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.
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.
環境標籤---地衣與環境污染的探討
隨著工商業發展，環境污染日益嚴重，對多數生長在這塊土地上的人，無疑造成了非常嚴重的影響。但若想要監控目前環境中的空氣品質，則必須具備專業的訓練，及昂貴的實驗設備，對一般民眾而言，根本就做不到。\r 藉由指標植物對所生長環境的高度敏感性，可以發展出一套純天然且免費的環境污染偵測器，不但方便、免攜帶、無須高級儀器協助、更不需要專業的分析技術。為此，我們以對二氧化硫等空氣污染物極為敏感的地衣作為指標植物，對其進行生態與環境污染關係的一系列觀察，並設計相關的實驗，找出環境污染物對地衣的實際影響，使其能夠實際的應用於日常生活，並可加以推廣，讓人人都可以利用地衣來了解自己所處的環境是否遭受污染，為自己家園的環境優劣把關。\r \r 文摘要 :\r With the development of industry and business , environmental pollutions become more and more serious . Undoubtedly , those pollutions have a great effect on us.\r However , by the means of the indicator plant which is highly sensitive to its environment , we can develop a set of natural and free environmental pollution detectors . In this project , we use lichenes,which are very sensitive to air pollution , to do a series of observations and to find out the influence the pollutants have on lichenes . If we can apply this to our regular lives , everyone can use lichenes to see if their environment is polluted or not .