全國中小學科展

出國代表作品

能量環

Quantum Rings are defined to be polygons with sides all of the same unit length that are connected with a fixed positive or negative angle. In the research, the number of Quantum Rings corresponding to a given number of sides and a fixed angle will be discussed. Quantum Rings could be expressed by many sequences which would involve the theory of partitions and ways to eliminate the many to one nature of the sequences in order to evaluate the upper and lower bound. Besides estimating the upper and lower bound, a lot of the qualities of the Quantum Rings under certain circumstances will be mentioned.「能量環」為許多單位長度的線段以定角首尾相接,並且最後接回原點的多邊形。本研究將要探討對於給定邊長個數與相接角度的「能量環」的個數。「能量環」可以被表示成許多種數列的形式。在數列的運算中會牽涉到許多數字分割的理論與排列組合的排除重複以求得能量環個數的上下界。除了定量的求算出上下界以外,報告中也定性的歸納出許多給予特殊條件的能量環的性質。

長期服用安非他命對小鼠腦部紋狀體內蛋白質表

安非他命的濫用在台灣是非常嚴重的公眾健康及社會問題。安非他命會導致一連串的行為異常,包括在中腦紋狀體內釋放多巴胺及阻止多巴胺回收來增加使用者的活動力。由於安非他命會對腦細胞造成傷害,本研究的目的為探討低劑量、無立即毒性之安非他命(類似於人類使用習慣)長期施打下,是否會對C57BL6 小鼠大腦紋狀體內的蛋白質表現有影響。因此利用西方點墨法分析施打低劑量安非他命(2 到6 mg/kg) 約一星期之後,C57BL6 小鼠的大腦紋狀體中一些重要蛋白質(包括腺.酸受體A2A-R、第五亞型腺.酸環化.AC5、caspase-8 及PARP) 的表現是否有改變。實驗結果顯示,低劑量安非他命處理對這些蛋白質的表現並沒有明顯的差異。但利用二維電泳法可看到有少許蛋白質,在經過安非他命處理下有顯著的差別,如KIAA0193 homolog 、GOS-28、gammacrystallin A、malate dehydrogenase 和phosphoglycerate mutase isozyme B (PGAM-B)。這些蛋白質中,malate dehydrogenase 和PGAM-B 與代謝和產生ATP 有關,但前者是增加的,而後者減少,推測安非他命會影響神經細胞的能量代謝,因此長期施打安非他命對紋狀體造成的影響值得進一步探討。;The wide spreading use of amphetamine (AMPH) in Taiwan has become a serious public health and social problem. AMPH evokes a series of behavior abnormality including enhanced locomotor behavior by releasing dopamine and inhibiting dopamine-uptake in the striatum. Since AMPH is known to cause brain damage, the purpose of this study is to investigate the expression of several important proteins in the striatum of C57BL6 mice after chronic treatment with low and non-toxic dosages of AMPH (mimicking the common usage pattern of AMPH addict). C57BL6 mice were daily IP-injected with various dosages of AMPH (0 to 6 mg/kg) for one week. Expression levels of A2A adenosine receptor (A2A-R), adenylyl cyclase type V (AC5), caspase-8 and PARP in the striatum were analyzed by Western blotting analysis. Most proteins examined were not affected by this 1-week AMPH treatment. By the aid of two-dimensional gel electrophoresis, expressions of a few striatal proteins (such as KIAA0193 homolog, GOS-28, gammacrystallin A, malate dehydrogenase and phosphoglycerate mutase isozyme B (PGAM-B) in AMPH-treated mice were altered. Note that malate dehydrogenase and PGAM-B are two enzymes involved in energy metabolism and ATP generation. Interestingly, the former was increased and while the latter was decreased in AMPH-treated mice. Collectively AMPH may affect the energy metabolism in neuronal cells. These results suggest that the injury induced by long-term AMPH exposure warrants our further concerns and investigation.

Vison-把台北101 玩弄於電腦之中

創意發想:在學習三角函數的三角測量應用時,由於立體感並非十分容易在平面中呈現,使得解題過程並相當困難。我們希望能透過程式,實際模擬出所看到的樣子,將有利於解決這方面的問題。學習美術者也需要了解一點透視的立體概念,皆可以透過程式來模擬。作品特色:我們的精神主要在於以高中的數學及物理為基礎,來研究其中的方法。除了研究3D 繪圖之基本原理,並著重於如何以程式實作,以達到高繪圖效能。預期效果:1. 讓電腦繪出有立體感(近大遠小)的圖形。2. 可以由不同位置及角度觀察物體。3. 讓立體影像具有光及影的效果。“想像您坐了一部直升機從1 樓向上到達頂端,觀看101 大樓有何不同的景象?!”Motive :In learning the technique of triangulation, it is hard to show 3D coordinates on 2D graphics so that this kind of math problems is difficult to solve. We hope that we can simulate the 3D surroundings by programming to provide references in dealing the problems. In addition, painting learners also need the simulation to realize the concept of one-point perspective. Feature :1. We do all the research based on mathematics and physics techniques learned in high school. 2. We not only figure out the method to draw 3D pictures but put some emphasis on how to use programming to run the method. Objective: 1. Let the computer draw 3D pictures, that is, the object looks big when near and small when far. 2. Making it possible to observe the object from different positions and angles. 3. Making the 3D pictures with lighting and shading effect. “Imagine how the sight would change while you are taking a ride on a helicopter from the ground to the top of Taipei 101.”\r

金屬的盔甲

Our aim to attend this science fair is to design an instrument that can plat and measure the mass at the same time. In hope of designing a simple, accurate and convenient apparatus, we created an electronic circuit to display our original idea. In the process of constant improvements, we finally accomplished a “Super Mass Plating Gauge”, which can be easily and widely utilized in school teaching. The production of microbalance and the arrangement of electric circuit are the most significant parts in our research. The major components of the “Super Mass Plating Gauge” include a straw, metal clips and our creativity—the well-arranged electric circuit. The idea of microbalance originated from the Internet, but we advanced it by numerous experiments. First, we attached a steel cord to one side of the cathode in the electricity supplier. Next, we fixed the other side to the negative plate. And then, on the end of the negative plate, we tied a metal clip with the metal that will be plated. Eventually a new “plating gauge” was invented. By doing so, we could use this instrument to make our experiments. Our experimental goal is to research how different kinds of metal, time, electrode and voltage can affect the reduced mass on the cathode. We made use of such metal as copper, zinc and silver to carry out the experiments. In the end, by analyzing the results, we concluded a plating formula that can be applied to metal plating. 我們做此科展的目的,是要設計一個可以邊電鍍、邊測量質量的儀器,我們希望這個儀器是簡便、精確、且線路簡單,並且能推廣到教學的器材。經過我們不斷改良,終於完成了「便利質量電鍍器」 。 其中製作微量天秤和線路的配置方法,是本研究的重要部分。微量天秤的主要結構是吸管、鱷魚夾、及線路。微量天秤的構想,是參考以前的科展作品並加以改良,可精準測量到0.00010g,而裡面的線路,則是我們的創意(如圖一) 。只要把電源供應器的正極,接上左右任一鋼條,負極接到容器另一端,並加上一個鱷魚夾,夾上被鍍物,便是一個可邊電鍍,邊測量質量的儀器了!如此一來,我們就能以此儀器來作我們以下的實驗。 我們實驗目的在探討電鍍時不同金屬、不同時間、電極大小及電壓,對正極金屬片所減少質量的影響。 最後,我們推導出一個有關電鍍時正極金屬片質量變化量的實驗公式。為此,我們也要做許多次、許多種的實驗,來驗證我們的公式是否正確,並以我們所學的理論來推論。

廉價取像設備之色彩校正

The applications of digital image are rapidly growing with the developments in computer technology. This enforces digital image industry to produce devices with better quality. Despite the today’s advanced level of technology, it is known that input and output devices somewhat cause color distortions. International Color Consortium suggests that we can use ICC profile to overcome the problem mentioned above. But the related hardwares and softwares are too expensive for the general users. In this study, we base on the ICC profile’s mechanism to develop a color calibration method for low cost image acquisitions. From the theoretical and experimental results, it can be demonstrated that our method appears satisfactory.數位影像的應用隨著電腦資訊科技的快速成長而蓬勃發展,這也促使著數位影像工業的相關產品漸漸地普及與廣泛地使用,時至今日,雖然有著很好的製造技術,但是任何數位影像設備均無法完美無失真地將原有的色彩呈現出來或紀錄下來,或多或少都有色彩偏差的存在,尤其在價格越低廉的設備上更為明顯。雖然可以依據國際色彩協會的建議,使用每項設備的專屬色彩描述檔來克服色差的缺點,但是用來產生色彩描述檔的相關軟硬體均價格昂貴,實非一般使用者所能承受的負擔,本篇研究以色彩描述檔的色彩轉換機制為基礎,發展出針對廉價取像設備的色彩校正程序,無論從理論數據上的探討以及實際影像上的測試看來,我們的校正方法確實有效,讓原有的色彩能精準地重現。

費瑪也瘋狂-平面上存在障礙時連接三定點的最佳網絡問題

在一個有障礙的平面上,給三個定點,我們探討連接此三點的最佳網絡。我們討論了諸如直線、射線、線段、圓、網格狀、三角形……等類的障礙,當網絡每穿越障礙一次,就必須付出代價,例如「拖延5 分鐘」。所以,設網絡穿越障礙的次數為y ,則網絡除了原本的總長度之外,還額外加入y 倍某固定數值的損耗。我們以費瑪點的各種性質及三角形不等式等方法為工具,就不同的穿越障礙次數綜合比較,而找出最佳網絡。在某些情況下,最佳網絡不是以費瑪點來連接三點,而是在障礙(如:直線)上找出符合某種與餘弦值相關特殊性質的點,以該點來連接三點,而此網絡可用GSP 軟體相當精確地作出。另外,我們也探討在考慮障礙造成損耗的情況下,兩點間的「實際距離」為何。 最後,我們考慮「混合障礙」問題。在此類問題中,除了前面所討論的障礙,還另加了如同「河流」的兩平行直線間區域之障礙,在這種障礙區域中,網絡的長度要乘以數倍來計算。我們發現,此類問題的最佳網絡也可用特定的正弦條件配合GSP 而相當精確地作出來。;Considering various kinds of obstacles in a plane, such as a line, a segment, a ray, a circle, a triangle or chessboard grids, which function like a red light, we research into the problem of finding the optimal network connecting three given points A, B, C in the plane amidst obstacles described above. Each time when the network crosses an obstacle, it will cause losses, such as five minute’s delay or a loss of one hundred dollars. Taking advantage of Fermat points, some basic inequalities concerning triangles and some special qualities about sine or cosine functions, we obtain the optimal networks in different situations. Besides, we consider what the “real distance” between two points is when there are obstacles in a plane. We also put another obstacle, including a line and a weighted region between two parallel lines, into consideration. In the region, like a river or a muddy ground in real life, the length of the network should be multiplied by a fixed time. Furthermore, we can use GSP to make the networks very accurately.

七星映月--都市靜水生態系連接度之模擬研究

目的:1. 以地理資訊系統分析臺北市靜水生態系的分布狀況;2. 分析靜水生態系的連接度。過程和結果:我實地踏察了臺北市區的381 個地點,在其中187 處發現224 個靜水生態系,首次統整出臺北市區靜水生態系的現況資料。靜水生態系的平均密度為0.82 個/km2,其密度與人口密度成正比。以 GIS 軟體標定這些水池,發現它們成任意或叢生分布。再以 VisualBasic 程式語言設計程式,以預測移動能力不同的濕地生物在這些靜水生態系間移動的情形。結論:由程式模擬可知,能在所紀錄地點間自由移動的濕地生物種類很少,顯示都市化對靜水生態系的隔絕效應。In a city, still water ecosystems (ponds and lakes) are divided by buildings and roads, so they are not continuous in the space. I surveyed 381 sites in Taipei City and found 224 ponds and lakes at 187 sites. The density of still water ecosystems is 0.82 per square kilometer. The density of still water ecosystems is higher in areas where more people live. I use a geographical information system software to mark the locations of these ponds. Their distribution is either random or clumped. I use Visual Basic to design a program to predict how do wetland creatures move among these sites. My program tells that very few creatures can move freely, indicating still water ecosystems in this city are quite isolated.

毛細管內液體流速之探討及黏度測量方法之創新

有一次上實驗課時看到鄰桌的同學正以實驗室的毛細管吸吮一瓶\r 葡萄汁,每當他吞嚥時,毛細管內殘餘的葡萄汁竟然以近似等速的狀\r 態降回果汁瓶裡,這似乎違背了重力加速度的常理,是毛細管的影響\r 嗎?還是葡萄汁特有的現象?這與毛細管插入葡萄汁的深度有關嗎?\r 這一連串的問題皆因升學壓力而無暇深究。\r 升上高中的那年暑假,我參加了學校舉辦的資優科學營,在物理\r 實驗課中恰好遇到了以毛細管測量液體黏度的實驗,使我有機會深入\r 思索毛細管內液體流速的問題。這個實驗很不好做,要調整兩個定高\r 容器,使水平毛細管兩端產生固定的壓差,讓流經管內的液體為等速\r 的流動。大家手忙腳亂地操作了近三小時,測出來的黏度不僅和老師\r 公布的答案差距甚大,而且各組同學所測得之結果也大相逕庭,不過\r 我們都體驗到了液體黏度對流速的影響。\r 實驗的誤差為什麼那麼大?扣除人為操作誤差後儀器本身還有多\r 大改進空間?有否更精簡的方法測量黏度?毛細管中液體的流速真\r 是固定的嗎?把毛細管斜置或是垂直架置,流速還會固定嗎?重力不\r 會影響流速嗎?若流速真為固定的,如何控制或改變流速呢?是否可\r 以利用流速來測出液體黏度?\r 由於我對這個實驗的專注,在學校選修的專題課程中即以此為題\r 目做長期的研究,在老師的指導下,我和同組同學不停地查閱有關書\r 籍及整理資料,漸漸研究清楚原理後定出實驗計畫,並開始購買材料\r 與工具,長期地動手實驗及改進,兩年來我們利用毛細管中液體的等\r 速及不等速流動的特性,發展出了兩種既精簡又準確的液體黏度測量\r 法,以下就是整個研究及創作的過程。\r \r \r The viscosity is one of the most important parameters of the fluids. In conventional viscosity experiments, capillary-based viscometers are widely adopted because of their user-ready devices and moderate prices. However, to accurately measure the viscosity, the fluid velocity must be kept constant; otherwise, the fluctuation may cause the serious deviation. Besides, traditional capillary viscometers often require a long time to make the measurement. This research aims at exploring the capillary fluid mechanics and developing accurate and rapid methods to measure the viscosity. In this study, we developed two creative viscosity-measuring methods, the gravity sloping helical structure and the gradational liquid-level difference, and constructed two cost-effective capillary viscometer prototypes accordingly. The gravity sloping helical structure employs a long helical capillary as the flow channel and utilizes the gravity force to keep the fluid velocity extremely constant. The highlight of this method is that we can see the fluid flow through the capillary directly. On the other hand, the gradational liquid-level difference method uses the pressure sensors to precisely monitor the liquid-level difference, which drives the flow in the capillary, and allows automatic measurement of viscosity. Compared with computer simulation, the experimental results agreed well with the theoretical values. The gravity sloping helical and gradational liquid-level difference methods achieve 0.5% and 0.8% accuracy respectively. In addition, the automation of viscosity sensing also greatly facilitates the viscosity measurement. Furthermore, these two methods are both valuable for incorporating into educational purpose and industrial application.

鄒之風聲-風笛

「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.

以彈性體模型評估心血管疾病之新方法初探

我們根據物理學的彈性體振動模型發現:主動脈硬化程度可由測量主動脈相對於心臟運動的延遲時間分析得知。我們除了由樣品之超音波影像分析驗證此一觀念之外,還用一自製模型進行實驗,模擬血管厚度對延遲時間的影響,實驗結果與理論相吻合,證實了彈性體模型之可靠性。在診斷方面,此方法可用目前臨床使用的心臟超音波儀直接進行測量,使得它具有方便、普遍的優點;而且可由體外的胸前超音波掃描(TTE)進行觀測,具有非侵入性、免除受測者的不適及避免副作用,此外,能定量分析、早期診斷、鑑別度高也是此方法重要的優點。According to the elastic oscillation model of physics, we found that the aorta stiffness could be obtained by measuring the delay time of the aorta relative to the cardiac motion. The idea was confirmed by an analysis of the echocardiograph images of several samples. A home-made mechanical model was also employed to simulate the effect of cardiovascular thickness. The experimental results fitted the theory very well, verifying the feasibility of the elastic oscillation model. This measurement could be carried out with the conventional echocardiography instruments, making it convenient and common. Furthermore, the delay time could be measured with TaransThoracic Echo (TTE) instead of TransEsophadeal Echo (TEE). This non-invasion can avoid patients’ discomfort and side effect during medical process. The quantitative measurement also enables that the diagnostics can be progressed in advance.