四等獎

The phenomenon of pedestrians nowadays is still found. Due to frequent walking, sometimes our legs feel tired and hard to move. This is become the basis for developing tools that are convenient for pedestrians. An easy tool for humans is needed for our activities, especially walking. The Synergy between our hands and feet provides a big and significant contribution to the appliance. Normally, the movement of our hand gets along with its motion with a different side of the foot. When the right foot step, then the left hand is swung forward, and vice versa. The tools can be developed by utilizing a variety of systems. The system includes the tools concentric wheel and axles system, spring system, and pulley system. The concentric wheel and axles system is useful in controlling the rope. Movement on the rope could activate the entire system on the appliance. Wheel that related with the hand is three times bigger than wheel that related with pulley that is applied on foot. Spring system is able to lighten the pressure of the foot with a given upward force, and able to provide downward force when the spring returned to its original position. While the pulley system on the tool used to provide mechanical advantage two times is also useful to lighten the pressure of the foot when walking. The tools can be designed with simple, and able to provide benefits to users. By trial and error, it shows that the tool is able to lighten human’s activity when they walk. The tool can be able to lighten the leg’s load by utilizing arm muscles work. Utilization of the arm muscles which helps to ease the pressure of the foot can provide more benefits. One of them is that it can strengthen the arm strength, so the tool can be used as sport equipment. Utilization of the tool can also be reserved for special people who have difficulty in walking due to an accident or birth with leg defect.

剛開始考慮平分物件時，我們從二維的多邊形部分著手，後來發現已經有人做過相關研究，並且得到類似的結論。這個部份顯現出面積平分線與其包絡曲線間的密切關係。我們將其中的方法和結果加以歸納、改善，為了更全面地研究，我們推導出一般性的包絡方程。之後當我們推廣到三維領域時，發現四面體體積平分面與之前的結論有些相似之處，平分的情況卻也更複雜，我們將推導的結果用電腦軟體呈現出來，以便更深入地了解它。最後嘗試了相當抽象的高維積平分，結果仍具有工整的對稱性，讓我們充分領略了數學之美！When considering bisecting a subject, at first we focused our attention on 2-D case, polygons. But afterwards, we found there were already some similar studies conducted by other students, which indicated the close relation between the area-bisecting lines of a polygon and their envelope. We rearranged their methods and results, and then made further improvement. Moreover, in order to study the bisecting problem entirely, we derived the general envelope equation. Then when extending the generalization to the 3-D case, we came to the conclusion that tetrahedrons’ volume-bisecting planes is similar to that in 2-D, but the circumstances are more complex. We tried to show our result with the aid of software, hoping to understand it fully. Finally, we tried to do the case in higher dimension, which is very abstract, and the result was clear-cut symmetrical. During the studying process, we had seen “the beauty of mathematics.”

洗滌用的界面活性劑分散系，沾在吸管可吹成泡，沾在框上則生成特定形體的薄膜；兩種不同現象，依據各自的性質原理，分別設計為可測量的裝置，研討表面張力與濃度間的關係，發現『兩泡連通法』，測量的靈敏度較佳，並且；薄膜總面積法則會因為框的形不同，測得薄膜總面積與表面張力大小的變化趨勢不一樣，而且數據誤差都比『兩泡連通法』大。市售的洗劑有肥皂與合成清潔劑兩類，它們溶於水的分散系，表面張力與濃度大小的變化趨勢正好相反；肥皂的濃度愈大表面張力愈大，合成清潔劑的濃度愈小表面張力愈大。這種現象發生的原因，和分散質是否含苯環結構無關。用數位照相輔助毛細管上升法，觀測『兩泡連通法』標準液的張力與濃度關係，數據顯示兩泡連通法與毛細管上升法，兩者比較各種分散系張力與濃度大小的結果相同。因此，用『兩泡連通法』比較不同分散系張力大小是簡便生動的可行方法。The dispersion of surfactant used for the purpose of cleasing,if dipped on a blowpipe,can be blown into bubbles and,if dipped on a frame,will form a certain shape of membrane.For these two different situations,according to the principle of their quality,measuringdevices can be respectively designed to explore the relation of surfact tension to its concentrate.It is discovered that,with the measuring device of the Two Bubble Connection Method,the sensitivity measured is better;and that,because of the difference of the structures of the frames,the total area of the membrane and the change trend of the degree of the surface tension will also be different and the probable error of the measured digits is always larger and it is not easy to find regularity. For the two categories of dispersion,soaps on the market and synthesis detergent,when they are measured with the Two Bubble Connection Method about the relationship of their surface tension to the degree of their concentrate,the trend of change is exactly opposite.The surface tension and concentrate of the category of soap are in right proportion whereas,for synthesis detergent used for cleaning bowls and plater and washing clothes,when its concentrate is less,its surface tension is more intense.Based on the findings of this study,the concentrate and the change trend of the degree of tension have no connection with whether there is benzene structure in the solvent. With the Capillary Rise Method assisted by digital photography to observe the relation of the tension of standard solution to the concentrate,we have found that they totally correspond to the result measured with the Two Bubble Connection Method designed in this study.

這是一種可在膨脹狀態及未膨脹狀態間轉換的膨脹收縮瓶塞。本設計之瓶塞包含一彈性橡膠之塞座及一剛性塑膠之旋轉控座。該瓶塞在未膨脹狀態，可將瓶塞置於平口內將瓶塞順時針方向旋轉90度使瓶塞由未膨脹狀態轉換至膨脹狀態將瓶子密封；欲開瓶時將瓶塞逆時針方向旋轉約90度使瓶塞由膨脹狀態轉換至未膨脹狀態，可輕易將瓶塞從瓶子內拉出。根據顧客之需求設計瓶塞並選定適當之塑膠材料以製作旋轉控座及適當之衛生橡膠以製作塞座，依廠商提供塑膠及衛生橡膠之特性資料做有限元素分析預測橡膠元件受撐大之變形量，進行加工與製造印證分析之結果，與預期目標有相當的差異，故製作簡易之試件進行探求塞座內縮量與瓶塞膨脹量之關係， 探求瓶塞膨脹量與瓶子所能承受的壓力之關係，進而逆向設計瓶塞之塞座內縮量。 This is a kind of bottle plug that can change at the situation of swell or unswell.The design of this bottle plug includes a rubber plug and a rigid plastic controller that can revolve around. We can put the bottle plug at the top of the bottle and rotate it 90° c.w., the bottle pug will be at the situation of swell and then seal up the bottle. If we want to open the bottle, we just rotate 90° c.c.w., and the bottle plug will be at the situation of unswell and then we can pull the bottle plug out easily. I design this bottle plug according to the need of the customers; choose the certain plastic material to make the rigid plastic controller, and the properly rubber to make the plug; analyze and predict the amount of deformation by Finite Element Method in accordance with the characteristics of rubber and plastic supplied by the factories. However, the result and the expected result are quite different. In order to solve the problem, I make an easy sample to search for the relationship between the contraction of the rubber plug and the swells of the plastic controller and also the relationship between the swells of the plastic controller and the pressure that the bottle can endures. Then I design the contraction of the rubber plug on the base of the result of the experiment I made above.

1. Purpose of the research While studying about insects for school club activity, we found that there are differences in several anatomical characters of the insects according their habitats. Especially, the unguis was different as whether the insect lives in water or on land. So we observed the structure of unguis of some insects by microscope, and physically analyze to relate with the habitat of each insect. 2. Procedures First, we read papers and books about insect morphology to study about insect's unguis. Then, we collected samples of Chironomus plumosus(larva), Neuronia regina(larva), and Carbula humerigera. After pretreatment of samples, we put them in the SEM (Scanning Electron Microscope), observed the unguis of each insect and took pictures. 3. Data First, the larva of Chironomus plumosus has prolegs with numberless hooks that has a certain arrangement and the same angle of 90º. They also has several tiny swellings around the hook. Next, the larva of Neuronia regina has pincer-like unguis which were sharp and bend, reminding the shape of a quadratic curve. Lastly, Carbula humerigera has two large, thick pincer unguis, its form same as the of Neuronia regina. The unguis are very sharp and faced towards the land. 4. Conclusions Both the aquatic insects and the terrestrial insects have structures in unguis developed to increase precision on land. Especially, the angle of unguis were all close to 90º. In addition, aquatic insects like the larvas of Chironomus plumosus or Neuronia regina have particular characters increasing friction force according to resist the flow of water.

Purpose of the research Experiments were performed to determine if the frequencies of the colours of pigment differ from the frequencies of the colours of filtered light. The third experiment was performed to determine whether the different colours of filtered light have an influence on plant growth. Procedures Experiments I and II were performed in sunlight and the temperatures of different colours of paper, as well as a white paper underneath different colours of transparencies, were measured by means of an infrared thermometer. The Stefan-Boltzmann equation was used for calculations. Experiment III was performed by placing ten spinach seedlings under each of the Code 40 red, green, blue and black/white shade nets. The control, 10 spinach seedlings, had no Code 40 shade net covering. All these spinach seedlings were grown under similar conditions and harvested after 4 weeks. Data In Experiment I the yellow paper was the only colour that did not perform according to the sequence of the white light spectrum (ROYGBIV). The temperature of the different colours of paper determined the amount of energy that was re-emitted. In Experiment II it was determined that the primary colours red, green and blue, as well as yellow of the filtered light, performed according to the white light spectrum. In Experiment III the spinach plants underneath the blue shade net have the highest average fresh mass (g), as well as the largest average leaf area (cm2), while the spinach plants underneath the red shade net have the lowest average fresh mass (g), as well as the smallest average leaf area (cm2). Conclusions In Experiment I the primary colours of the white light spectrum are red, green and blue. When red and green are combined, yellow is obtained. Therefore the temperature of the yellow paper was lower than expected, because only blue light was absorbed, while red, green and yellow light were reflected. In Experiment II all the colours of the transparencies performed according to ROYGBIV. By comparing the amount of energy of the colours of pigment to the colours of the filtered white light spectrum, it became apparent that there is a difference between the frequencies of the colours of pigment and the frequencies of the colours of filtered white light spectrum.

1. Purpose: The purpose of this project was to design a theoretical tempered-air system to be integrated into an existing heating system in a home equipped with an air-to-air heat pump. This was to overcome the cost and environmental challenges of heating in cold climates as well as provide an environmentally friendly air-conditioning system in the summer at little to no cost. 2. Procedure: In the winter of 2010 an underground high-density polyethylene (HDPE) pipe (10cm diameter, and 30.5m length) was buried 2.5m underground around the footings of a new residential project. A fan with a flow of 3.4m³/min was attached to the pipe outside, and used to push air underground through the pipe and into the house. The ambient and incoming air temperatures as well as the date and time were recorded daily using a temperature probe with an error margin of ±0.1ºC throughout the summer and winter seasons of 2011. This data was then plotted and analyzed. A number of options to best extract thermal energy for potential use for heating and cooling were examined. Design components were selected to create an air chamber for an air-to-air heat pump to increase its coefficient of performance (COP). 3. Data: Graph 1 Graph 2 Winter Graph (Graph 1): The blue line represents the outdoor ambient temperature and the orange line represents the temperature of the tempered air. These are both arranged chronologically. The grey lines represent one standard deviation on either side of the incoming temperatures. The ambient temperatures vary dramatically, while the incoming temperatures remain quite stable. The lowest recorded temperature was about -9.0ºC, at which point the temperature exiting from the underground pipe was about 10.5ºC. Summer Graph (Graph 2): With dramatically varying ambient temperatures, the temperature of the incoming air consistently stays between 11.1 and 16.2ºC. The highest recorded outdoor temperature was about 30.0ºC, while the incoming temperature at that point was about 15.5ºC. This cold air was used as air conditioning.

1. Purpose of the research Implement injector tester and timer button in mechanical, electrical for Correct Use Hypothesis: if humans contribute to the contamination of unconsciously by technological convenience. Give solution with the same! 2. Procedures Needed human and material resources. Besides a ventilated area with excellent ventilation. Having basic knowledge of electricity and automobile electrical systems. 3. Data This device is intended total replacement bulbs and multimeters tests relating to auto injectors of this system is important since in automotive history have been looking for improvements, part of technological development and of necessity, be have been implemented in complex systems such as electronic fuel injection, but what if our system does not work properly? Humans would contribute to contamination of the ozone layer, this natural process accelerate global warming. Hey there a social problem today becomes a global problem. Here we can see that, sophisticated equipment, are of little technical solution with a higher cost. Not to mention that the technician who works on the vehicle: save time in making a diagnosis which will be successful. 4. Conclusions The solution: provide the necessary equipment that is available to countries that do not have low resource enough. Through a reliable and safe product for the sole purpose of showing that young researchers are able to provide improved technology in the automotive industry with no expectation of this project. You should use this factor as important in society: it is the technology for the environment thereby demonstrates the certainty of our hypothesis.

「重複圖形」是本篇報告研究的問題，我們利用「方程式」建立一個尋找重複圖形，並証明其個數的方法。利用此方法得出下面的結論：1.會形成lap 2 的凸多邊形只有2 種，即三角形和四邊形。(1)「lap 2 三角形」只有1 種，即等腰直角三角形。(2)「lap 2 四邊形」只有1 種，即二邊之比為1： 且內角是45°、135°的平行四邊形。2.會形成lap 3 的凸多邊形只有2 種，即三角形和四邊形。(1)「lap 3 三角形」只有1 種，即內角為30°–60°–90°的直角三角形。3.其他的lap k 三角形：(1)任意內角為30°–60°–90°的直角三角形都是lap 3k²，其中k是正整數。(2)邊長比為1：m： 的直角三角形是lap (m²+1)k²三角形，其中m、k是正整數。 To find repeated figures, we construct a method to search them with the help of algebraic equations. Here we arrive at：1. There are only two kinds of lap 2 convex polygons, triangles and quadrilaterals. (1) The only lap 2 triangle is isogonal right-angled. (2) The only lap 2 quadrilateral is the one that contains angles 45°, 90° and two neighboring sides with the ratio 1: . 2. There are also two kinds of lap 3 convex polygons, triangles and quadrilaterals. (1) The only lap 3 triangle is the one with angles 30°, 60° and 90°. 3. Other kinds of lap k triangles are listed as following: (1) A triangle with angles 30o, 60°, 90° is a lap 3k², the k is a natural number. (2) A right-angled triangle whose ratio is 1 : m : is a lap (m2+1)k², the m and the k are natural numbers.

看到環球城市數學競賽2003年春季賽國中組試題中，一題有關方格遊戲的問題： \r \r 在一塊9 × 9的正方形方格紙板中，最多可以挑選幾個小方格， \r 使得沿著這些小方格的二條對角線割開後，原正方形方格紙板 \r 不會分裂為二片或二片以上(即沒有小片紙板會從原正方形紙板 \r 中“掉下來”)？\r \r 原題目雖然只有一種圖形解，但我們發覺在其他方格紙板中，圖形解不一，在對幾個圖形分析和研究過後，發覺“似乎”有其特定作圖法，而且可挑選的小方格數也頗有發展的地方，令我們覺得相當有趣，而且此題目和之前看過方格類的問題不大一樣，因此，決定以此問題當作科展主題，加以延伸、研究，自我挑戰。