我的研究是利用一些特殊的手法來探討所有情況皆會產生共點圓或共圓點。在一個由四條直線(無平行線組、無共點)所構成的圖形中，可以找到四個三角形及它們的外接圓。我知道它會共點，在此稱其為限制點。且若再添加一條直線，則可以任意的取出四條直線，分別找出它的限制點，而這些限制點又會共圓，吾稱其為限制圓。我欲證明此種情況會不斷延續下去。即是六條線時又會有限制點，七條線時又會有限制圓…。在本研究中，我利用了數學歸納法、特殊的編號方法以及「方向角」來做出此證明。由於固定的線組對應至固定的限制點或限制圓，希望能向找出其性質的方向發展。In my study, I use some skills to discuss all the situations which satisfy following conditions. The result is that concurrent circles or concyclic points will be found in every situation. In a graph consisting of four lines, conforming to conditions that any three lines won’t be parallel or intersect at one point, I can find out four triangles and their circumscribed circles. I know these circumscribed circles will be concurrent and I call the point at which all the circles meet “restricted point”. If another line is additionally added in the graph, I can discover that restricted points determined by any four lines in the graph will be concyclic. I call the circle “restricted circle”. What I want to prove is that the above situation will go on. In other words, restricted points will exist when I have six lines, and restricted circles will exist when I have seven lines and so on. In my study, I used Principal of Mathematical Induction, special ways of numbering points and circles, and “orientated angle” to prove my hypothesis. Because of particular line groups corresponding with particular restricted points or restricted circles, the further work I want to attain is to find the relation of them.

高中光學用三稜鏡或光柵分光，用肉眼判讀每條光譜對應特定波長，但誤差很大，很難客觀描述光譜顏色。偶然發現，透過光柵，可在夜間看到汽車頭燈為連續光譜、水銀燈為亮點光譜(Pic.1)，從光柵看世界竟是如此奇妙。 我們只使用攝影腳架、相機、凸透鏡、刻度圓盤、1200條/㎜光柵便組裝「攝譜儀」 (Pic.2)，不但成功鑑別鈉雙線，也可靈活拍攝遠方光源的光譜。 天文攝影常使用紅、藍、綠3種濾鏡，利用電腦影像疊合得到彩色的星雲照片，提供我們將「光譜影像數位化」的靈感，因為電腦不但可靈活放大影像，至少可鑑別3 萬 2 千種顏色，將各種顏色的光譜線轉成數位座標，不但可測量未知光源的光譜線所對應的波長、顏色，也成功鑑別5890、5896Å相差6 Å鈉雙線，深具實用價值。

第 37屆的科學展覽，我們曾經做了一個有關橋墩的研究。在實地觀察中，我們發現一個奇特的現象，就是在橋墩的周圍會出現一個水坑，老師告訴我們：「這是河道中的渦流所造成的」。「究竟 『 渦流 』 是如何產生的呢？」「對橋墩會有什麼影響？」我們心裡起了疑問，便在老師的帶領下展開了這個研究。

Anthocyanin is a water soluble pigment that may appear in various colors such as red, blue, and purple according to the pH. Ube is a fruit in the Philippines that is 3rd of the most cultivated crops. Since Ube contains a lot of anthocyanin, it helps to make the anthocyanin solution. As Anthocyanin reacts to the oxygen quickly it is also used as air pollution indicator because it changes its color according to what substances they are attached to it. To check if the solution reacts to the pollution such as SO2 and NO. When those pollutions are made artificially, examining the intensity of the anthocyanin solution depending on different Mol of the pollutions was able. The power of penetration of lights though the UV-VIS spectrophotometer increases according to the number of molecules of SO2, and also NO. To examine the change of intensity of anthocyanin solution in actual atmosphere, the solutions were exposed outside for several hours. The power of penetration decreases when exposed to an actual atmosphere. The other substances and oxidation were the causes of the changed in color of the solution To facilitate the usage of anthocyanin solution efficiently, it should be preserved, so that the density of specific color will be preserved when used as real air pollution indicator. In order to check what kinds of chemicals can preserve the anthocyanin solution; different kinds of strong acids, strong base, salts, and metals were added to the solution. After getting the data, the characteristics of the chemical which preserved the anthocyanin were scrutinized, than compared to the density of pure anthocyanin solution. To use anthocyanin as air pollution indication as a solid, the Korean traditional paper and cloth were dyed using ube which contains lots of anthocyanin than checked the pixel of red, green, and blue color. Firstly, chose 6 different salts. And then filter and boiled the anthocyanin solution. And then put each different salt in each paper. After that, dried the paper and check the difference of pixel of each paper. As a result, Calcium hydroxide (CaOH2) has highest pixel point. So, using calcium hydroxide to dye clothes is useful and it’s also useful for the air pollution indicator through the experiment. Especially it reacts to Nox and Sox, according to this experiment, it can use for eco-friendly air pollution indicator.

本專題研究之目的，在於運用簡單的原理自製出準確、廉價、適用於低風速範圍的風速計；方法是藉由將一連接轉軸的玻璃片迎風，探討迎風時，玻璃片偏轉夾角和風速之間的關係。實驗過程中同時發展出可以用馬達旋臂的裝置與v=rω的原理，產生穩定可計算風速的環境。研究結果發現：在低風速的環境下，θ 範圍小時玻璃片與地夾角和風速大略成正比的關係，所以我們可以得到近似式” v≒aθ+b”，參數(a,b)依玻璃片而定。另外θ 範圍大時，我們可以使用二次逼近曲線的方程式與內插法來作角度與風速的對應。藉由控制玻璃片的厚度、質量與形狀，我們可以製造出相對應風速範圍的風速計。The purpose of our research is to use easy theorems to make accurate and inexpensive anemometer which is available in low wind velocity. To make such anemometers, we made a piece of glass, which was connected to a axle, to face wind; then, we could figure out the corresponding relation between wind speed and the angle created by the original and the resulting positions of the piece of glass. While we were experimenting, we found that we could make a steady-wind-speed environment by using motors, sticks, and the theorem ”v=rω”. The research showed that the angle created by the original and the resulting positions of the piece of glass and wind speed are in direct proportion in low wind velocity in small θ range. Consequently, we\r can derive the formula ” v≒aθ+b” , for each piece of glass (a,b) can be different. In addition, when in bigger θ range, we can use quadratic approximate equation and interpolation to describe the corresponding relation between the angle and wind speed. By adjusting the thickness, mass , and the shape of the glass, we can make anemometers corresponding to different wind velocity ranges.

日常生活中，隨處可見被拋棄的廢鋁罐，這些廢鋁罐若任其自然分解反應，約需一百年的時間才能完全分解，是一種不易被分解的廢棄物。在這次實驗中，我們試著利用很簡單的方法來回收廢鋁罐，並探討不同環境因素（例如表面積大小、溫度高低）溶液的種類（例如酸、鹼）對明礬產率之影響及探討明礬可否有淨水之功能。結果發現影響明礬速率快慢及顆粒大小有：１冰水浴溫度的高低２溶液是否達到飽和３放置時間的長短４加入晶種。尤其明礬結晶之冰水浴溫度在－６℃時，結晶析出量可高達8.2605ｇ；硫酸濃度再12Ｍ時，鋁的回收率最好，為85.51％。另外我們也觀察得到的明礬結晶，發現它為透明多邊體型。混擬劑試驗中我們發現pH值控制在4~5之間，會產生膠體顆粒，且明礬量只要加100mg/l於染料廢液中；它的處理量就非常驚人，另一個發現明礬對重金屬(硫酸銅、二烙酸鉀及過錳酸鉀)是否有潔淨之功能，濃度分別降低原來的7.683%、3.466%及6.470%，其中我們做出來的硫酸銅溶液顏色有變淡，證明明礬對硫酸銅也是有淨化之功能。

最近我們在各種報章雜誌中，都常看到有關船的新聞。（如美國派遣來保護我方的軍鑑 ─ 尼米滋號和獨立號）看到這樣雄赳赳氣昂昂的航空母鑑在海上航行引發了我們對船的興趣，而決定和同學在老師的指導下作次有關船的研究。

我們想了解鐵皮屋溫度、室內溫度以及溫差發電之間的關係，先直接測量鐵皮溫度，得知「鐵皮面積大小不會影響表面溫度」。接著，我們釘製大小不同的模型鐵皮屋，分密閉及通風兩種條件，得知密閉比通風室溫更容易升高，室內採取通風有助於室內降溫的條件；而室內體積小，室內溫度升或降都比室內體積大的效果來得明顯。 我們又在鐵皮浪板內面加裝散熱風扇模組，實驗結果：讓風扇向地板方向吹，則有助於熱空氣與冷空氣對流，能夠降低室內溫度，使鐵皮溫度和室內溫度產生較大溫差。我們再加裝致冷晶片散熱模組連接三用電表，實驗得知鐵皮浪板表面溫度與室內溫度溫差越大，產生的電流、電壓也越大，於是再將鐵皮塗上黑色塗料以增大溫差，最後，再增加晶片散熱模組串聯，結果顯示電流、電壓均有明顯增大，我們可以利用這樣的太陽熱溫差來產生電能。

我家後面的小河是我常去遊玩的好地方。夏天裹玩河水是我最高興的事，早上河水比較涼，但是中午戲水又覺得神清氣爽。靠河邊低窪積水的地方，水溫暖和些，可是潺潺流動的水，很奇妙的叫人覺得涼快。因此我急著想知道為什麼水溫會有這些變化呢？

利用野外實測我們發現旗尾山的位態為N45°E45°E而龍肚山為N20°E75°W，且兩者同屬糖恩山砂岩層。據此推測兩座山脈是受旗尾山西側旗山斷層影響所造成的向斜構造，因而造成兩者隔著美濃平原相望。透過室內模擬實驗發現泥的沉降和壓密過程可分成三個階段，初期泥漿水的濃度越大，沉降的速率越快；當濃度逐漸下降後，泥的沉降速率會趨近於一個穩定的值約為0.2cm/小時，最後當水中不再含有泥的懸浮顆粒時，泥受自身重力影響，開始以約0.05~0.1cm/小時速率產生壓密作用，顯示我們在野外看到的泥岩是經過長時間緩慢沉降和壓密的結果。