全國中小學科展

未得獎作品

三角形之相似四分割

任意一個三角形要如何分割成四個彼此相似的組成三角形呢?我們透過嚴謹的數學推理,先對三角形作二、三分割的可能情形進行驗證,並藉由已完成相似二、三分割的三角形,運用「內分」和「外加」的觀念,使相似四分割的討論變得明快,並得以將各式三角形的所有相似四分割的圖示作完整而有系統的呈現。 \r 我們也對「比例四分割」的作圖法與其相關幾何性質,進行猜想與討論,並驗證得出一些結果。尤其對「黃金三角形」經比例四分割後,組成三角形之對應邊長的比值也是「黃金值」,以及使用五條摺痕線的摺紙方式,可以摺出一張黃金三角形紙張的比例四分割,這些研究結果都令我們感到獲益良多。 How to divide a triangle into four similar little triangles? Possible situations of dividing a triangle into two or three parts could be testified by strict mathematical inferences, and then the concepts of “internal division” and “external addition” could be applied to make our discussion clearly and briefly. With above discussions, figures about four similar divisions of all kinds of triangles could be presented completely and systematically. Some results were come up after making some conjectures and discussions about the geometric constructions and geometric properties of “four proportional divisions”. We learn a lot by these researches especially on the discoveries that the ratio of those corresponding sides in each four similar triangles which form a golden triangle, is also golden ratio; and that we could divide a golden triangle into four similar triangles by using five folding lines.

火災逃生指引系統

在台灣公共場合快速成長下,例如:大賣場、百貨公司、展覽會場,這些公共大型場合都有很好的消防設施,但始終有人葬身於火場? 原因就是幾乎所有的人都不會去特別注意逃生平面圖,導致花太多的時間尋找出口,這樣生存機率就大大降低。火場裡面有太多的致命因素,像是:高溫的空氣,毒氣、濃煙…等,所以必須把握每一分每一秒。為了加快逃生速度,我們將所有的通道都設有導引警示器,逃生者只要順著導引警示器就可以安全到達出口。為了因應公共場合有龐大的人群,所以逃生路線不能只有一條,因此我們設計上是有多條路線,一、可以解決龐大人群,二、可以加快速度。;With the rapid growth of public places in Taiwan, evacuation system is of more and more importance. Actually, public places, such as hyper malls, department stores and exhibitions, are not without fire-fighting equipment, but why is that there are still people getting killed in a fire? The reason is that almost no one actually pays attention to the evacuation plans. As a result, it often takes too much time to find the exits, which lowers the possibility of survival. In a fire, there are usually too many fatal factors, which could lead to death, such as high temperature and heavy smoke; therefore time is precious when escaping from a fire. To fasten the speed of evacuation, we set guiding alarms in every passageway. By following the guiding alarms, people can get to the exits safely. Besides, owing to the huge amount of population in public places, there can’t be only one route out. With regard to this, we design many routes in order to enable and fasten the speed of evacuation of huge amount of population.

摻入奈米碳管的液晶面板之穿透光譜研究

本研究計畫主要探討液晶摻雜奈米碳管後,液晶面板對可見光區之穿透光譜。由於奈米 碳管在應用上有一大缺點是容易聚結糾纏在一起,不容易排列整齊,為了使奈米碳管能夠依 照所希望的方向排列,並且能動態地改變碳管的排列方向,我們將奈米碳管散布在液晶內, 藉以控制奈米碳管的排列。為此,我們自製液晶面板以便能夠自由改變液晶材料的成分,即 調整奈米碳管的種類及粗細長短程度和奈米碳管與液晶材料的混合比例,並量測其穿透光 譜,探討奈米碳管對液晶分子偏轉程度的影響,及摻雜奈米碳管後的液晶面板,其穿透光譜 對各波長光的關係。 第一階段的基礎實驗中,我們先經由控制不同的外加電場,了解液晶分子對各波長的光 之穿透程度隨電場變化的關係;第二階段的實驗中,再進一步控制更多的變因,依需求將控 制不同變因自製液晶面板,並且逐步探討其穿透光譜對於種種變因的關係為何。

短暫高鹽刺激提升番茄果實品質

本研究透過對蕃茄施予短時間的不同高鹽份濃度刺激,觀察植株成長 情形並對果實進行品質測定,本研究對於品質之定義著重於總抗氧化能力、糖度及硬度的檢測。由實驗結果得知Na+、Cl-離子所造成的滲透壓差,確實有助於可溶性固形物及Na+、Cl-離子的累積,對於果實糖度及硬度上皆有顯著變化。但對於如何造成總抗氧化能力值的提升,在未來的研究中會再深入探討。We observe the germination of the tomatoes and assay "the quality" of the fruits in our research by giving plants short-range acridness of different high salinity. In this research, the definition of “quality” emphasizes the anti-oxidized ability, the brix, and the hardness. By the experimental result knew Na+ and Cl- ion creates the osmotic pressure, truly is helpful to the Soluble Solid Content and the Na+ and Cl- ion accumulation. Yet regarding by what the anti-oxidized ability promotes, we will treat in-depth in our intended research.

棋子跳躍問題

This is a study about the solution to a chess flipping game. The game is based on a 4*4 game grid. First, place some chesses on the grid randomly to start a game. Move any chess by jumping over one or two neighboring chesses in the same row (left or right), same column (up or down), or on the same diagonal. Chesses which get jumped over should be flipped. The ultimate aim is to make all the chesses upside down. In this study, I try to find the rules of the beginning arrangement that ensure solution. Here are the steps I take: First, break the restriction of the 4*4 grid, and set the coordinate system. Second, find out a few “basic illustrations” that can be solved and moved in order to cope with certain complicated problems. Third, with “basic illustrations”, find the rules applying to games on n*n grid. 這是關於翻棋遊戲的可行解之探討。棋盤是一個4*4 的方格,遊戲開始時在棋盤上任意擺上一些棋子,均是正面朝上,利用相鄰棋子的水平、垂直、斜向跳躍,棋子被跳躍過一次則翻面一次,遊戲目的在於使所有的棋子都翻為反面。我要探討的是關於棋局可解不可解的問題,找出棋盤上可解棋局的規則。研究步驟大致如下:一、打破棋盤4*4 的限制,將棋盤座標化。二、找出若干個可解並可移動的「基本圖」。三、利用基本圖,找出n 列棋盤可解的規律。

以自製式裝置探討兩成分系活性係數與蒸氣壓及拉午耳定律的偏差

在本次的實驗中,我們藉由拉午耳定律的公式及一條由作者從實驗中推論而得的公式,可以簡單的求出不同溶液的分壓。我們只需要一個自製式的簡易裝置,在裝置底下放置被測量的溶液,並密封使其成為封閉系統,其頂端為一銅箔,在銅箔上使用適合的溶液,藉由上方溶液蒸發量與下方不要放置溶液蒸發量的差異之值比較,即可求出其下方兩種成份系的溶液中各種溶液在不同莫耳分率下的分壓以及能量的傳遞,雖然會有誤差的存在,但比照一般利用光譜法來測量的方式,成本卻降低很多,且經由公式,也可估計各點的活性係數,比之以往簡易很多,因此可當作針對的高中生示範教學及教具,使同學更能了解兩成分係非理想溶液在拉午耳定律中之差別。This study shows that is easy to figure out the partial pressure of the different solutions by applying the formula of the Raoult's laws and a formula computed by the authors from their experiment data. All that is needed is a simple hand-made device. In the experiment, the device was sealed into a closed system after the solution to be measure was placed at the bottom of the device. A proper liquid was put in the top piece of the device, which was made of copper foil. By computing the difference between the amounts of evaporation of the top liquid with and without the bottom solution, we figured out that the two-component solution is the partial pressure and energy transmission of the solutions at varied mole fractions. Though errors do exist, cost was much lower by this method than by the spectrum method. Besides, the formula makes it easier to estimate the activity coefficients at different points. Therefore, the study can be applied in physics teaching in senior high school to facilitate students' understanding of the differences between two-component solutions in the Raoult's laws.

利用電化學合成P型半導體--碘化銅(CuI)光感測器的製作

碘化銅(CuI)為一種P型半導體,在一般文獻中大部分被用做催化劑,合成極為不易。我們利用一簡單電化學合成的方式,可將銅控制在一價銅( Cu?O ),如在有碘離子( I- )的溶液中便形成CuI。在這研究中我們將所合成出之P 型半導體CuI 製成光感測器,在偵測不同光強時有良好的線性關係(r2=0.9961)。在光感測器的實驗中我們利用CuI 電極,讓它接受光照,使其電流產生光電流,如果能儲存其光電流能量,就可成為一太陽能電池,利用其原理,未來可以發展成為替代能源。 CuI is a kind of P type of semiconductor in the general literatures. Most of the CuI is use to catalyst. Except that, CuI is difficult to synthesis. We use a simple way of Electoctrochemistry complex to keep Cu?O under controlling. For example, in the I- solution, Cu becomes CuI. In the study, we make the synthesis P type of semiconductor to be light sensor. In different lightness, the procedure showed good linearity(r2=0.9961) In the light sensor, we use CuI pole to accept sunlight. Then the current will produce light current. If we could store the energy of light current, it will be a solar energy battery. When we apply the theory, it can develop to be substitute energy.\r

彩色數位影像資料庫檢索架構-以國立自然科學博物館為例

國立自然科學博物館推出《數位博物館》,內含大量生物圖鑑及豐富館藏文物之圖文資 料,無論用於資料查詢或提供進階研究資料皆有極大貢獻。但經使用後發現,其檢索架構仍 只提供關鍵字搜尋及分類瀏覽,無法精確檢索出欲查詢之資料,尚有改進之處。 於是針對現有之影像檢索系統,我們跳脫出傳統以文字為檢索之依據,而設計出一連串 之改進方案,如下: 1. IRHI 色調辨識影像檢索,針對色調相近之影像類群提供良好檢索架構。 2. IRCI 輪廓辨識影像檢索,針對輪廓相近之影像類群提供良好檢索架構。 3. IRHCI 色調暨輪廓辨識影像檢索,綜合前述兩種方法之優點所設計。 A while ago, the National Museum of Natural Science put forth the “Digital Museum,” which contains great amount of biological pictographs and abundant collections of textual as well as pictorial materials. This has contributed tremendously to information search and advanced research. However, after employing them, we come to discover that its retrieval paradigm only provides key-word search and categorization browse, without enabling us to precisely pick out the desired data. Thus, this paradigm leaves something to be desired. To make up for the insufficiency of the existing system, we have escaped from the concept of searching by texts. Instead, we have designed a series of improvements. They are as follows: 1. IRHI(Image Retrieval by Hue Identification): Providing a sound paradigm for the image groups composed of similar hues. 2. IRCI(Image Retrieval by Contour Identification): Providing a sound paradigm for image groups composed for similar contours. 3. IRHCI(Image Retrieval by Hue and Contour Identification): Combining the strengths of the above two paradigms.

引擎排氣噪音反饋至道路交通流量與車輛排放控制

運用自製低頻噪音(

烷類數位密碼

本研究主題主要是解決化學上複雜同分異構物的繪製以及其命名,因為物質在結構複雜時其同分異構物變化之多令人難以捉摸,於是我應用電腦強大的邏輯處理以及運算判斷的能力來讓電腦繪製。以下是我想達成的目的:(1)排列出分子式的同分異構物(2)顯示出同分異構物之示性式、結構式(3)預知尚未創造出物質的性質研究中我創造出以下原則讓我方便達成研究(1) 數位密碼:為了讓電腦方便執行我使用數碼的方式表達各種同分異構物(2) 五大原則:此原則能讓不僅是電腦甚至是各個要繪製同分異構物的人都能有架構的繪製,不會遺漏任何的組成。(3) 3D顯示:透過X3D軟體的協助我能讓使用者透過立體的方式了解到物質的結構。The purpose of this research is to solve the problem of Isomer’s structure drawing and named problem. It’s hard to predict the status of complex Isomers, so we use the powerful logic and calculational ability of computer to draw the structure of Isomers. The following points is the goal that we want to reach (1) Arrange the structure of the Isomer’s formula (2) Show structural formula of Isomers (3) Predict the chemistry of things that haven’t been created During our research, we create the following principle to help us do the research (1) Digital Codes: In order to let the computer to run the process, we use digital codes to express all the Isomer’s formula. (2) The “5 Rules”: The 5 rules can help not only computers but all the people who try to draw the structure of Isomers without losing any of compositions. (3) 3D Display: Helping our user to understand the structures of materials with the 3D images producing by the “X3D”.