在正n邊形的n個頂點各放一面鏡子，並將其中一個鏡面順時針轉動90°/n，將雷射光線沿該點切線方向射向此鏡面，使光線在正n邊形各頂點的鏡面間反射，本文主要在探討光線在各鏡面間反射路徑之規律性與其應用，研究分為兩大部分：一、將雷射光線射向一順時針調整角度θ=90°/n的鏡面且其餘鏡面皆不轉動之情形下，探討雷射光線的反射路徑之規律性及尋找正多邊形邊數與反射數間的關聯性。二、在正n邊形的n個鏡面中，每個鏡面可依順時針或逆時針旋轉一個角度θ=90°/n或是不轉動。此部分我們只針對n為偶數的情況去探討，我們採用數學上函數的對應方式取代了物理上反射原理的路徑操作，由數學的模式去探討鏡面調整的規則，擬訂出適當的策略調整鏡面的轉動，並找出最大反射數。

氫是一種非常理想的能源。不僅效率極高，且不會造成環境污染。空氣中的含量極少，常用的電解水方式又效果不彰。我們利用Ag、Ru、Cu 、C-CuPu、C 等數種電極，與H2SO4、 H3PO4 、HNO3 電解液，分別在10V 雙電極與-0.8V 三電極下做電解水實驗，研究何種電極與何種電解液能得到最多的氫氣量。在低電壓下找出最好的電極，液與太陽能電池結合，成為電池中的一部份，讓發電效果更好，以利未來燃料電池H is a kind of great power.It is not only effective,but also no environment pollution .Owing to the H in the air is very little,so it is not easy to take .Addition to,we often to take it by electro liquid,but the electrolysis effect is not ideal. Except Ag、Ru、Cu、C-CuPt、C and so on ,in theH2SO4、 H3PO4 、HNO3 electro liquid,we have a experiment in the 10V dual electrode and -0.8V triple electrode to study which electrode and which electro liquid to get the most of H.Under the low voltage,we can fund the best electrode.It is easy to bind with solar energy battery,andit can be a part of battery.Besides, it makes the generator effect better,and it is convenient to make the fuel cell commercialize in the future.

「風笛」是台灣原住民鄒族的信號用具及祈雨法器，由一條繩子綁一支竹片構成。轉動風笛時，竹片會繞繩子自轉並拍打空氣而發出聲音，並有上下飛舞的現象。風笛產生聲音的原因，為竹片拍打空氣而造成的渦流共振現象；又由於繩子扭力大小及方向改變，使風笛的音調忽高忽低、響度忽大忽小、且竹片會在兩個平面上公轉，而有週期性變化。施力使風笛公轉轉速加快時，竹片自轉速率也變快，使其音調愈高、響度愈大；而繩愈短、愈粗時，竹片的公轉週期將愈短。The wind whistler was once used by Tsou aborigines as a tool for message transfer. It is composed of a string and a bamboo flapper. When swung around, the flapper spins, beats the air, and makes sounds. Moreover, the flapper flies up and down during the revolution. The spinning flapper beats the air, causes the vortex resonance phenomenon, and thus produces sound. As the twist torque and direction change, there is periodical variation in the sound volume, sound pitch, and the movement of the flapper, which orbits up and down at two planes. If given force to speed up its revolution, the flapper，s spinning frequency also increases, which makes the sound pitch higher and the sound volume greater. Besides, when the string is shorter or thicker, the flapper，s revolution period will be shorter.

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。

To contribute to the feeding of the popular sector using a product of the basic basket of\r consumption and in simultaneous form to operate a natural resource, that when being combined\r will derive in a rich product in nutrients. With this project we try to offer to the population an\r innovating product, based on a food of daily but added consumption with all the nutrients of the\r nopal, of this form will be a better nutrition in the tortilla consumers. In Mexico, like in some\r countries of Central America, the maize products, like the tortilla, are the base of the popular\r feeding, its consumption is related closely to the obtaining of energy, calcium, fiber, iron and zinc,\r which usually display deficit levels in the population of the region. The contributions of the nopal\r are diverse, because it counts with some different nutritional and medicinal properties.

此研究是探討在目前全球因聖嬰現象後北極暖化，造成溫度持續在三十年內以每年上升攝氏零點五度，目前多數資料以顯示，對於地球內的生物生態產生了微妙的變化，在本文中將引述著名雜誌─科學人雜誌所刊登之關於全球暖化造成的生態環境影響；然而早在三億五千萬年前就已存在地球上的古老生物─蟑螂，順利的度過了多次的大滅絕，走過冥霜與煉獄。但是否會因為暖化作用而造成其生態影響呢？他又會不會成為少數存留並且大量繁殖的征服者呢？所以我們開始查詢白堊紀之資料，在研究、討論並製作改造完成實驗室氣溫控制冷熱溫差調節器，並從專業研究蟑螂生態的業界專業實驗室取得同一時期的實驗蟑螂物種，以期待本實驗更能具有更高的正確可信度；於特殊自行改造的觀察箱內進行整個實驗，已改變溫度並測量其進食狀況，瞭解蟑螂在溫度變化下的生態狀況。\r \r It’s easy to find the cockroach at any corner, such as school or house. They also hide in the refrigerator and stove.Thus,we are curious why they have durable vitality. This is the reason why we want to uncover the mysterious veil. According to data, we are curious about the environment of the cockroach and the temperature.Therefore,we want to imitate the situation of the ecosystem temperature at that time and inquire into its mystery. The purpose of Research is to make the violent changes, then discussing the meal which has attained its biggest existence rate. This uncontrolled experiment will influence the accuracy by factors.Therefore,we go to visit the laboratory personally and obtain some species of cockroach. Through the professional explanation and introductions, we make sure the direction of this experiment further. In this experiment we measure their appetite and the controls of the temperature everyday. They almost can crawl quickly along any material. We adopt the professional suggestion to measure with CO2 and O2.When the cockroach inhales CO2,we can observe the construction of the each part carefully. Through long-term observation, the food of the cockroach decreases, when the temperature rises to 20.6℃ or declines to 16.3℃,and it will stop moving when the temperature rises to 31.8℃ or declines to 8.7℃. When the temperature rises rapidly or reduce more than 15℃,the cockroach will look for shelter. Besides they easily get fainted when cockroach inhales CO2 without soil. The dinosaur were all buried underground, but why can the cockroach survive up to now? Probably, large land is their savior! Our conclusion is (1)The temperature that cockroach can exist from 49℃ to 3℃.(2)The suitable environment of cockroach growth is between 28.5℃ and 25℃.(3)The cockroach maintains their existence by eating under the low temperature 20℃ to 15 ℃.(4)Above 32℃ and under 7℃ the antenna is close to ground, its life is weaker.(5)The cockroach almost can live at any dilemma. But it can’t keep the prosperous life when it’s short of water.(6)From the above cockroach will be king of the world forever.

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.

My project explores the practicality of biodiesel. It researches the argument of food versus fuel, compares the energy efficiencies of petroleum diesel and biodiesel and studies the effect of temperature on biodiesel. To study the effect of temperature on biodiesel, I blended biodiesel with petroleum diesel. Biodiesel blends are represented by the letter B, and the percentage of biodiesel. I used B5, B10, B20, and B50 blends, as well as pure biodiesel. I then observed the reaction of the biodiesel blends with cold weather. My pure biodiesel and B50 blends gelled to an unusable point within 15 minutes outside at -20oC. The B20 blends didn’t gel until about a temperature of -20oC. I have concluded that the B20 blend would be best for the summer, and the B10 or B5 blends would be the best for winter in northern climates, where I live. Although the B10 blends gelled slightly around -30oC, this would only be a problem for northern climates. As I predicted, more energy is produced by biodiesel than is consumed in the production process. The process of making biodiesel uses 0.31 units of energy to get 1 unit of energy out. More energy (1.2 units) is used to produce petroleum diesel than is yielded (1 unit). Although B20 isn’t as energy efficient as B100, the energy factor is still only 0.98 units of energy in for every 1 unit of energy out. When I started this project I thought that Canada would have enough farmland to produce the canola needed to run the country on biodiesel. This is only partly true. Canada would have enough farmland, but only a fraction of that land is actually used to plant canola. By my calculations, Canada has enough canola to generate enough B20 for a year. This may seem like a drawback but realistically, a higher blend would be impractical due to the gelling factor. Also, if a B20 blend was used, land would be available to grow canola for other markets. If B100 was used, there would only be enough diesel for about three months consumption. By using all of the land for biodiesel feedstock, canola would become unavailable for other markets. If canola exports ceased, the countries that depend on our canola will be in a lot of trouble. Canada already produces a lot of canola and vegetable oil. Most of it goes to the fast food industry. The United States produces over three billion gallons of fryer oil yearly. This could provide Canada with a B50 blend for a year. Utilizing used vegetable oil in making biodiesel actually reduces emissions even more. This is accomplished by using a product that would normally go to waste and decompose, producing more carbon dioxide emissions. During this project, I have found that biodiesel is a practical alternative to petroleum diesel, if it is used in a blend. My experiment proves that biodiesel is a fuel alternative that could be implemented immediately, and one that does not require the research needed for other fuel alternatives such as hydrogen or electricity.

這是一系列關於水蒸氣冷凝為極細微水珠的實驗。其中可以歸納為三大部分，第一部分是基礎實驗，將水蒸氣導引至親水性介面上，觀察冷凝水珠的結構。雖然看似簡單平常，但是卻發現：不同溫度的水蒸氣，其冷凝最初始的細微珠粒，尺寸相同；爾後溫度高者，堆疊速率較大，以至於最後同時呈現的水珠大小不一，尺寸不同！ 第二部分，是針對冷凝水珠自我組裝機制的探討。實驗是將水蒸氣導引至密度小於1的高分子溶液上，並藉由揮發性溶劑快速揮發，將水珠粒「分層保留」以便更深入了解「解構」後的水珠群聚機制。在這組實驗中得到兩張有趣的圖片： 在討論時，我是從對流機制切入，嘗試解構上面兩張圖。 第三部分的實驗，是將水蒸氣導引到磁場及靜電場上，觀察冷凝的機構。這部分呈現出來的結果，推翻了一般「水分子為電中性應該在電場與磁場中不受影響？」刻板觀念，實驗呈現水分子：不但在電磁場上不易長大同時也有固定的散佈模式(assembly pattern)。同時也觀察到：水分子在正電場形成的凝結水珠較為均勻，在負電場則表現出較大親水性特質。這部分的實驗對日後研究細胞膜上水分子通道應有助益。 I have tried to ask a famous math professor if he can create a formula describing the ordered array of water droplets. “Then, I should study Physics first!” He said. Condensation is the thing we live with, being found everywhere, passing without notice. But we never know when it dose start? By coalescence, water droplets grow bigger, but are not round again. We used the polymer film as template and designed the solution lighter than water, so the minute droplets will sink to the bottom and layer by layer. After seconds we may have multilayers of ordered array. This experiment presented here is actually the diary of the growth of water droplets through condensation, upon volatile fluid, magnetic field and electric field. Through convection, it discusses the self assembly mechanism of water droplets and peep into the uniformity of the size of water droplets. In this experiment, convection and magneto-electric force did play important roles in the self assembly mechanism of water droplets. The topic is mostly concerned as we are surrounded by magneto-electric waves in today’s world. This is the first step in discovering the homogeneous state of water droplets, providing insights into the self assembly mechanism of water droplets with nano sizes.

By comparing eight different epoch images of the crab nebula taken through 1942 to 2004, we have calculated the expansion velocity of 27 optical bubble features and 60 filaments. The mean expansion velocity of bubble features and filaments is 0.173 arcsec/yr and 0.15 arcsec/yr, respectively. We also estimated the maximum radial velocity of the expansion by analyzing the emission spectrum of the nebula. The maximum radial velocity is 1385.5 km/s. Combining these measurements indicates that the crab nebular is approximately 5870 light year away. In addition, if we assume that the nebula has been expanding at a constant rate, our expansion velocity projected backward indicates the mean date of the supernova event as A.D 1124, more than 70 yrs later than the accepted date of 1054. The result confirms the well-known acceleration in the crab's expansion. Although we have analyzed eight images with a 62 yr baseline, the acceleration still can't be derived from this study. 透過量測由1942年到2004年之間八張不同年代的蟹狀星雲中爆炸後殘骸的位置變化，可以計算出蟹狀星雲爆發的擴張速度。本研究選定了27個包狀物和60個纖狀物，計算出的擴張速度分別為0.173 arcsec/yr.和0.150 arcsec/yr。再透過分析蟹狀星雲的光譜所計算出的徑向速度（radial velocity）為1385.5 km/yr，進而推得蟹狀星雲的距離分別為5430光年和6370光年，平均值為5870光年。 另外，如果假設擴張速度是等速運動，那麼把求得的擴張速度倒推出的爆發日期是在西元1124年，這比中國紀錄中超新星爆發的1054年晚了70年。這顯示出蟹狀星雲的確非等速擴張而是有加速度的狀態，才會造成以等速倒推發生日期時，晚了70年。雖然本研究中分析了相差62年之久的八張影像，仍然無法分析出星雲的擴張的加速度情形。

利用范式起電器將靜電導入蒸餾水、甘油、苯、環己烷、乙醇、正丙醇、正戊醇，以及HCl(aq)、NaCl(aq)、CuSO4(aq)……等不同溶液中，我們發現：非電解質溶液可以藉由極性分子的媒合作用"貯存”電子，而其中H2O效果最好，即水合電子是可以穩定存在的！但在水中若添加HCl、NaCl等電解質會提高容易導電性，以致於無貯存電子的效果。我們也發現苯雖不是極性分子，但因具有π共振系統，也能有效貯存電子。另外，從引入密度泛函數理論結合類導體可極化連續模型加以計算的結果，也能發現極性分子容易的溶劑電子親核能比非極性分子容易來的大，與實驗結果吻合。By using a Van de Graff Generator to put electrons into various solutions or solvents (such as water, alcohol, benzene, propyl alcohol, solutions of sodium chloride, etc.), we find out that nonelectrolytes can "store" electrons through hydration of polar molecules. And water has the best ability of keeping electrons among others. In other words, hydrated electrons can exist stably. However, if we add electrolyte into solvent, the solution won't store electrons because of its increasing electric conductivity. The experiment also shows that benzene can keep electrons though it is a nonpolar molecules. We infer that it is the " π resonance system " which contributes to its high ability of electron storage. In addition, by introducing the calculations of CPCM (Conductor-Like Polarizable Continuum Model), we find out that the electron affinity of polar solutions are stronger than those of nonpolar solutions. The computed results are in agreement with our experiment.