全國中小學科展

臺灣

圓來如此─西姆松「圓」的研究

若從一個三角形的外接圓上取一點,作其對三角形三邊的垂足,我們知道這三點共線,是為西姆松線。\r 那麼當此點不在圓周上的情形呢?自平面上一點對一三角形的三邊分別做垂線,得到三垂足,並作此三垂足的外接圓,我定義其為:此點對此三角形的西姆松圓。這篇作品主要成果便是對西姆松圓的研究。透過不斷的研究,發現了許多關於西姆松圓的神奇性質,並得到了一些結果,主要的研究方向:討論共點、共圓、相似。\r 這篇報告是循序漸進的,後面的結果常用到前面的知識為基礎。此篇另一特點是:全篇的證明皆是自已給出的,採用方法皆為一般幾何證明,而沒有用到解析證明。\r 在研究過程中也得到關於著名的費爾巴哈定理及大上茂喬定理的另一種證明。

碳黑受閃光產生爆鳴聲之研究

紙杯底部用蠟燭燻出碳黑,經數位相機閃光拍攝後會聽到爆鳴聲。探討的結果為爆鳴聲是由相機的閃光與碳黑之間的互動所引起,甚且到冒煙程度。\r 探討結果得到爆鳴聲大小會受電場、溼度的影響而且碳黑量愈多,電子傳遞路徑會縮短、導電性則增高,且與產生的電量接近線性關係。\r 發現波長較短的可見光可形成較多的電荷;若照度大、受照射面積大或碳黑的粒徑小,這些會產生較多的電量。\r 經由電顯及AFM圖可知去漬油、蠟燭、瓦斯、95汽油、酒精燃燒後產生的碳黑,大小範圍都是在30nm~100nm範圍內。將蠟燭碳黑接受不同次數的閃光後,看出表面碳粒會變成灰燼。

抽籤機

此篇報告中,主要是在敘述以單晶片8051為主體,運用其所具有之功能,製作成此作品,稱為記數抽籤機,又稱抽籤機,根據本篇報告結果,可歸納出以下結果:1.本實驗能讓初學者對單晶片8051之特性與功能有更深的了解,以增進實驗與成品實作的能力。2.此作品以便利為原則,故其體積不大,重量輕攜帶方便。3.使用之元件普遍,價格便宜,在電子材料行均可買的到,成本低。4.依本品之功能,可用於學校讓老師進行抽問,也可用於其他有抽籤或抽獎活動之場合,公平又公正。;In the report, we take the single chip 8051 as a main body, making use of function to do the counting drawing lots machine, which are also called drawing lots machine. According to the resultof this report, conclusions are as followings: 1. With the experiment, the beginners egt deeper understanding about the characteristics and the finished products. 2. This machine is light and its volume is small, so it is easy and convenient to carry with. 3. The essential elements are common,cheap and can easily be bought in the store which is sellong electronic materials. 4. The drawing lots machine can be used at schools when teachers want to pick out some students to ask or it can be used for some drawing lots occasion as well. The outcome is just and fair.

以數位像素分析法探討兩棲類變色行為之研究

本研究是以數位科技改良生物實驗上的傳統比色法,並探討中國樹蟾及台北樹蛙的變色行為。有些兩棲類有變色行為,這是眾所皆知的現象,過去一向採用比色法判斷生物體的體色變化;然而,以人眼去測定色差,會有相當大的主觀誤差。本研究及是探討以數位科技量化並比較實驗對象的變色情形。在研究過程中,用電腦量化數位相機所拍攝的影像,以像素的方式呈現出來,得以取的準確且客觀的實驗數據,並加以解析,也經由此一實驗方式,交叉比較中國樹蟾及台北樹蛙在不同環境和不同時間下的變色情形。結果顯示:樹蛙變色和環境顏色及時間有密切關係,且在短時間內以數位量化的方式解析其變色行為的方法極為可行。The purpose of this study is to investigate the color variation behavior of tree frogs using an image processing technology. It is known that some of the amphibians have the ability to change their skin color under different circumstances. In the past, a conventional “color comparison” method was frequently used whenever it comes to analyzing the color variation of organisms. However, it is realized that evaluation of color difference by human eyes is extremely unreliable. An advanced image processing technology is thus suggested to quantify the variation of skin color of tree frogs under different conditions in this experiment. Accurate quantification can be determined from the pixel number of exhibited digital images during the experiment. The color variation of different species of frogs (Hyla chinensis & Rhacophorus taipeianus) is also compared under different parameters. It is found that the color variation of tree frogs is closely related to the color of back ground as well as time. The proposed digital quantification technique has been successfully demonstrated to be an effective method for analyzing the color variation of frogs within a very short time.

利用雷射光碟(CD)做光的繞射實驗

雷射光碟(以下簡稱CD)除了在電腦、音響方面有甚佳的視聽功能外,在光線照射下,呈現彩虹狀的光譜,必定引起你我研究其光學性質的興趣。國內以CD研究光的繞射的著作,有李偉等四人近三年發表五篇,國外科教期刊自1991年迄今共有19 篇,在老師指導下,利用CD進行了8 項實驗,分成三大項。1.利用氦氖雷射分別照射舊唱片、CD、DVD,反射光形成繞射現象,由dsinθ=mλ,量出槽距。2.將CD-R 的鋁層刮掉,(整疊購買的CD-R上下有數片未鍍鋁的瑕疵片),成為透光式CD(透射式光柵),將其中心半徑5.5 公分部份,用黑紙遮住,正對陽光,螺旋狀的溝槽將陽光聚成一點,量出各色光到CD的距離,可算出色光的波長。3.透射式CD置於投影機鏡頭前方,投影機置物台上,放置化學藥品,可直接在屏上觀察吸收光譜。The rainbow of colors reflected from the surface of an audio compact disc (CD) is a familiar sight.It is the phenomenon of light diffraction. A standard CD has 20,625 turns of the spiral, and each line is spaced by 1.6μm. This provides a grating of 625 lines/mm. We used ordinary CDs as reflection grating in our experiment,and transparent factory rejects with no coating but printed data spirals as diffraction grating. We conducted eight experiments of diffraction using the two kinds of CD. (a) Determined the grating spacing of an ordinary CD using a laser beam. (b) Determined the grating spacing of a transparent CD using a laser beam. (c) Studied the diffraction patterns caused by a laser beam held at angles to a transparent CD. (d) Measured the wavelengths of sunlight using a transparent CD. (e) Measured the wavelengths of sunlight using an ordinary CD. (f) Formed a rainbow using a transparent CD. (g) Observed the scattering of light using a transparent CD. (h) Demonstrated the absorption spectrum using a transparent CD and an overhead projector.

臭氧事件日-氣象與地形對臭氧於近地大氣層之生成與傳輸影響

2001、2002 年監測資料被用以探討風場、時間、地形對臭氧傳輸影響。完成沿海地區與盆地內各二次採樣分析,探討各污染物與風場之垂直變化,及地面臭氧分布與風場變化。結果顯示各月份與全年之日間,其相對濕度與O3 相關度最高,日照次之。提高濕度,最能抑制[O3]。夜間NO 與O3 的相關度最高,濕度次之。臭氧事件日時:(1).11:00 即可產生高臭氧,(2).沿海地區在臭氧事件日仍保持低[O3], (3).盆地效應改變風場,使近山地區[O3]居高不下,(4).因處O3 不斷被吹入,沿海地區傍晚時之[O3]下降速度減緩。臭氧事件日之O3 生成速率R 與消失速率常數L 被求出,其中14:00 後之R 與L 值均由正值轉負值,顯示大氣反應型式明顯轉變。R 與L 值在14:00∼15:00 間最小,係因O3 反應生成光化學煙霧所致。16:00 後另一低R 與L 值,則可能導因O3 與微粒或水份反應。分析結果顯示:(1).污染物會隨高程而略增,最高濃度在300∼500 m 處,(2).各高程大氣均可分析出73 種主要HC,其隨高度之分布被繪出與探討,(3).低層大氣會有較多低分子量HC,而高層大氣則有較多高分子量HC。結果亦顯示: (1).盆地內[O3]、[NO]與[NO2]不僅較沿海地區高,且於各高程之變動亦較大,(2).沿海地區THC、烷、烯類均較高,且隨高程增加而增高,但在盆地內則相反,(3).二地區各高程之鹵化物、芳香族、氧化物與其他有機物之平均濃度相近,但沿海地區之濃度變動較大。探討O3 之二傳輸現象獲知:(1).風吹向盆地內時,[O3]隨風向遞增,R 與L 會由12:00 之正值,轉為14:00 之負值;(2).風由盆地內外吹時,[O3] 隨風向遞減,R 與L 值提前於12:00 即為–202.561 與–1.621,但14:00 時R 與L 值增大為–76.411 與0.244, (3).風向並非決定[O3]的主要因素,地形與環境因素才是。實驗結果證實:(1).不同HC 會影響O3 之生成與消失,(2).改變[NO]o 對[O3]影響不大,但高[NO]會使得[O3]下降略緩,(3).降低HC 與[NOx]雖可使 [O3]略降,但提高濕度最能抑制[O3],(4).在O3 的衰減量上,[O3]隨濕度增加而快速降低,但衰減率則隨[O3]o 的增加而降低。一個臭氧之統計模式被建立,臭氧與水反應速率常數與速率式也被求出。 The monitoring data were used to investigate the effect of surface wind, time, and terrain on the transformation of ozone. The sampling and the analysis in the coastal and in Taichung basin were completed. The vertical distribution of O3, NOX and HC and the different altitude wind were investigated. The contour of O3 and surface wind with 3D map were plotted. The results show that the correlation behaves relativity of relative humidity with ozone is the best, and solar radiation is the next. Enhancing environmental moisture can efficiently decrease ozone concentration. In each ozone event day are: (1) the high [O3] always starts from 11:00, (2) the ozone concentration on the coastal is always low due to the high humidity, (3) the high [O3] in the east of the basin is due to the basin effect which causes changes the surface wind, and (4) in the evening, the descend rate of [O3] in the coastal area is lower because ozone blows into the coastal area. The formation rate (R) and disappear rate constant (L) of the ozone event day were obtained. The values of R and L change from plus to minus before 14:00. The values of R and L are lower at 14:00∼15:00 due to the photochemical smog formation. And another lower R and L value before 16:00 may be due to ozone react with particle or water. The results of analysis indicate that: (1) the concentration increases with increasing altitude, and the maximum is at 300∼500 m height, (2) 73 kinds of hydrocarbons were identified, and the concentration variation with altitude was also investigated, and (3) most of low molecular weight HC are at lower altitude, otherwise high molecular weight HC are at higher altitude. The results also show that: (1) [O3], [NO], and [NO2] on the basin are not only lower than on the coastal, but also their variability of concentration are big, (2) THC, paraffins, and olefins on the coastal are higher than on the basin, and the concentrations increase with increasing altitude on the coastal, but on the basin is decreasing, (3) the average concentrations of halides, aromatics, oxides, and others are similar on both area, but concentration variability on the coastal is obvious. Two types of O3 transformation was investigated, the phenomenon indicts that: (1) when wind blew into the basin, [O3] increased with wind direction. The value of R and L change from positive (12:00) to negative (14:00); (2) when wind blew out of the basin, [O3] decreased with wind direction. The more small value of R (−202.561) and L (−1.621) appeared at 12:00 earlier. But the value of R and L will become bigger to –76.411 and 0.244; (3) ozone concentration does not just dependent on wind direction., topography and surrounding conditionsa are more important effect. The experimental results show that: (1) ozone formation or disappearance depends on different HC, (2) the effect 2 of [NO]o is small for ozone photochemical reaction, but [O3] decreases with increasing [NO], (3) the descend rate of O3 depends on high humidity more than different kinds of HC or [NO], and (4) the descend amount of ozone increases with increasing humidity strongly, and the descend rate of ozone decreases with enhancing [O3]o. A statistical model was developed. The reaction rate and rate constant of ozone reaction with water were also obtained.

Amazing Fairy Chess -討論多元方形鏈的數量

在這篇研究報告中,我們討論的是一種方形集合圖形的數量。”多元方形鏈”約略在 60 年代被提出,衍生出一系列的問題和遊戲,例如熟知的電玩軟體 『 俄羅斯方塊 』 ,或是 『 益智積木 』 的遊戲,都是多元方形鏈的應用。在這些問題當中,最令人頭痛的難題就是 n 元方形鏈的圖形總數。為了解決這道難題,我們採用一種轉換方法將圖形轉換成序組,並且給出序組的性質,再據此寫成 C 語言的程式;反覆地修改程式以增進執行效率及速度,最後利用該程式成功地統計出圖形總數。 In this report, we discussed the amount of polyominoes, the graphs of a set of squares. “Polyominoes” has been brought up in 1960s, and later developed into a series of questions and games, such as a well-known video game — Tetrix, and the game of puzzle blocks. Both are the applications of polyominoes. Among those questions, the toughest one is the amount of n-polyominoes. To solve this problem, we used a method which transforms the graphs into sequences. By looking into the properties of those sequences, we obtain a set of rules that can be used to determine the quantity of n-polyomines. The rules are implemented into computer codes in C language with proper modifications made to speed up the efficiency of our algorithm. The computational results show that the amount has been successfully calculated.

倍位元灰度影像產生器

本研究設計一新型的影像投射系統,可將影像顯示的灰度位元加倍,例如,顯示面板只需用4位元,即可顯示8位元的影像;亦能充分利用光路光源,增加光源使用率。此系統使用兩片相同灰度位元的顯示面板,此兩面板所顯示的影像經過灰度的重新處理,且各經由不同光源強度比值的光路合成後,其灰度分佈將可增為原來的平方倍。經模擬與實驗顯示,此種系統很輕易就能獲得預期目標。無論使用穿透式或反射式皆可應用於目前單片液晶面板之投影系統中;未來可望利用網板來表現灰度,應用於紅外線景物投射系統中,作為紅外線影像式尋標器靜態模擬時所需的高強度動態範圍與高解析度之影像產生器。In this study, a novel image generator utilized in a projecting system has been proposed; it can double the bits of gray-level for image display and enhance the efficiency of illumination of lamp in the optical path. With this system, a 4-bit display panel can achieve an 8-bit image display. Two display panels with same gray-level bits is adopted, images on them will be processed, and then go through different path with a proper intensity ratio. The gray level distribution of image displayed which the two images combined afterward, will be the square of that of original one. The results of simulations and experiments have approved to meet the requirements. No matter transmitting or reflective types can be applied to current projecting systems with single LCD panel. It is expected that a halftone-gray-level pattern will be suitable for this system to form an infrared scene projector, and to act as an image generator with high dynamic range and resolution for static simulation of infrared imaging seeker.

光速的測定

本實驗改良菲左測定光速之實驗,將原本的光路以光纖取代,並將原本的光源改為紅外光。做了上述的改良以後,可將實驗的空間及時間縮小。實驗中輸入固定頻率的紅外光載送週期性的訊號經光纖傳輸後,利用示波器觀察訊號的延遲時間,以此實驗技巧可精密計算出光速。在輸入訊號為0.1~5MHz時,光在光纖的平均速率為2.09×108 (m/s)。換算真空中光速c=折射率n(1.467)×光纖中速率v(2.09×108m/s)=3.03×108 (m/s),平均百分誤差0.43%,平均誤差為0.13×108 m/s,準確度為99.57%。 若取最佳輸入頻率2~3MHz所得到之數值,光在光纖的平均速率為2.05×108 (m/s)。換算真空中光速c(3.00×108 m/s)=折射率n(1.467)×光纖中速率v(2.05×108 m/s),平均百分誤差為0.33%,平均誤差為0.01×108 m/s,準確度為99.67%。 A method using optical fiber is described for measuring the velocity of light . Measuring the velocity of light usually needs a long distance and in a brief time. These experiments use optical fiber and TOSA and ROSA

天方葉談–利用葉錠浮沉來測定植物的光合作用速率

本研究以葉錠浮沉實驗來測定植物的光合作用速率。由文獻探討發現,影響植物行光合作用的因素很多,但如何以葉錠浮沉實驗來了解這些因素的影響卻鮮少被討論。在這次研究中,我們找出進行葉錠浮沉實驗所需的最佳方法及條件,再以此比較不同光源、不同的植物特性以及不同葉齡等變因下的光合作用與呼吸作用速率的差異。 由實驗結果可知,0.24%的碳酸氫鈉溶液具有最佳的時間穩定性。此外,陽性植物的光合作用速率較快,陰性植物的光合作用速率較慢,耐陰性植物的變異較多,這些結果與植物生理特性一致。為了追根究柢,我們進一步做了葉片的組織切片,發現不同的葉片組織結構與光合作用速率快慢有關。