When you draw a wet finger around the edge of a half filled wine glass, a sweet musical sound comes forth. The pitch of this sound is directly correlated to the amount of liquid in the glass- the higher the height of the liquid is, the lower the frequency is. It means that the shorter the air column in the glass is, the lower the frequency is. This phenomenon differs from the variance in pitch in a wind instrument. In a wind instrument such as a flute, the shorter the air column in its chamber is, the higher the resulting pitches are. In order to study the wine glass phenomenon, we used a piezoelectric crystal loudspeaker connected to an oscilloscope. We recorded the resulting data by using a digital video recorder to capture the images of the waveform of sound, and than analyzed the waveform by using the computer. Our conclusions are as follows: 1. The frequency of sound thus produced was the same whether we draw our finger around the rim, or we strike the glass rim. The higher the height of the liquid is, the lower the frequency is. But the frequencies vary when we strike the glass and when we blow on the edge. 2. When we used a glass without liquid in it, the frequency emitted when we drew our finger around the edge, this frequency varied inversely as the cube root of their weights. 3. In a glass with liquid, the emitted frequency did not have any correlation to the weight of the contents. By taking two identically filled glasses and placing in each a solid object of the same size but different weight, we were able to see that there was no change in the frequency emitted between the two glasses as long as the height of the liquid remained constant. 4. According to “The Flying Circus of Physics”, if we tap the side of a glass of beer, because of the air bubbles in the beer, the frequency emitted will be lower than that from a glass of pure water. This is according to the book, because the speed of sound is lower in air than in water, therefore the speed of sound in an air-water mixture would be lower than in pure water. The resonant frequencies of the mixture will also be lower. However, in our experiment, we discovered that\r when the glass contained air bubbles, the frequency emitted higher. Our explanation is that the sound emitted since the rim of the glass oscillated transversely, the frequency depends only on the retard of the rim and that the frequency is independent of the speed of sound. The intention of this research is to clarify the many misconceptions of this interesting phenomenon.以溼的手指在玻璃酒杯邊緣摩擦，會有悅耳的聲音，而且頻率會隨著內裝液體減少（空氣柱變長）而變高，這種變化與管樂器隨空氣柱的變長而音調變低不同，為了研究它的原因，我們利用壓電晶片喇叭連接到示波器上，並且利用數位錄影機錄下示波器上的訊號，再以電腦分析出瞬間的頻率，結果發現：一、摩玻璃杯與敲玻璃杯，杯所發出之頻率相同，都是所裝液體愈多發出之頻率愈低。但敲玻璃管與吹玻璃管所發出之頻率不同。二、不裝液體之高腳杯，摩擦時所發出之頻率與重量之立方根成反比。（與鐘相同）\r 三、裝液體之高腳杯發出之頻率，不再與總重量有關，而是與液體之高度有關，保持液體高度不變，即使在杯子中央加入不同重量之固體，杯子振動頻率還是不變。若改裝不同密度之液體，則密度愈大頻率愈低。四、在“The Flying Circus of Physics”書中提到輕敲裝有啤酒之杯時，會因杯中含有氣泡而聽到較低之音調，書中解釋是”空氣中之音速低於水中之音速，混有空氣之水中音速變低，其共振頻率也會降低。”但我們的實驗結果是有氣泡時頻率反而高。我們的解釋是杯子所發出之聲音是由於杯面之振動也就是杯壁的橫向振盪，振盪頻率與液體對杯壁之阻尼有關，但與液中聲速無關，密度愈大之液體阻尼愈大。有氣泡時接觸杯壁之液體變少，阻尼較少所以頻率高。希望本研究能使大多數人對這有趣之現象不再有誤解。

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.

在本次實驗中，我們發現溶液中的帶電離子，會因為離子團的熱運動，和電偶極的庫倫吸引力(electric dipole)的交互作用下，使得電解質溶液的I-V curve(電流-電壓 曲線)，具有類似磁滯曲線(Hysteresis curve)的效果，同時我們運用光學干涉的原理，證實此時在電場作用下，離子團會互相順著電場方向作條列鍵結，而加熱實驗也證實，熱運動會使溶液的I-V curve(電流-電壓 曲線)變的不一樣。另一方面，我們也發現，在給予電解質溶液一外加的衝擊電壓時，該溶液的電荷分布，?會因為彼此的互相擠壓以及自由擴散的作用下，而形成一震盪分布，其所顯現出來的，則是電壓的震盪變化。最後由於震盪波紋的變化，在起始時與中段之後有著明顯差異，我們對此變化提出看法和證實，相信內容是精采可期的！ In this experiment, with the interaction of the heating action of ionic atmosphere and electric dipole, we find that ionic in the liquor makes the I-V curve in the electrolyte liquor show up with the effect similar to Hysteresis curve. Meanwhile, we practice the principle of interference to prove that at this moment, under the influence of electric field, ionic atmosphere will connect to each other in line following the direction of the electric field. It is also proven that in the heating experiment, heating action will make I-V curve in the liquor different.On the other hand, we also find with extra electric impact, the charge distribution of the liquor will form a oscillation, that is, the changes of the voltage oscillation under the inter-collision and the free spread. We offer our viewpoints and proofs about the obvious changes of oscillation wave in their beginning stage and after their middle stage. We believe that the marvelous content is surely worth of your expectation.

DNA感測器近年來蓬勃發展,應用層面包括基因工程,醫學及藥物的開發等,然而目前較常使用的感測方法,需要繁瑣耗時的標定過程,且所使用的化學藥劑對環境容易造成傷害,鑒於以上方法的不完善處,我們決定設計一套新的感測系統,此研究結合了氮化鎵奈米線(GaN Nanowires)及延伸場效電晶體(EGFET)的優點,成功的發展出創新的DNA感測系統,氮化鎵奈米線的高生物匹配性及高感測面積,能有效提高靈敏度,延伸式場效電晶體的設計,史感測器具由免標定及時感測的特性,且易於組裝及操作,我們將探針DNA(probe DNA)修是在氮化鎵奈米線作為之延伸閘極上,由於DNA在中性水溶液中帶負電,且DNA之間具有強烈的互補特性,因此當目標DNA(target DNA)與探針DNA接合,形成雙股DNA,氮化鎵奈米線(閘極)的表面電位即會有所變化,並造成FET特性的改變,藉由此性質及能成功感測DNA,研究結果顯示,此研究所發展出的DNA感測器,愈有相當高的靈敏度(10-18),相較於其他以FET技術所設計出的DNA感測器,靈敏度提升了三個數量極,此外此感測器亦具有高選擇性,即使單一鹼基對的突變也能成功辨別;-hybridization based detection techniques are widely developed due to their promising applications in genetics, medicine and drug discovery. However, current DNA detection techniques based on labels or reagents are time-consuming, environmentally-harmful and complex to implement. In this study, we have successfully demonstrated a label-free extended-gate-field-effect-transistor (EGFET) sensor utilizing a GaN-nanowires electrode with DNA probes immobilized, capable of specific DNA sequence identification. The principle behind the design is based on the change in surface potential and charge transfer after hybridization. GaN nanowires, being bio-compatible, provide direct transfer path and high surface area, thus offer an unprecedented opportunity of DNA sensing with high sensitivity. In addition, our EGFET design facilitates easy assembly and operation of DNA detection. Comparative studies on complementary and non-complementary DNA were performed to verify the specificity of the sensor. By adapting GaN nanowires structure, the assay time of DNA was shorten to within thirty minutes. Moreover, our sensor displayed an ultra-high sensitivity in the level of attoM: three orders of magnitude higher in resolution than that of other FET-based DNA detection methods.

此研究著重於機器瓢蟲在不同的操控變因下所走出之路徑是否存在著某些性質。對於轉向次數k→∞且轉向角θ為任意角時，我們計算各收斂點P於坐標平面上恰形成圓C：(x- 1/(1-r2)2+y2=(r/(1-r2))2。將瓢蟲的轉向點P1、P2連線，圓心C與收斂點P連線，則P1P2與CP之交點S的軌跡形成長軸長為圓C半徑(r/(1-r2))的橢圓，且此橢圓的焦點為P1(1, 0)與C(1/(1-r2), 0) 。各轉向點Pn(n∈□)位於一個方程式為R=mrθ-π/α，m=OP=√1/(1-2rcosα+r2)定角為cot-1(㏑r/α)之等角螺線上；同時繪出轉向次數k在不同值時，瓢蟲行進終點之軌跡，以驗證當k愈來愈大時，各終點形成的軌跡會趨近於一個圓。當k=2時，圖形為蚶線並證明其經平移後之極坐標方程式為 R=r+2r2cosθ。最後我們展示行進公比r→1- ，r=1，r→1+時所呈現的終點軌跡，並對此軌跡所呈現出的意象與自然界連結，而其實質關聯性則有待未來研究。

In this paper, we use telephone network to remote-control household appliances and monitor security system through the implementation of software and hardware. The purpose of developing this system is to build up a system that makes everyone take advantage of the telephones through pay phone network everywhere as and when he needs to set up the household appliances, meanwhile two-ways system of monitoring household security. In addition, due to the advances of communication technology and the remarkable boom of those products, the popularity of cell phones for local people is developing tremendously. We can link the portable cell phones up to the household appliances and monitoring household security through the offer network of communication companies. This system adopts public telephone network via multiple frequency to receive KT31 70 IC which is connected to EM78P45 i p Chip. And then the Chip is connected to the driving external circuit in order to control electric appliances, sensors on doors and windows. The utilization of LEPROM (93C66) memory to set up telephone and mobile phones number equips the telephone network with two-ways system of remote-controlling electric appliances and monitoring household security. In the part of controlling electric appliances, a monitor is used to display the status of electric appliances, to control the appliance switches and to set up the timer. In the part of monitoring household security, we use the system to receive the instant images of the house and to report on the closing or opening of doors and windows. The system will be informed on any occurrence of abnormalities. The memory of the system can record and update new data at any time and is able to set up twenty sets of telephone and mobile phone numbers. Besides, the system adopts identification codes to avoid malfunctioning and thus upgrade system reliability.本文旨在應用電話網路作遠端遙控家用電器及防盜保全歟控系統軟硬體之規劃與設計 。本系統研製的目的，是希望建立一套系統，讓每個人不管身置何處，都能利用電話透過公眾電話網路，輕易地控制家中的電器設備及進行環境設定，以達到控制家電及防盜保全之雙向監控系統。此外，由於通訊的進步與通訊產品的熱賣，使國月雍有手機的普遍性相當高，若能透過隨身攜帶的手機，經由通訊業者所提供的網路通訊管道，連結到家庭自動化與防盜保全系統亦可達到進行遠端遙控的目的，彌補出門在外無法使用室內電話的空檔。本系統利用公眾電話網路經複頻接收 IC ( KT3 170 ）連接至單晶片（ EM78P45 IP ) ，透過單晶片驅動外部電路與家中電器及門窗的監視感測器連接，再利用 EEPROM ( 93C66 ）記憶體設定電話及手機號碼，藉由電話網路傳輸，以達到控制家電及防盜保全之雙向監控系統。在家電控制部份，採用顯示器可隨時瞭解家電使用狀況及控制其開啟或關閉，且可設定使用時問。在防盜保全部份，可隨時監控家中門窗，若有異狀可即時通告。記憶體可隨時記錄或更新資料，並可設定二十組電話及手機號碼。此外，本系統採用確認碼設定，可防止產生誤動作，系統可靠性高。

本研究為首次由台灣本地作者進行的擬蠍研究，擬蠍歐美稱書蠍(Book scorpion)，在中國又稱偽蠍，屬蛛形綱的節肢動物，體型微小約2-5mm，台灣目前已知8屬10種，作者收集整理過去相關文獻，並對作者所採集到的加氏赭擬蠍Ochrochernes galatheae，長指地擬蠍Geogarypus longidigitatus，及緩步威擬蠍Withius piger進行描述、拍照與繪圖，並首次記錄大衛天牛(Batocera davidi)的鞘翅下的緩步威擬蠍與雙首冠擬蠍(Lophochernes bicarinatus)。另外還採集到1種暴擬蠍(Tyrannochthonius sp.)與1種小肉擬蠍(Microcreagris sp.)待後續研究。

我一直在想，為什麼植物的美麗不能永恆呢？美麗的花朵，伴隨答淡雅的香氣，往往能美化環境，更能淨化人心，自小生長在鄉間的我，更能感受到這份來自花草的神奇力量，因此深深愛上這花草世界．但為何花朵的美麗總是短暫，為了想讓植物開花的時間長久，於是，我著手進行在自然科技雜誌及網路上搜尋相關的資料及訊息，但是找到的大多都是使生長速率變快的報告，卻找不到使生長速率變慢的報告。終於，曾經有人運用圓周運動的原理，而成功的使動物的生長速率變慢，於是，我針對直線運動及圓周運動分別依速度快及速度慢來分成四組，以及一組靜止狀態的綠豆，將五組實驗後的數據相互作比較，結果發現，除了陽光、水、空氣、土壤、養分及本身具有的胚胎外，在不同的運動狀態下也會影響到植物的生長速率 ·I was thinking about the reason why the beauty of plants couldn’t last forever. The beauty of flowers that accompanied with sweet-smelling could beautify the landscapes and purify our heart. I felt strongly about the magic power of the plant because I lived in the country in my childhood. Therefore, I loved plants deeply. Why was the beauty of flowers transient? As a result. I started to search for the related data and information on science and technology magazines and Internet. Most of the reports increase the growth rate of plants, but I cou1dn find the reports about slowing down the growth rate.At last, someone had successfully used the principle of circumference movement to slow down the growth rate of animals. Therefore, I focused on linear and circumference movement and divided them into four groups and one group of green beans with still state. I compared the data of five groups, and found that different movement affected the growth rate of plants m addition to sun, water, air, soil, and embryo.

The World Trade Center in New York City was collapsed after attacked by the terrorist. Although the design of this building did not consider the attack by the terrorist, however, this event also exposed the weakness of a high-rise building. This study is aimed at examining the cause of the collapse of the World Trade Center. A series of experimental studies was carried out to examine the strength of steel material under elevated temperature. Experimental studies were also performed on model steel frames under fire to simulate the situation of World Trade Center under fire. It is found that the strength of steel structure decayed under fire event. The upper stories lost its support from the floor that was subjected to fire load and the collapse of the floor under fire induced impact load from the upper stories. Progressive failure occurred on the subsequent floors due to the impact from the upper stories. This phenomenon was also observed in the experimental study of the model frame tests. This study has successful reproduced the failure mode of the World Trade Center in New York City. 紐約世界貿易中心大樓在遭遇恐怖份子攻擊後倒塌，雖然大樓之設計可能並未考慮恐怖份子的攻擊，但此次事件亦暴露超高層大樓的脆弱，本研究乃探討紐約世貿大樓破壞之原因，研究過程中首先以一系列之試驗探討鋼鐵材料在高溫下之行為，尤其是高溫對鋼材強度之影響。其次並進行鋼骨模型骨架受火燒之破壞試驗，發現在高溫燒烤下鋼骨軟化而失去承載能力，而無法承載上方樓層之重量，上方樓層倒塌後往下形成一衝擊力，並造成往下連續之衝擊，最後導致整體結構倒塌，模型結構試驗亦證實世貿大樓之破壞模式

本研究以b04課程中的巴斯卡三角形為研究對象，將原先巴斯卡以「1」為首、「+」為運算符號的規律三角形，改為以「-1」及「ω 」為首、「×」為運算符號，分別就其產生的新三角形作探討，發現其中似乎隱藏著原先三角形所沒有的規律性。為了更瞭解這種規律，藉由電腦軟體繪出其圖形，圖形顯示出如碎形般的複製關係，不論放大或縮小，其中的遞迴關係並未改變，頗令人好奇，因此著手研究。研究過程中對於圖形的規律性採用先臆測、接著歸納、最後給予證明的方式呈現。得到以下的結論：一、分別以數列呈現新三角形圖形的規律性。二、分別將新三角形中每一列中的某數字（如-1、ω 或ω 2 ）的個數予以通式表之。三、分別推算出新三角形第n 列第j 行的數是「1」或「?1」及「1」或「ω 」或「ω 2 」。四、相同的模式，在特定的圖形範圍中，不斷重複出現。許多研究將巴斯卡三角形中的所有數，以某數為模的餘數紀錄下，去探討其餘數在新產生的巴斯卡三角形中的分布情形；而在碎形的研究中，大部份著重如何畫出碎形。本研究著重圖形其規律性的探討，提供上述研究不同角度的詮釋與探討。 This research subject is based on Pascal’ s triangle in senior high school curriculum. The regular triangle begins with「1」and use「+」as operation. Let 「1」 be replaced with「-1」and「ω 」, the operation sign「+」be changed into「×」. I do research on the new triangle and discover the seemingly hidden regularity which doesn’t exist in the original one. To understand more about this regularity, I draw figures through the computer. The figures show the relationship of reproduction as fractal. Whether the figure is enlarged or minimized, it’s surprising curious the recursive relationship doesn’t change, so we begin to work on research. In the process of the research, we make careful observations, assumptions and deductions about the regularity of the figure. Finally, we come to some conclusions by means of giving proofs:（1）Present the regularity of the new triangle figure with progression.（2） Present such numbers as「-1」, 「ω 」, 「ω 2 」 in each row of the new triangle with formulas separately. （3）Figure out the number in the row n and in the column j of the new triangle is「1」or「-1」,and「1」or「ω 」or「ω 2 」. （4）The same model appears again and again in the specific range of figure. Many researches record Pascal’s triangle modulo certain number to explore the distribution of remainders in the new triangle. In the research of fractal, how to draw fractal is mostly focused on. The exploration of this research emphasizes the regularity of figure, offering the interpretation and exploration of researches above from different angles.

電風扇在炙熱的夏日中為冷器以外不可或缺的生活用品。一個典型的電風扇是由架在可調高度鐵柱上的馬達及風扇構成。現行傳統電風扇有幾個缺點，一、馬達風扇(即重心)位置高，有易傾覆的缺點。二、風力分散，風速不高。三、吹出不可調室溫溫度的風。四、外觀呆板，傳統無奇。五、多噪音等。本研究根據這幾點傳統電風扇缺點，試著設計新的電風扇。首先將柱子移除使重心降至接近地面處。接著根據連續方程式(continuity equationρ1A1V1 ＝ρ2A2V2)製作圓錐狀「號角」裝置套於電風扇上以集中風力並減少噪音。最後企圖使用熱電半導體的致冷器降低輸出風的溫度。研究結果發現號角裝置有效達到預期的集中風力增加範圍目的。不幸發現以熱電半導體降溫的方式效率低且耗損過多能量所以可行性較低。雖然沒有降溫功能，本電風扇仍較傳統電風扇多出許多好處，例如加強的安全性、集中的風和強大擴充性。號角裝置可包含空氣清淨甚至音箱功能充當喇叭。Electric fans are a necessity during summer, especially in a hot and humid place such as Taiwan. A typical electric fan is primarily composed of an electric motor with fans mounted on a strut with user adjustable elevations. This setup presents several problems, including (a) the danger of an accidental tip-over due to the fan's elevated weight center (the heavy motor), (b) high wind dispersal rates, (c) room temperature winds, (d) excessive noise and (e) old, antiquated exterior appearance. This particular study attempts to alleviate all these problems. First the weight center is lowered to ground level by removing the entire strut and placing the motor close to the floor. Next by using calculations from the continuity equation(continuity equationρ1A1V1 ＝ρ2A2V2)a cone shaped “horn” device is placed over the fan in order to concentrate the wind, effectively increasing its speed while decreasing the audible noise level. Finally, an attempt was made to lower the temperature of the air in the interior of the horn by the placement of a thermoelectric semi-conductor cooling device. Our results were that the horn device worked, significantly lowered the wind dispersal rate and achieved an important objective. However, the thermoelectric cooling solution proved to be highly inefficient unless accompanied by precise wind speeds. Even without the cooling function, this new electric fan still has many distinct advantages over traditional fans such as improved safety, concentrated winds and high expandability. For instance, filters can be integrated to purify air, even an audio speaker can be made into the form of this fan.