consumed an average of 2,020.16 liters of gasoline, in schedules of 13 hours (from 7:00 AM to 8:00 PM) to lessen this figure would have a good ecological impact since all the hydrocarbon emission are harmful to health.

甘蔗渣中含有豐富的木質纖維素，其上的官能基可以吸附重金屬離子，我們在此研究中找到適合甘蔗渣吸附Cu2+的最佳條件。在一次實驗中，我們偶然發現甘蔗渣溶液中的有機物能吸附Cu2+，而碳粉能將有機物吸附，利用這點特性，能大幅提升Cu2+的吸附率。在經過兩道程序的吸附之後，20ppm Cu2+(aq)中Cu2+的吸附率大於99%。

At the website “MathLinks EveryOne,” we found a problem “Snakes on a chessboard,” which was raised by Prof. Richard Stanley. The following is the problem. A snake on the m n chessboard is a nonempty subset S of the squares of the board with the following property: Start at one of the squares and continue walking one step up or to the right, stopping at any time. The squares visited are the squares of the snake. Prove that the total number of ways to cover an m × n chessboard with disjoint snakes is a product of Fibonacci numbers. We call the total number of ways to cover a chessboard with disjoint snakes “the snake-covering number.” This problem hasn’t been solved since it was posted on September 18, 2004, so it aroused our interest to study it. First, we used the way in which we added each block to the chessboard, and therefore we discovered some regulations about the snake-covering number of the1 × n , 2 × n and 3 × n chessboard. Through “recursive relation” and “mathematical induction”, we proved the general term of the snake-covering number of the1 × n , 2 × n and 3 × n chessboard. In the following study, we found a key method in which we added a group of blocks to the chessboard. Finally, we proved the general term of the snake-covering number of the m × n chessboard. Also, we discovered the way to figure out the snake-covering number of the nonrectangular chessboard.在網站“ MathLinks EveryOne ”中，我們找到了一個有趣的問題“棋然上的蛇” ( Snakes on a chessboard ) ，這個問題是由教授 Richard Stanley 所提出。問題如下：在m x n棋盤形格子上，蛇由任意一格出發，但蛇的走法只能往右 → ，往上↑，或停住 ‧ 若此蛇已停住，將由另一條蛇來走，且不同蛇走過的格子不可重疊”證明：將 m × n 棋盤形格子完全覆蓋的總方法數為費氐（ Fibonacci ）數列某些項的乘積。我們將把棋盤形格子完全覆蓋的所有方法數稱之為“蛇填充數” 由於這個問題自從 2004年 9 月 18 日被登在網站上後，還沒有人提出解答，於是引發了我們研究的興趣。首先，我們使用了將一個一個格子加到棋盤上的方法，並發現了 l × n 、 2 x n、 3 × n 棋盤形格子蛇填充數的一些規律。我們使用遞迴關係及數學歸納法來證明 l x n 、 2 x n ， 3 × n 棋盤形格子蛇填充數的一般項。在接下來的研究中我們發現一個特別的方法，一次增加數個方塊 ‧ 最後我們證明了，m x n, ，棋然形格子的蛇填充數的一般項 ‧ 而且，我們也找到如何求出不規則棋盤形格子的蛇填充數。

黑棘蟻利用成蟲的唾液與末齡幼蟲吐的絲，將樹枝纖維、枯樹葉、沙粒、植物種子等黏合而成紙蟻巢。蟻巢大部分築在靠近地面的灌木枝條間，其外觀形狀略成橢圓形、顏色近黑褐色。冬天黑棘蟻會將族群遷移到地面上可保溫的遮蔽物內，例如不透風的帆布和塑膠袋、枯樹葉和水管內都可見其築巢，巢穴通常不直接接觸陽光。黑棘蟻的社會結構包括卵、幼蟲、蛹、工蟻、雄蟻、蟻后等社會成員。工蟻由卵發育至成蟲約需工蟻需45～60天。黑棘蟻的社會成員各司其職；體型最大的蟻后負責與雄蟻交配及產卵，而且卵通常成堆，由工蟻負責照顧，幼蟲已具有體節，由工蟻負責餵食；雄蟻具有兩對膜翅，負責與蟻后交配。我們從飼養過程中，發現工蟻日常生活的主要活動為清潔身體、到處走動巡邏、覓食和搬屍。我們推測黑棘蟻會分泌訊息費洛蒙來通知同伴特有的訊息。黑棘蟻可以在水中存活數小時並可互相勾結腳產生氣泡，我們也發現雄蟻上的翅膀會阻礙其翻身。我們將從實驗中更瞭解這群與人類生活息息相關的小小朋友。

細胞質流（cytoplasmic streaming）的機制，目前通常被認為是藉由ATP提供能量，使肌動蛋白分子連接胞器而沿著細胞骨架移動，並以此促進相鄰的兩個細胞透過原生質絲（plasmodesmata）交換物質。本研究建立水蘊草（Egeria densa）之細胞質流流速的觀察及測量方法，並以能量的角度去探討其機制層面。我們發現當光度小於1000 lux時，細胞質流流速及淨光合作用速率具有高度正相關。硝酸鎳能明顯促進細胞質流流速及淨光合作用速率，而40℃、pH1、pH13、硝酸汞、4℃一天能使細胞質流停止。

本實驗利用「閃光攝影術」，由拍攝桌球碰撞球拍拍面瞬間照片，希望能測量桌球與拍面的接觸時距、摩擦力、恢復係數。近年來，數位相機已經具有單眼相機所有功能，所有攝影參數可記錄調整，並且可以馬上看，作影像處理，大幅降低拍攝費用，若配合高速閃光燈，可以拍到重複曝光照片，所有的數據由照片測量，是計算碰撞問題的新的構想，適用於所有球類的碰撞。

This study is to investigate whether colony of the spiny-weaver ant, Polyrhachis dives, have biological clock so as to observe the locomotion activities of the ants in the nest and find out if the Light period will interfere the rhythm. The conclusion is the colony of the ants get the rhythm is 23.8 hours during in L:D=12:12.There are ants not significant difference between large colonies and small colonies. While in Dark (D:D)the ants appears free running with 23.1 hours as the rhythm, so, the colony of the ants has obvious light-rhythm movement, showing that the biological clock will act on group and being controlled by light period. 本研究是在探討黑棘蟻 (polyrhachis dives) 聚落是否有生物時鐘(biological clock)，以觀察黑棘蟻在巢裡的活動情形，找出週期並探討光是否會影響週期。結果觀察出黑棘蟻 的聚落在有光的時候(L:D=12:12)以23.8 小時為週期，沒有光的時候(D:D)黑棘蟻仍呈現自由律動(free running)，以23.1 小時為週期，所以黑棘蟻的聚落有明顯的日週律動，顯示生物時鐘能作用在聚落上，且受光週期之調控。