This study was to explore the nature of two basic constitutes of the regular pentagon,With these two constitutes, the regular pentagon could be multiplied into any times in size. We used four multiplication methodsto show how the regular pentagon enlarge and to verify that the enlarged regular pentagons derived from computer did exist. By integrating these four multiplication rules, we were able to arrange regular pentagon of any length of side, and evidenced the equation was ( If m,n is the number of A,B of a regular pentagon respectively ) When we tried to verify if any regular pentagon could be constituted by other smaller regular pentagons, we found that it was un-dividable only if the length of pentagon side were (the number of A, B were the 2n and 2n-1 item of Lucas Sequence), otherwise, any regular pentagon is able to be constituted by other smaller regular pentagons. The divided forms could be multiple. We also found that any pentagon could be divided by two successive un-dividable pentagons, which is called “standard division rule”. We expected to derive all kinds of division by analysis of two successive un-dividable pentagons in standard division rule. 這個研究起源於一個拼圖玩具：利用兩種黃金三角形排出指定大小的正五邊形。我們的研究動機是：一、 假如無限量供應A 和B，能夠拼出哪些邊長的正五邊形？二、 哪些拼好的正五邊形不能拆成一些較小的正五邊形？我們將研究的主要結果分述如下：

The purpose of this project was to create a detection device for alcoholic drunk condition in human by using the principle of vapor pressure difference between breath samplings from normal and alcoholic-drunk men. The work comprises of three major steps. The first task was an experiment to determine an average air volume that can be fully blown out from the lungs of non-drunk people as a control. Twenty adult Thai volunteers weighing between 50 - 80 kg (average 59 kg) were used. The average blown out air volume was found to be 369.9 mL, with the range in values from 340-400 mL (sample size N = 20, SD = 15.47). The second task was an experiment to measure relationship between the blown air volume (100-700 mL, both from alcoholic-drunk and control groups of people) and the resulted vapor pressure by using manometer. The vapor pressure of normal breath increased from 400 to 1,600 newton/m2 with increasing blown air volume, whereas that of the alcoholic-drunk was found to be 600 to 1,800 newton/m2. The last task was to create a detection device prototype to gauge the alcoholic content in the human body from the breath. Air volume of 300 mL was arbitrary chosen to trigger lighting up of indicator lamps. The breath samples of low vapor pressure (low amount of alcohol, 21.12-44.00 mL, equivalent to 14.00-29.17 mg%) would trigger a green lamp to light up. A moderate vapor pressure range (medium amount of alcohol, 88-132 mL, equivalent to 58.33-87.57 mg%) would trigger green and yellow lamps to light up while a high vapor pressure (high amount of alcohol, 250 mL, equivalent to 165.72 mg%) would trigger green, yellow and red lamps to all light up. None of the three lamps would light up from (non-alcoholic) breath of control people. This device has also been tested to external group of volunteers. The work in this project has successfully demonstrated a useful application of simple principle in chemistry on partial vapor pressure.

本實驗的目的在於探討凌日時的黑滴效應。實驗以投影機在螢幕上投射出亮區模擬太陽，以保麗龍球模擬內行星橫越太陽表面，以相機作為觀測記錄器材，結果發現在內行星與太陽的第二及第三次接觸時會有黑滴現象。黑滴效應在光源顏色越接近紅色、拍攝相機的光圈值越小越明顯、相機對焦比實際值越小越明顯；光源的明亮度對黑滴效應沒有顯著影響。金星大氣、地球大氣不是造成黑滴現象的主因，而影響黑滴效應的因素與光的繞射相同。實驗結果發現，黑滴效應的成因主要發生在觀測紀錄的器材上面。This study is conducted to explain the black drop effect for the transit of a planet. A video projector projects a bright square on the screen to simulate the Sun. A ball simulated the planet crossing the sun’s disk. And a digital camera takes the images of transit. The Black-drop Coefficient is defined and a computer program is designed to analyze the image of black drop. The results show that the resolving power of the observation instrument is the main factor in the effect. The atmosphere and the solar limb darkening do not directly respond to it.

本研究比較2003~2005 年，冬季及夏季西經168 度之「海平面溫度異常」對「緯度」的分布圖，結果呈現在赤道附近的變動較小，在高緯度地區的變動較大，為更精確的描述此變動，將每日高緯度地區的變動以「標準差」及「最大振幅」數量化，發現在南、北半球不論2003、2004或2005 年，每7~12 天南、北半球的「冬夏季海平面溫度異常」的變動變大，上述變化在北半球較為明顯，在南半球較不規則。 與2005 年冬季1 月31 日~3月17 日的北半球地面天氣圖進行分析比對發現，溫度的變動和極地天氣系統的形成關係密切，推測原因和冬季時極地為永夜，地面空氣溫度受到兩個跟月球有關的熱源影響較大，其一為海流和極地間每日有接近2 次的潮汐交替運動，其二為月球反射日光後投射到極地時，極地大規模的冰對月光的反照，對極地微弱的加熱作用。 針對2005 年6 月1 日~7月22 日之地面天氣圖作分析，結果發現夏季緯度的溫度變異和高中低緯度天氣系統的改變關係密切，推測此時和月球對海水的吸引使地表(特別在海陸邊界)的溫度，週期性的重新分配，或對大氣應也會造成週期性的質量分配有關。 以農曆為主重製溫度的變動圖並進行比對發現，無論2003、2004或2005 年，在月相為朔及望時常出現低值。此分析結果顯示，接近朔望時，高緯度海平面溫度有較穩定且變動較小的情形。而從天氣圖、農曆標準差綜合，所得結論為地月運動應和地球上高緯度天氣系統存在某種相關性。 ;Our topic is about how the moon phase variation influences the high-latitude weather system. This study analyzes the sea surface temperature anomalies (SSTAs), along 168°W in winters and summers from 2003 to 2005. The results show that the SSTAs varied relatively small around the equator and relatively large in high-latitude regions. So we next analyze the high-latitude SSTAs by the standard deviations, the maximum amplitudes, and the north surface weather graphs. After analyzing, the result shows that the SSTAs rise for every 7 to 12 days. Moreover, they relate to the winter high-latitude weather system very much while relating to the summer medium-and-low latitude weather system a lot. We think it’s because in winter eternal night, the sunlight won’t shine on the arctic zone easily. Other heat sources may become important: (1) the tidal movements between the ocean and the arctic zone. (2) The heat radiation of the moonlight and the moonlight reflection by the polar ice shields. But in summer, the moonlight effect becomes extremely small. The tidal force becomes the bigger influence factor: (1) the tidal attraction may distribute the temperature of the border between seas and land periodically. (2) It may cause the periodic atmosphere mass distribution. Additionally, after repeating the same experiment according to the Chinese lunar calendar, we found near full-moon and new-moon time, the SSTAs are more stable. Probably because of without the moonlight, the movements of rip-tides occur and help stabilize the polar weather conditions. In conclusion, the relative movement of the moon to Earth is likely providing a crucial heat source which will affect the high-latitude climate, and the heat source size probably influences the weather system cycle.

本實驗是以實際探勘的地質及泉水資料和文獻為基礎，對於幾個可能造成冷泉降溫的原因(岩石種類、泉水pH值、流通氣體之壓力、流速)進行實驗。我們製作了一個模擬地下泉水流動的實驗管路，此管路並可同時觀察紀錄氣壓、氣體流速，以及實驗前後模擬管路的溫度變化。透過對實驗管路的熱容量校正，我們可以找出各變因對泉水降溫的關係，以建立出一個模型，期望可套用於實際冷泉的狀況，進而推論出更多冷泉的性質。This experiment uses data and bibliography from real exploration as bases to find the possibilities of why the cool spring drops in temperature. (Mineral types, spring water's pH value, air flow pressure, and movement flow.) We created a model of underground spring water for the simulation. From this model, we could observe the air pressure, movement, and the spring's change of temperature before and after the tests. By adjusting the thermal capacity in the model, we could find the direct cause of the spring's temperature drop. And hopefully be able to adopt this model to the realistic problem, increase the effort of analyzing the natural cool spring's properties.

In the last two decades, there has been increased interest in the utility of quantum scale semiconductors. These fluorescent single crystals can be as small as 1 nm in diameter, and their size and shape has been shown to be controlled by the duration, temperature, and ligand molecules used in their synthesis. Quantum dots, provide clear benefits over the organic dyes currently used for tracking biological processes. Yet, as the production of quantum dots is often very costly, the search continues for finding an industry-ready synthesis for a quantum scale semiconductor which would have high yield, optimal durability, high luminescence, and a broad absorbance range. Silicon, in particular, has been of great interest as it is the second most abundant element on the Earth’s crust and is generally a bioinert and electrochemically stable element. We report the synthesis of water-soluble, luminescent silicon nanoparticles with potential applications to bioimaging. Through a solution state top-down approach, the synthesis of hydrogen capped silicon nanoparticles was achieved in various organic solvents. The surface of the nanoparticles was capped with the functional organic molecules rendering the Si-QDs both air and water stable. Cell studies performed with our silicon nanoparticles and human monocytes show the direct applications these particles could have for tracking biological processes and the progression of cancer in the human body. In attempt to shift the luminescence of these particles, alterations of experimental methodology was also explored in the areas of reaction solvent and heating time. Through these changes, shape control of silicon nanoparticles was achieved in the form of silicon nanorods. The synthesis of this new shape of silicon at the quantum scale was confirmed by ultraviolet spectroscopy, photoluminescence, and transmission electron microscopy. The results of this study indicate that the use of silicon nanocrystals for biomedical applications is feasible.

科展的指導老師在高中發揮了極為重要的角色，他指導學生閱讀前幾屆的重要作品，提出是當的新問題，領導研究與討論，給予類似專家的常識性建議，有些甚至成為學生的共同研究者，我們看到優秀的高中科展作品中，有許多作品背後都有一個優秀的數學老師，以本屆為例如第一名第，第二名。 指導老師在小學更是作品之母。但是小學指導老師的定位，至今仍然非常模糊。在高中由於作品水準很高，教師不易越殂代庖，但是在國小，國中指導老師很容易不由自主的陷入教的陷阱，以至於許多人認為國小指導老師就是把材料成功地教給學生。其實這是極為錯誤的看法。例如初小組肥皂泡膜角度與經濟網絡的作品，我們注意四一Ｏ四到如果教師讓學生先實測各種泡膜的角度，在得出角度都是120度的經驗歸納結果。相信兒童對於自人界的現象的數學性會有更大的驚奇，如今教師先告訴學生120度的事實，再去檢查，這種「驚奇」的驚人浪費，令我們感到非常可惜。事實上，現在已經有少數小學老師已經覺察到，如果指導老師可以更早成立研究群，更有耐心，更願意傾聽兒童在做什麼，只要找出適當的問題，兒童一樣可以有探索研究的活動。只是這種活動還需要數學教育的學者做更進一步的研究已歸納其研究活動的特質，可?科展評審的參考。當然初小和高小的差異很大。至於適當的問題雖然難找，但也不是沒有。例如初小四一Ｏ一從數字方塊到數字八卦以及高小正多邊形分割成三角形的分割總數及類型都指出值得效法的新趨勢。 國中生正處於進入文字符號運作的尷尬期，加上國中各種測試卷的反覆練習繁多，剝奪兒童從事研究的時間，一向是科展最弱的一環。這也是本組第二名從缺的原因，其實國中組無強將，反而是指導老師可以大加發揮的地方。事實上，國中生透過科展活動也可以順利甄試昇學，由於名額較少限制，更應多鼓勵學生參與。 本屆和上屆來台的美國ISFF學生作品，都和代數數論有密切關係，事實上，高中生的極限觀念的發展，比代數抽象思考的方展慢。基於此點，建議高中指導老師可以給予學生初等數論以及初等待數數論的標準教科書研讀，增強其運作的層次，代數數論的應用很多，而且也很好，如本屆的問題是說如果「n」事一個個邊皆為有禮數的直角三角形的面積則有此解可以生出無線多個有理直角三角型面積都是n。 科展研究問題的開發一向是科展師生最頭痛的問題。有一本英國空中大學教授MASON所著的「大家來數學地想」可以大大的拓展研究的想像力，數學傳播季刊，Mathematical magazine,Mathematical monthly,Mathematical Gazette,Fibonacci Quarterly,國際或亞代奧林匹克試題,Putnam試題都是傳統方法已外找材料的地方國小可從國中高中取材,但切忌獎什麼微積分代數等名堂。 另外科展老師也必須善於累績資源，以及累積自己的經驗與聲望，以吸引校內的優秀學生參與科展，本屆初小組四一Ｏ依從數字方塊到數字八卦和高中組四四一四方塊數論就是源自同一問題，但兩者的方展缺是大異其趣。四一Ｏ一大做奇偶類型經運作後演化的樹型圖，但四四一四在初步地用符號說明演化後，既一舉跳過此一過程，進入決定性的証明。其中的對比有如GORDON等數學家在不變式的工作和Hilbert一舉用一個存在性定理暫時地結束此一時期的歷史事件。另外科展老師也必須善於累積資源，以及累積自己的經驗與聲望，以吸引校內的優秀學生參與科展。

Purpose of Project: To save energy and to help the underprivileged with a cooler that uses no electricity to make their lives better. Procedure/method followed: STEP 1: Collected 28, used, 2 litre plastic bottles. STEP 2: Chose the window with the best wind flow. Measured the size of the window and the room chosen. STEP 3: A sturdy thick polystyrene board was cut to the size of the window. Holes were drilled to the rim size of the bottles spacing them according to the body size of the bottles. STEP 4: Bottles were cut in half. STEP 5: The bottle necks were slid through the holes with the necks open to the inside of the room and the bodies open to the outside. STEP 6: Fixed a thermometer in the room and measured the temperature and recorded it. STEP 7: Fixed the Powerless Shack Cooler with the necks of the bottles open to the inside and the bodies open to the outside of the room. STEP 8: The temperature variation was checked and recorded every 30 minutes for 3 hours. STEP 9: Another room of the same size and window was also chosen. Fixed a thermometer and temperature variation was checked and recorded every 30 minutes for 3 hours. This served as the control of the experiment. Data/results: The room temperature decreased over time inside the room where the Powerless Shack Cooler was installed onto the window. But the control room maintained the initial room temperature although slight fluctuations in the room temperature were observed over time. Conclusion: The hypothesis was supported. As the air molecules moved through the bottles, it bounced off each other, and off the walls of the container, holding the air. A small volume of air passed at a high velocity. When the molecules moved faster the collision became more often. These collisions and the push increased air pressure. When the container’s space was getting smaller, the molecules picked up speed and the temperature went up. When the air was released out into the room, the volume suddenly expanded. The intermolecular spaces became larger; so less agitation and vibration of molecules took place. The molecules moved slowly. The room temperature reduced. Air inside the room became cooler. During the adiabatic expansion, air molecules used heat energy from the room and converted it into kinetic energy for faster movement.

The objective of this project is to investigate styrene butadiene rubber(SBR), which is the most important synthetic rubber. The project contains production methods, properties, safety methods and applications for emulsion SBR. The goal is to determine which production technique of SBR is the most beneficial. This is based on the chemical and physical properties of the final product and its quality. The process that is used in the project is emulsion SBR with combined coagulation stripping. The rubber production plant is a profitable venture. The total capital cost is estimated around $31,361,572, with an annual production cost of about $67,281,378 yearly, generating revenues of $73,801,760 per fiscal year, with an interest rate of 5%. The life of the plant is 15 years and would produce 50,000 ton/year.

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。

流體旋轉時，外圍及底部流體，因槽壁及槽底摩擦力的影響，流速較慢，相對的壓力也較大，導致外圍的水流會轉入中心。發現本實驗的渦流為強迫與自由漩渦組成。實驗中，探討f(轉動器的頻率)、H(總水深)、y(?入深度)、R(轉盤半徑)四者與角形數間的關係。若y、R 愈大、H 越小，隨著f 的增大，可觀察到的形狀邊數越多；反之，若y、R 愈小、H 越大，則f 愈高，所形成的圖形半徑愈大，易超過轉盤，不易觀察。依白努利方程式，外層水流的流速較慢，而內層水流的流速較快，故外層壓力大而內層壓力小，水會由外往內流，而此渦動流於轉動液面產生的剪力，可能為產生N 邊形漩渦的主要原因之一。流體旋轉系統中，因轉動而產生流體離心力與內外層壓力差交互作用下，於某特定相關的因素條件下，形成特定角形數漩渦，是本實驗的重要發現。When fluids are in rotation, fictitious force given by the container brings about the relative decrease of speed of the bottom and outer layer of water, which causes its pressure to increase, and water to spin inward, resulting in a vortex motion with N-corner polygons formed at the surface of the rotating plate. During this experiment, we discover that the vortices consisted of free and forced vortex and the polygons vary as control parameters f(rotation frequency), H(height of fluid), y(depth of the plate), and R(radius of the plate) change. The larger y and R are,the smaller H is, the more corners show up as f increases. On the contrary, the smaller y and R are,the larger H is, few polygons are identified since the rotating radius of polygons are larger than the plate. According to Bernoulli’s principle, smaller velocity of the outer-layer water causes water pressure to increase and water to spin inward. During this process, shear force is developed at the surface of the rotating fluid, which we believe is the main cause of N-corner polygons. In a rotating system, the interaction of centrifugal force and differential pressure causing a certain Ncorner polygon to be formed under different controlled parameters is our main discovery.

Nano-sized calcium phosphate was used in the synthesis of starch-based composite plastics to provide a cheap but sturdier biodegradable alternative to petroleum derived plastics used in film packaging. Nano-sized calcium phosphates were produced from the precipitation reaction of calcium nitrate tetrahydrate (Ca(NO3)2 ‧ 4H2O) and phosphoric acid (H3PO4). The nanoparticles were co-extruded and molded with thermoplastic starch (TPS) at ratios of 0%, 1%, and 5% by mass. Tensile strength and elongation percentage of the resultant composite plastics were tested in three replicates. The results show that there is a significant difference between the tensile strengths of the 0% and 5% calcium phosphate composites at a 5% level of significance. The trend between the composite’s tensile strength and percentage calcium phosphate follows a geometric progression, enabling a projection for the 10% nano-calcium phosphate to have a tensile strength of 10 MPa, the average tensile strength for low-density polyethylene (LDPE). This shows that it is feasible to synthesize a 10% nano-calcium phosphate-TPS plastic that can be a viable substitute for LDPE plastics in film packaging, paving the way for the commercialization of starch-based plastics. The use of biodegradable plastics with improved physical characteristics will lessen consumer dependence on petroleum derived plastics and solve the environmental issues brought about by the use of such plastics.