滿足
之M點是否為重心之探索
滿足之M 點，我們稱之為Pi(i=1…n)的均值點。當n=3，M 恰為△P1P2P3 的重心 (G); n=4 時，M 亦為三角錐P1P2P3P4 的重心！因此不免引人遐思：滿足之M 點是否皆為其重心？
我們藉由電腦幾何作圖軟體GSP 協助觀察，掌握了圖形變化間之不變性，再配合向量解析及推理，得以發現均值點、多邊形的重心、以至多面體的重心、及平行多邊形的一般性作法。附帶又發現：任意相鄰三頂點即可決定一平行n 邊形。並進而證實：平行四邊形為四邊形M＝G 的充要條件。但當n≧5 時，平行n 邊形只是n 邊形M＝G 的充分非必要條件！一般而言，具有對稱中心O 的n 個點所構成的圖形必可使M 與G 重合於O 點上。
The point M satisfying is called “the mean point of Pi(i=1…n)”. As n=3, M is the center of gravity (G) of the △P1P2P3. If n=4, then M is also the center of gravity of the triangular pyramid P1P2P3P4. Therefore, I began to wonder if the following assumption stands: The point M that satisfies is always a center of gravity.
By using the computer software GSP (The Geometer’s Sketchpad) to observe figures. It is found that when a figure is changing there is still constancy. Furthermore, supported by the analysis based on vectors, general constructions can be established concerning the mean point, the center of gravity of polygon, the center of gravity of polyhedron, and the parallel polygon. Also, I find that any three neighboring vertexes decide a parallel polygon. And thus it is verified that the parallelogram is the sufficient and necessary condition for quadrilateral M=G. As n≧5, the parallel n-sides shape is the sufficient, not necessary condition, for n-sides shape M=G. In general, a central figure of n points having the center of symmetry O can make M and G meet on O.
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.
旋光性介質對電磁波影響的分析與討論
This experiment mainly aims at three kinds of solution - Dextrose, Saccharose, and Fructose. By changing its temperature, density, length of tube, as well as different wave length factor of polarized light, we observe the influence of the direction of polarization by those factors. The experimental result showed as follow. The Dextrose and the Saccharose can cause the polarized light with the rotary direction of clockwise, so both are ‘dextrorotatory’. The Fructose can cause the polarized light with the direction of counterclockwise, so it is the ‘laevorotatory’. For the Dextrose, when the\r temperature is lower than 20℃, the direction of polarization has changed observably, but doesn’t have any rule. When the temperature is higher than 20℃, the direction of polarization increase slowly. For those three kinds of solution, when\r density increased, the polarization increased observably. When the polarized light passed through the solution with longer path, the direction of polarization has more change. When the wave length of the polarized light changed, the direction of polarization has been changed observably. When the wave length of the polarized light is shorter, the direction of polarization change increased.本實驗主要針對葡萄糖、蔗糖、及果糖等三種旋光性溶液，改變其溫度、濃度、容器管長、以及不同波長的偏振光等因子，觀察這些因素對偏振方向所造成的影響。實驗結果顯示：葡萄糖與蔗糖會使得偏振光的偏振方向以順時針旋轉，屬右旋性之光學異構物；果糖會使得偏振光的偏振方向以逆時針旋轉，屬左旋性之光學異構物。若溶液為葡萄糖，當溫度低於20℃時，偏振光的偏振方向會有明顯的改變，但無規則可尋；當溫度大於20℃時，偏振方向旋轉角位移則以非常緩慢的方式增加。當此三種溶液之濃度增加時，偏振光的偏振方向有明顯遞增的現象。此外，當容器長度越長（即偏振光在介質中的行程越長）時，偏振方向的改變亦越明顯。當偏振光的波長改變時，偏振光的偏振方向有明顯的變化，且當偏振光的波長越短，偏振方向的改變越大，似乎與波長呈反比，但此結果與理論值（即旋光度與波長平方成反比）仍有一些差距。
MTU值與網路效率的關係
中文摘要：\r 本研究旨在探討，在TCP/IP 協定之下，最大網路傳輸效率之MTU\r （Maximum Transmission Unit,最大傳輸單位）值。根據IEEE 所公\r 佈Ethernet 之標準，經實地模擬實驗，本研究之結論如下：（1）在\r 單純兩台電腦直接串接時，由於幾乎無任何干擾與封包的碰撞，可設\r 定之MTU 最大值以1500bytes 為最佳；（2）但在模擬真實的大型廣域\r 網路時，由於碰撞增加及雜訊增多，經模擬實驗顯示，MTU 值為\r 1500bytes 時無法在資料傳送、接收及重組時取得平衡，最佳之MTU\r 值落於500 到600bytes 之間，進一步研究顯示MTU 值設在500 到\r 600bytes 時可提升傳輸效率約50%。同時，本研究亦討論將此機制應\r 用於未來新網路標準之可行性及其必要性。Abstract：\r The main purpose of this research is to explore the best network\r transmission efficiency's Maximum Transmission Unit under TCP/IP\r protocol. According to the Ethernet's standard of IEEE and simulated\r experiments, the outcome of this research are :( 1) When connecting two\r computers serially, there is almost no interference and impact of packets,\r the best MTU that we can set up is 1500bytes ;( 2)When simulating the\r truly wide area network, interference and impact are rising. The result of\r this simulates experiment shows that when MTU is at 1500bytes, it's\r unable to keep balance when sending, receiving and re-composing. The\r best new MTU is between 500bytes and 600bytes. And when MTU is\r between 500bytes and 600bytes, the network transmission efficiency can\r be promoted about 50% higher. At the same time, the research is also\r discussing the feasibility and necessity of applying it to the standard of\r the future network.
台灣地區青少年體表面積與相關生活因子之研究
人體表面積在醫學的應用相當重要：燒燙傷的評估是以全身面積被灼傷的百分比 表示；營養狀況的評估，新陳代謝率也以單位表面積表示之；體液或藥物之需求量也 是以體表面積來決定劑量；然而人體是一不規則物體，應用一般幾何面積計算公式有 其困難處，如何快速的計算人體表面積，以作為醫療的指引，有其必要性。而青少年 正處於快速發育期，各部位的成長是否會影響表面積的計算，由於目前鮮少對青少年 之專文報告，尤其缺乏台灣地區之調查。為了探索這些問題，乃進行調查與研究。 本研究以台灣地區國民中小學10 至15 歲青少年為對象，探討在此發育期間體格 之變化及可能之影響相關因子，並建立體表面積之快速計算公式。本研究隨機取樣以 1209 人形成樣本，其中男生623 人，女生586 人，利用尺秤，取得身體各部位的資料， 並以問卷調查運動、飲食與睡眠等問題，以探討影響此成長期發育之因子。結果發現： 台灣青少年體表面積快速計算公式為(身高x 體重 ÷37)0.5；其體表面積九分法計算方 式也有別於一般歐美成年人的計算法；及此年齡層的身高與體重受運動的頻率、運動 持久性、飲食習慣多寡的影響，而與運動種類及主食種類相關性不大，這項研究的發 現，將有助於醫護人員對青少年問題的處理。Body Surface Area (BSA) has been used in many clinical conditions to calculate the percentage of burned area, to evaluate the nutrition status - the unit of the metabolic rate, to determine the need of fluid supply or the medicine dosage requirement. So precise measurement of BSA is very important, however the human body is an irregular shape, a laborious task using the geometrical method. To establish a simple quick formula to guide the therapeutic treatment is a necessity. Also the rapid growth phase during the adolescent stage might change the BSA in some way. BSA has not been established for the teenagers in Taiwan. To investigate this issue, a total of 1209 healthy elementary and junior high school boys (623) and girls (586) aged 10 to 15 in Taiwan were recruited by random selection. By use of anthropometrical measurements and a health questionnaire to the subject simultaneously, the data was analyzed statistically. The results revealed that a quick adequate formula derived from the body height and weight for Taiwan teenagers was determined by the formula, BSA = [ Height (meter ) x Weight (Kg) ÷37 ] 0.5, the Taiwan teenage “rule of the nine” of BSA is different from that of the adult, and that the frequency and the duration of exercise, the diet habit, and the duration of sleep significantly influence both body growth and weight. These findings may provide significant references for the physicians to treat the clinical conditions of teenagers in Taiwan.
氣候變遷對台灣地區異常降水的影響
Drought and inundation are two unusual natural disasters in Taiwan. The two natural disasters\r have some relation of abnormal rainfall become more and more in Taiwan. So it let me think about\r can climate vicissitudes make the chance of abnormal rainfall become more?\r The study have researched the chance of abnormal rainfall by "rainfall duration" and "total\r rainfall". It collect the day by day total rainfall from 1960 to July 2002, collect locals are Taipei,\r Taichung, Kaohsiung and Hualien. Than enter the data into the computer, let computer calculation\r total rainfall, rainfall days, heavy rain days, pouring rain days and torrential rain days. Then\r analysis the tendency of long-term change.\r According to the analysis, the chance of abnormal rainfall happened become more in Taipei,\r Taichung, Kaohsiung and Hualien. The ratio of Hualien and Kaohsiung is the most obviously. It's\r also find that there temperature and total evaporate became higher, the total sunshine duration\r became lower. Then El Nino have some influence in abnormal rainfal. In El Nino year, total rainfall\r will become lower. When La Nina year, the total rainfall will become more in Taipei and Hualien.\r Then the long influence is clearly in Taipei.\r 乾旱與水災是台灣地區相當常見的二項天災，這二項災害的發生都與異常降水有直接的\r 關係。近年來台灣地區因異常降水造成的天然災害，似乎有逐年增加的趨勢。因此讓人聯想\r 到氣候變遷是否會導致異常降水頻率增加。\r 本研究主要由「降雨時數」與「降雨量」二方面探討異常降水發生頻率。先收集台北、\r 台中、高雄、花蓮四地自1960 年至2002 年七月三十一日之逐日雨量資料，將資料輸入電腦\r 後，統計各站歷年降雨量、降雨日數、大雨、豪雨、暴雨日數，並分析長期變化趨勢。\r 分析結果，台北、台中、高雄、花蓮四地異常降水發生機率，有增加的情形；其中以花\r 蓮及高雄變化的比例最高。再與其他各地氣象要素比較可發現，可能與氣溫及蒸發量數上升，\r 以及日照時數縮短有關。另外聖嬰現象也可能對異常降水有長期性的影響。一般而言聖嬰年\r 雨量減少，反聖嬰年台北、花蓮地區雨量反而會增加。而長期性的影響，以台北地區最顯著。
約瑟夫問題
最後留下數字會是多少？該問題在台灣的全國中小學科學展覽出現多次。而資訊界演算法大師Donlad E. Knuth 在其著作The Art of Programing，CONCRETE MATHEMATICS （具體數學），針對該數列作詳細的說明；但是，不論是歷屆全國中小學科學展覽或是大師著作，對於該問題，都只是談及殺1 留β或是殺α留1。本研究利用獨創α分類、n 及k 分類、d 函數、b 函數及循環、n 及y 分類、碎形數列和演變關係，將約瑟夫問題探討範圍提升至殺α(個數)留β(個數)，直到剩下最後1 個數時就不能再殺了，遊戲終止，倒數第k 個留下的自然數是多少？同時，本研究在殺α(個數)留β(個數)下，指定自然數y 為酋長，酋長不能被殺，殺到酋長時遊戲停止，求剩下的自然數有幾個？會發生什麼情形？The Josephus problem refers to what will be remaining when arranging n natural numbers in a circle and starting killing one and leaving the next one alive. The problem has been on display for many times in Taiwan National Primary and High School Science Exhibitions (as shown in Table 1). And, the information algorithm master, Donald E. Knuth has elaborated on the array in his works The Art of Programming, CONCRETE MATHEMATICS. However, both the past science exhibitions and the master’s works are limited to discussions on cases of killing 1 leaving β or killing α and leaving 1. This research employs uniquely created α classification, n and k classifications, d function, b function and loop theory to extend the Josephus problem scope to killing α leaving β to find out what the remaining natural number is by No. k counted recursively. Meanwhile, this research designates natural number y as the chieftain, which can never be killed. The game is over when the chieftain is to be killed. The problem is to work out how many natural numbers are remaining. And what happened?