國王的海市蜃樓
在夏日的午後，在炎熱的柏油路面上很容易可觀察到遠方的 路面上，出現如鏡子般的倒影，看起來彷彿前方有一灘水，但當 我們向前進一些時，倒影卻突然消失了，這個現象，一般稱為海 市蜃樓。 一般解釋海市蜃樓的成因，都是由於在上層的低溫空氣，和 在下層靠近路面的高溫空氣，因密度的不同，以致於折射率的漸 層差異，繼而產生全反射。 但我們觀察發現，地面與上層空氣的溫差，並非柏油路面上 假積水現象及倒影出現的必要條件；反而和入射光的角度、路面 的平坦程度及路面的性質有關。我們提出了粗糙面在入射光的入 射角接近90度時，可發生單向反射的模型。並由實驗來驗證假積 水現象及倒影主要的成因是「柏油路面的單向反射」而非「空氣 的折射與全反射」。 Under the scorching sunshine, we can see the reflection on the tarmac in the distance just like a water puddle on the road. And the water also reflects the people and object nearby. But, in fact, the tarmac road over there is very hot and dry. Therefore we call the phenomenon as the “false water puddle on the tarmac.” According to the textbook , the main reason for “false water puddle on the tarmac” is that the temperature difference leads to the refraction of the light and causes the phenomenon. However, from our observation, the theory still can’t explain some phenomenon, For example, the “false water puddle on the tarmac” remains to appear when the wind blows fiercely. Even with little temperature different at night the phenomenon is still obvious. Therefore, in our opinion, the temperature different of the air is not a necessary condition of “ the false water puddle on the tarmac.” We bring up the model to explain the phenomenon that when the incident angle of the light approach 90 degrees, the light will result in one-way reflection. According to the model, furthermore, we make experiments at midnight and at dawn. The result of the experiment assures us the hypothesis of the model, Consequently, we hold the ideal that the main condition of the “false water puddle on the tarmac.” Is not because of the refraction and the total reflection but because the light reflects off the road and result in the one-way reflection on the tarmac road.
凸多邊形完美分割線的尋找
1) First, we studied the properties of lines and segments that bisect a triangle’s perimeter. By observing the properties, we found a “revolving center” what we defined. We employed the revolving center in the construction with ruler and compass to make “triangle’s perimeter bisectors” that pass the points we desire. Later, we found out the “envelope\r curves’” equations of the “perimeter bisectors” on the triangle’s two sides are parabolic curves. Moreover, the focus of this parabolic is just as same as the revolving center. 2) The curves envelope of area bisectors formed a hyperbolic curves. By similar method of constructing a “perimeter bisector”, we can also construct an “area bisector”’ by using the hyperbolic curve’s focus. We accidentally found out that we can construct the tangent of the conic by using our method, too. Different from the information we found, It supplies a easier method to construct the tangent of a conic. 3) With the rules of constructing perimeter (area) bisectors, we can expand the method to constructing the “perimeter (or area) bisectors” of any convex polygons. 4) We call the lines that bisect the convex polygon’s perimeter and area at the same time the "perfect bisect lines”. Based on the properties of the” perimeter bisectors” and the “area bisectors” in our research, we found out that the” perfect bisect lines” pass the intersection of the” perimeter bisector’s effective segment” and the hyperbolic. Thus, we can construct the “perfect bisect lines”. Moreover, we proved the esistence of the “perfect bisect lines.”1. 首先我們先探討三角形等分周長線的性質，利用性質及觀察等周線的變化，我們找到可利用本研究所稱的「旋轉中心」，以尺規作圖的方式，作出「任意點的三角形等分周長線」。接著我們導出三角形兩邊上等周線所包絡而成的曲線方程式為一條拋物線的曲線段。進而發現上述的旋轉中心，即為等周線所包絡而成拋物線的焦點。2. 三角形兩邊上等積線所包絡出的曲線是一條雙曲線的曲線段。利用等周線的尺規作圖，我們找到同樣可利用焦點當旋轉中心做出等分面積線。意外的發現出圓錐曲線的切線作圖，皆可利用我們的研究方式(有別於已查出的文獻上記載)，較快速的作出切線。3. 利用三角形等周線(或等積線)的尺規作圖，可擴展到「過任意定點作出凸多邊形的等周線(或等積線)」。4. 我們將同時分割凸多邊形等周長與等面積的分割線稱為「完美分割線」。利用三角形研究出的等周線與等積線相關性質，我們找出完美分割線必通過同角的等周有效段與等積曲線段之交點。利用這結果可作出完美分割線。並進一步，我們證明出凸多邊形完美分割線的存在性。
分子篩包覆奈米銀製作與應用
本實驗合成之奈米銀粒子產物分為水溶液與固態形式。奈米銀粒子水溶液態製造方法以多芽基之檸檬酸根離子當保護劑，再以NaBH4 還原生成奈米銀粒子。而固態形式之奈米銀粒子是先以四級銨鹽界面活性劑當保護劑，經過NaBH4 還原生成奈米銀粒子水溶液後，再用二氧化矽包覆奈米銀粒子，藉由高溫燒去保護劑，得到含奈米銀粒子之二氧化矽分子篩材料。 將含奈米銀粒子之二氧化矽分子篩材料產物浸在純水中，除了不會改變水溶液性質外，又能以分子篩通透的特性，讓奈米銀漸進地釋放出銀離子，而達到長效性抗菌效果。 至於具抗菌性棉衫或濾網的製作，則採直接浸泡在奈米銀粒子水溶液中的方法，使奈米銀粒子吸附於上，針對上述實驗非常成功，洗滌超過十次且放置時間長達一個月以上，其抗菌效果仍佳，表示此簡易法製成的棉衫或濾網具有長效性的抗菌功效，為本研究重大突破。 奈米銀粒子對環境的影響是利用黑殼蝦來測試，控制適當奈米銀粒子濃度，使黑殼蝦能生存，亦可達到水中殺菌的效果。本實驗為首次針對奈米銀粒子對環境影響的測試並獲得重大的成果。;In this study, two Ag nanoparticles samples including Ag nanoparticles in aqueous solution and in solid form were prepared. The Ag nanoparticles aqueous solution readily obtained from reduction of AgNO3 aqueous solution with NaBH4solution in the presence of the sodium citrate as protecting agent. To prepare the Ag nanoparticles@porous silica sample, cationic alkyltrimethylammonium surfactant was used as the protecting agent of Ag nanoparticles and template of the porous silica. The Ag nanoparticles@porous silica was synthesized via reduction by NaBH4, silicification in silicate solution and calcination for the removal of surfactant. When adding the Ag nanoparticles@porous silica, the property of the aqueous solution was not changed. In addition, the Ag+ ion was gradually released from the accessible silica matrix to achieve a long-lasting effect on anti-bacteria. To prepare anti-bacteria clothes and sieves, these objects were soaked in Ag nanoparticles aqueous solution. The Ag nanoparticles were spontaneously absorbed into the clothes and sieves. The anti-bacteria efficiency of the Ag-nanoparticles containing clothes and sieves still remains even after ten-time washing and a period of time longer than one month. These worthy results indicate that this synthetic method provides a simple way to prepare the long-lasting Ag-nanoparticles containing clothes and sieves for anti-bacteria application. To investigate the influence of the Ag nanoparticles on the environment, shrimps are used as testing objects. With a well control on the Ag nanoparticles concentration, the shrimps survived well and the bacteria content was reduced. It is the first time to have testing result about the effect of the Ag nanoparticles on the environment. Thus, this is the most remarkable achievement in our experiments.
直角三角形生成關係的研究與發展
k(2αβ ,α2 ? β2,α2 + β2 )是大家熟悉畢氏定理的通式解，且一般書籍的証明大都採用代數的手法證明。以國中生而言，上述的代數方對國中生來說不夠直接且較無推展的實用性。因此幾何觀點出發發展另一種思考方式，利用角平線的性質給予畢氏定理比例解另一種全新的詮釋，並賦予比例解中的參數α 、β 在幾何的意義。在推理的過程中，我們得到一個相當有用的對應關係：一個有理數對應到一個直角三角形、兩個有理數對應到海倫三角形，再將此對應關係運用到各種幾何圖形上面，即可證明出他們所對應的通式解。最後我的興趣鎖定在海倫三角形、完美海倫多邊形與超完美海倫多邊形上的做圖方法上，善用我們所發展的對應關係，上述的問題皆可迎刃而解。k(2αβ ,α2 ? β2,α2 + β2 ) is a popular formula in Pythagoras Theory, often proved in algebra approach among books. Nevertheless, in light of junior high students, the aforementioned algebra method is neither direct nor practical. Hence, a different thinking method is derived from geometry perspective, using the straight line concept to reinterpret Pythagoras Theory and define the geometric meanings of α andβ . In the process of logical development, a useful correlation emerges: a rational number correlates with a straight-angled triangle, and two rational numbers correlate with Heron Triangle. This correlation can be applied to all kinds of geometrical diagrams to prove the correlated homogenous solution. Ultimately, my interest lies in the diagram methods of Heron Triangle, Perfect Heron Polygon, and Super Perfect Heron Polygon in order to apply our developed correlations to solve the above mentioned problems.
西瓜成熟與否和聲音關係
一般人從小就知道如果要判斷西瓜有無成熟，只要用手輕拍瓜皮，利用聲音的特性就可以知道西瓜是否成熟，此技術看起來容易，卻需有多年經驗之西瓜商始可為之。本研究利用拍擊西瓜所造成之聲音進行非破壞性音波檢測，來探討西瓜之成熟度。換言之，本研究希望在依照西瓜商拍擊的習慣下，從客觀的科學角度，探討存在於西瓜商手上「聽音辨瓜」的奧秘。由研究結果得知，西瓜的拍聲在頻譜中可分為三個頻區，即西瓜殼所造成的高頻區，水及含水量高的果肉所形成的中頻區，及由空洞及含水量低的果肉所造成的低頻區，而西瓜商就是藉由這三種音頻所表現出的綜合效果進行判斷。The method, tapping the watermelon rind and listening to the sound, has been often used to judge whether the watermelon is mature or not. Although it is not difficult to tap the rind of a watermelon, it is not so easy to have a correct judgment of the maturity just from the sound you heard, unless you are an experienced watermelon farmer. In order to investigate the secret that the farmers have, this research detects and analyzes the sound of tapping watermelons in an objectively scientific way. According to the experimental results, the sound could be approximately partitioned into three regions in the frequency spectrum, denoted as high-frequency, mid-frequency, and low-frequency regions. The high-frequency region and mid-frequency region are resulted from the hard solid rind and the juicy flesh of a watermelon, respectively. As for the low-frequency region, it comes from the vacant holes or flesh with little amount of water. Based on the experiment, it can be concluded that the maturity of a watermelon can be correctly judged from the combination of these three frequency regions, just like the farmer’s method.
垂直水柱的成節機制探討
本研究欲探討垂直水柱遇障礙物成節的形成機制。以數位照相機、光電計時器等進行觀測。 實驗結果如下： （一）因往返水柱波速不同，而且節無波腹大幅振動現象，故節不是駐波現象。 （二）細針插入水柱表面時，當針上方超過某長度後，針下方產生Ｖ字形震波。但不論針相對水柱的速度是否超過波速，針上方都有節，故不是震波所產生的現象。 （三）根據水波槽模擬實驗，不論木條是否超過波速，木條前方均產生波紋。木條前方的水受到木條推動，往前方加速，因此顯現出波紋了。 我們認為，在水柱中所看到的節，不是震波或駐波，而是相對於木條往前傳遞的波。波源是撞擊物，改變了水柱表面的壓力，而成為波源，水柱的水因受撞擊，某個範圍內流速會小於波速，使得撞擊物前方存在波紋。This experiment uses digital camera and photoelectric timer to discuss the mechanism of causing spouts to form nodes on its surface. Because the downward wave velocity of the spout is different from that upwardand there are no significant vibrations of antinodes, standing waves are not the mechanism of causing nodes. In the experiment of inserting a needle into the spout, we found out that while the needle was inserted above a certain length of the spout, v shaped bow waves emerged. However, no matter the velocity of the needle related to the spout is over the wave velocity, there are always nodes above the needle. Therefore, bow waves are not the mechanism of causing nodes. According to the ripple tank simulating experiment, no matter whether the speed of the wooden stick is faster than the wave velocity or not, there are always waves forming in front of the wooden stick. The wooden stick pushes water in front of it and causes the water to accelerate forward. Therefore, waves appear. We think that the nodes we see on spouts are neither standing waves nor bow waves. The nodes are rather caused by the relatively moving wooden stick. The object, which impacted the spout (wooden stick), changed the pressure of the spout’s surface and became the source of wave. Because of the impact, the velocity of the water current of a certain area became slower than the wave velocity and causes nodes forming on the surface of the spout.
以離子溶液催化醇與酸酐的之酯化反應
在酯化反應中，經由實驗結果，我們發現離子液體對於此反應有催化的效果。離子液體 是在室溫下呈現液態的離子化合物，將醇類與酸酐放入離子液體中有助於酯化反應的進行， 基於這個新的發現，我們開始尋找使用不同種類的離子液體做實驗，選出適當的離子液體， 並且測試離子液體在不同環境下的催化效果，以及適合的使用計量；更進一步，我們找出離 子液體在催化反應之後，將離子液體回收的方法：利用有機溶劑將離子液體和產物分層並萃 取出產物，把離子液體回收再利用，符合現代推動綠色化學的趨勢。接下來我們探討離子液 體對催化反應的擴展性與應用，先由不同結構的一級醇反應到醯胺鍵的生成，最後推展到合 成阿斯匹靈，實驗結果說明，用離子液體做催化劑，也可以成功的合成阿斯匹靈。 We have established for the first time that ionic liquids, which possess the property of Lewis acid, can facilitate acylation of alcohols with anhydrides to form esters with photo-excitation. With the initial finding, we then screen through different types of ionic liquids with varying counter anions, loading, and external light or heat sources to sort out the best reaction conditions. To gain insights into the working mechanism, the dynamic profile of the catalytic reaction was monitored by analyzing the reaction mixture by using ‘H NMR spectroscopy. The ionic liquids can be recovered by extractive separation from the acylation product, which meets the major theme of green chemistry. To extend the substrate scope and applications of the new catalytic process, different functional primary alcohols and amines were further examined. More importantly, we have utilized the new catalytic protocol for the acetylating of salicylic acid, leading to aspirin with high efficiency.
聽聽貝多芬作品的下一代：將碎形及基因演算法應用於數位音樂產生器
本研究整合了碎形圖形的迭代運算方法與基因交配觀念來達到音樂創新，並透過音樂和諧性判別機制來提高創新音樂的悅耳程度。利用基因觀念之交配的方法來解決長短的問題。這個方法是把原始音符輸入後，找出它們的中心點，以這個中心點為準，其他的音符按照一定比例向外延展，成為新的迭代點。再利用這些迭代點，迭代出新的音符。把製造好的音符染色體放置到交配池中，以隨機的方式在交配池中選取其中之一個染色體進行交配的動作，此二音符染色體會交換彼此的基因，產生下一代新的代表音符長短之染色體，隨後以「模仿母體判斷式」來判斷這新一代的音樂是否與母體音樂相似，藉此淘汰掉「不肖的」下一代，而若新一代與母體的相似程度高的話，它的悅耳性相信也會相對提高。最後把這些技術應用於數位音樂創作，以衍生新穎應用與創新的結果。Fractals can be produced by IFS (Iterated Function Systems). By iterative computation of many times, we can obtain the similar graphics. In my research, the methods to generate the iterative algorithms were presented. In addition, I would discuss the regularity and the content as well as the properties of those digital patterns. At last, the advanced application of fractals to digital music pieces was presented. The program took a note of several measure of music as the beginning point, and made the IFS calculations for each new note in each measure. But there was no difference in beats if you just make the IFS iteration. So I changed the beats with genetic crossover method. In this research, the expression of the DNA to each beat of note was adopted. The same way, it took a note as a beginning point. And the system obtained the new DNA from the old notes for new ones randomly. After producing the new pieces of music, I want to know if it is good to listen. So I used the algorithm that checks the simulation to the shape of mother music. If its shape is similar to the mother music, the probability that the new music is pleasing may even increase. That would make a piece of brand new music. What I want to do in this research is improve the multiformity of music and find what the relationship is of ‘good music’ and mathematical algorithms
表面粗糙結構對疏水性影響之應用與研究
本研究從大自然中之「蓮花效應」引發學習興趣與研究動機，在蒐集相關資訊與文獻後，發現疏水功能不只是防水，還關係著日常生活品質之許多材料特性，包括防水、撥水、防潮、防銹、防蝕、抗菌防污、自清潔…等。而影響固體表面疏水性之兩大特性，包括物理之表面粗糙度與化學之超低表面能，本研究針對物理之表面粗糙度與疏水性之關係做探討，以相同之化學特性來比較不同號數之工業用砂紙之疏水行為，並就廣泛被引用之兩種模擬表面粗糙度與疏水性關係之模式：Wenzel and Cassie model，比較現有文獻對兩種模式之特性，選擇Cassie model 來進一步實驗驗證，以量測之平均接觸角 Θ 推算Cassie model 之表面粗糙係數Φ 值，並簡化不同砂紙顆粒模型為相同粒徑之球狀，以簡化之方程式來求得水珠與砂紙顆粒之實際接觸面積與球心夾角 θ，以提供高中學校能在經費與設備之限制下，仍能有效應用與印證Cassie model，獲得砂紙顆粒直徑與球心夾角 θ 自然對數值之關係。並就疏水性之生活應用，建立接觸角與 Φ 之關係曲線，驗證實驗之方程式，與延續過去之科展成果，以實驗成果提出可行性應用之建議。The interest and motivation of the present work was introduced from “lotus effect” in nature. After we collected related literature and information, we found that the function of the so-called “superhydrophobicity” behaves not only water repellency, but also a variety of real-life applications, including anti-fog, anti-corrosion, anti-bacteria, anti-fouling, self-cleaning, and so on. Pervious studies have pointed out that two criteria affecting the performance of hydrophobic surfaces are physical (roughness) and chemistry (surface tension) properties. This study focused on influence of physically surface roughness on hydrohyphobicity. Based on an identical surface chemistry, we employed different types of industrial sandpapers to mimic the lotus leaf, and investigated the relationship between roughness and hydrophobicity by using two famous models: Wenzel and Cassie models. Comparing with their basic assumptions to our study, we applied Cassie model to confirm our experimental results, in where one Cassie parameter (?) was proposed to simplify the Cassie equation. This superhydrophobic behavior can be well predicted by the Cassie model. This study continues previous achievement and offers some practical utilization according to our\r experimental results.