本文從原始的題目「三組平行線定理及其一個猜想」出發，我們猜想n組平行線也會有類似的定理。 於是試著將n組(n≥3)平行線：a11//a12, a21//a22, a31//a32,……, a(n-1)1//a(n-1)2, an1//an2，表示成n×2階的矩陣： [a11 a12 a21 a22 a31 a32….. a(n-1)1 a(n-1)2 an1 an2] 我們令A1=(a11,a22)，A2=(a21,a32)，A3=(a31,a42)，……，An-1=(a(n-1)1,an2)，An=(an1,a12)，再令A'1=(a12,a21)，A'2=(a22,a31)，A'3=(a32,a41)，……，A'n-1=(a(n-1)2,an1)，A'n=(an2,a11)。 設n邊形有號面積為SA1A2A3......An-1An，另一個n邊形有號面積為SA'1A'2A'3......A'n-1A'n ，則利用平行線的斜率相等和n邊形有號面積的行列式表示法：S=1/2Σ|Xk Xk+1 Yk Yk+1| ，可推得SA1A2A3......An-1An=SA'1A'2A'3......A'n-1A'n。若A1,A2, A3, ....., An-1, An n點共線，則SA'1A'2A'3.....A'n-1A'n=0，但A'1,A'2, A'3, ....., A'n-1, A'n n點不一定共線。

Harmful microorganisms in food can cause deterioration of human health, poisoning and in some cases even death. Especially fresh meat and chicken products create a suitable environment for the growth of microorganisms in terms of the nutrients it contains, water activity and pH level. For this reason, detection of microorganisms in meat products is an important issue in terms of food safety and human health. In this project, it is aimed to detect live microorganisms in meat products, especially chicken meat, in a simple, non-destructive, non-contact and fast way using laser speckle method. Laser speckle images of healthy and stale chicken meat were taken, contrast parameter and correlation analysis of the obtained patterns were made. It was observed that the contrast parameter for staled chicken meat increased by approximately 3 times compared to fresh chicken. This increase provides an understanding of the difference between contaminated chicken and fresh chicken. Speckle density changes over time in relation to the movements of living microorganisms. Thus, the correlation in laser speckle density patterns taken from contaminated tissues is disrupted. In the measurements taken with photodiode, by analyzing the change of light intensity of the speckle patterns on fresh and contaminated tissues over time, the detection of microorganisms was made easier and more precisely without the need for image processing. The proposed measurement system is a new method that detects meat contamination with laser speckle imaging. It can be developed and made portable and can be used easily in homes. Since it is a simple, non-destructive and fast method, it can be used to determine the shelf life of meat in food distribution places and markets. In addition, it has the potential to be calibrated and used for other food products other than meat products. The system developed with this study is cheap and easy to use, and the laser speckle imaging method is used in a different field other than biomedical, contributing to the literature.

本研究的目的是要設計海洋漂浮垃圾收集器，研究中第一代的主機採單螺旋、收集器採浮桶式設計，但浮桶的設計遇到水的浮力過大及容易進水的問題。經過改良後，第二代的主機維持單螺旋、收集器改為網撈式設計，但降低主機桶身高度和捨棄浮桶的設計以減少浮力，卻因網子在水中的阻力過大造成網撈無法旋轉、主機自轉的問題。第三代的主機改為雙螺旋、收集器維持網撈式，雙螺旋主機使主機不自轉、網撈旋轉，且網撈進行七大改造並在內部加裝長形邊框，最後在實測中成功收集球狀、長管狀及片狀等三種形狀的塑膠漂浮垃圾，實驗中發現：同一長度的邊框都是以球狀漂浮物乒乓球的收集成效最高；不同形狀的漂浮物收集成效最佳的長形邊框，其長度則各有不同。

以仿生魚尾鰭做為船隻推進裝置，探究對船隻運動的影響。用自製船體拍攝其運動影片加以分析，依各實驗探究目的比較其平均速度、波峰加速度平均值、平均或最大推力。仿金槍魚與仿石斑魚尾鰭各在適當的軟硬材質、擺動幅度及頻率下可得最大推力。考慮船舶使用情境的多元性，故選用形狀介於兩者間的中間型尾鰭，配合渦流觀察，進行後續探究，結果發現：以1/2前翼展2.5公分、中軸長4公分的尾鰭，加裝12公分木籤作為連桿，可有效提升船隻的平均速度及最大推力。比對渦流運動得知尾鰭推力與渦流完整度，噴流效果相關。加裝適當破阻裝置能有效降低阻力，使前進合力顯著提升。由雙尾鰭實驗得知兩尾鰭相反位相擺動可同時提升船隻平穩度及推力。

Wireless transmission products are widely used in our daily life. In this research, we focus on knowing how solid-state tesla coil works in different conditions and finding the best parameters through an easy way. In our work, a commercial electroscope was used as detector for measuring the strength of radio wave created by our simplified tesla coils. In fact, many factors would lead to experimental erorrs such as detectors, selected types of NPN BJT components, applied voltage and measuring position of height. Therefore, all of the factors were under control to make sure of accuracy and precision for our designed measuring method. In our experiment, graphics of radio wave distribution around tesla coils were drew by mathemetic software of GeoGebra. It shows the BJT types of 2n2222 had good performance for wireless transmisstion efficiency. To our surprised, we found the extended wires (called antenna) from the top of tesla coil also had an ability to transfer electromagnetic energy, and had good retention if the extended wires were within the length of main coil’s height. Finally, the shape’s and size’s effect was determined by our testing work. The result shows that pipe’s length, pipe’s diameter and turns ratio of two coils had great influence on tesla coil’s transmission efficiency. It was found that the tesla’s performance would be more efficient if wire was used to make the length twice rather than make the diameter twice. However, the turns ratio of secondary coil to primary coil would change while making the length twice. To avoid that, we fixed the length and decrease the turns of primary coil. At last, we found tesla coil must work at the turns of primary coil higher than two. Furthermore, the frequency of radio wave not only had less relationship with their length or diameter but also had less relationship with types of BJT In our study, our handmade tesla coil was succesfully applied for wireless charging and we find that the induced voltage decrease in propotion to cube root of distance between tesla coil and induced coil.

Aquaponics是一種「請魚來種菜」的系統，節省人力，也節省水。簡單來說，魚的排泄物會汙染水質，進而讓魚隻死亡，但魚排泄物中的含氮廢物，卻是菜最好的養分。因此，只要把養魚的水抽到植栽床來澆菜，菜把多餘的水排回魚缸。 本實驗的主要目的，就是要穩定被我認定為影響魚隻存活的主因：pH值，在系統中加入足夠的蛤蜊殼，可抑制pH值得變化。而我也發現，除了pH值外，還有許多其他的因素，可能掌握著魚隻的生命。經由實驗，最後會得出一種最佳的系統比例，只要有了這個比例，就可以輕易的穩定Aquaponics初期的水質，有利於他所有架設系統的人。

本研究探討如何提升養殖於冬季降解亞硝酸不良的問題。養殖益生菌中潘朵拉菌Pantoea sp.可在冬天生長並降解水體亞硝酸，不同於其他菌其在低溫時生長較好但降解較差，顯示兩者無直接關聯，進一步得知溫度會影響Pantoea sp.細胞內代謝機制。水體中添加葡萄糖可使冬季亞硝酸降解能力多7倍，且不影響其生長，與文獻添加碳源會促進益生菌生長不同。比較各式糖類後得知單醣和雙醣皆可提升降解能力，其中單醣較雙醣好(單醣50%、雙醣95%)，而碳源可提升降解能力，推測因其影響細胞內TCA cycle運作。最後添加碳源做法適用各鹽度環境，具廣鹽性，對改善台灣冬季亞硝酸過高問題有高度應用價值。

第一代版的瓦斯爐節能熱水器製作是在爐架外圈包一層薄的銅片，增加熱收集面積，銲接銅管環繞外圍通水循環收集熱能，二代瓦斯爐節能熱水器製作的水路是在設計在瓦斯爐節能熱水器裡面，熱收集面積效率更佳，水道收集四面八方熱量，這樣產出的熱水溫度比一代高。我們將瓦斯爐節能熱水器做成內凹式斜面，這樣火到鍋底時會在將熱能反射到瓦斯爐節能熱水器斜面，讓熱能更集中在鍋底且防風效果佳。 系統功能方面，當瓦斯爐開火後，「瓦斯爐節能熱水器」溫度感測器偵測到溫度上升時，水循環便開始啟動回收熱量。設有水位偵測器，當儲水桶內水量有變化時，顯示介面的水位指示燈會顯示訊息。熱水管路有加裝洩壓閥保護，避免壓力過高造成危險。使用者也可以透過手機APP 監控系統情況。

每種物質都會結晶嗎？它們的結晶形態都相同嗎？在偏光鏡檢下是否都能呈現旋光性？如何培養出鹽的大結晶？鹽的結晶能做什麼應用呢？本研究利用自製的偏光顯微鏡和科學maker手機偏光顯微鏡的觀察得知：不是所有物質都能產生結晶，像白醋、米酒、蛋白、麥芽糖等無法產生結晶，而能產生結晶的鹽和醬油類沒有旋光性；糖、味精、紅酒和清潔類物質則有不同程度的旋光性。每一類的結晶形態也都不相同，可以用來判斷溶液中可能含有什麼成分。實驗中還發現，容器中的細小鹽結晶會跟主要培養的晶體競爭鹽分子，勤於更換容器才能養出大結晶。利用鹽的結晶可以做成具有療癒效果的偏光萬花筒、鹽燈、晶洞和鑽石樹等。

一群人依序入座在r列c行的座位中，每個人都盡可能地不坐在其他人的旁邊。我們定義在某一入座順序中，入座時的座位，相鄰座位都還沒有人入座，此時我們稱這個座位為滿意座位，否則就稱非滿意座位。明顯地，滿意座位不能與其他的滿意座位相鄰。而滿意座位分布狀況就是圖論中的極大獨立點集問題。 我們先以Excel VBA程式進行模擬，對座位排列進行確認及優化，再利用程式模擬的結果及根據極大獨立集定義，探討極大獨立集的基數狀況。當矩形的列數和極大獨立集基數固定時，我們運用極大獨立集零件拼接的變化求出極大獨立集的排列數。此外，當極大獨立集基數固定時，極大獨立集圖形藉由獨立點移動而擴大的規則，我們意外發現其狀況與費氏數列有關。

給定一個圓，可構作一四邊形ABCD，令其面積為T，而ABCD可由對角線形成的四個三角形，畫出四個內切圓，其圓心連線形成一長方形EFGH，令其面積為t，本研究目的即在討論T/t的比值範圍。 ABCD≈55.22平方單位 EFGH≈9.16平方單位 ABCD/EFGH≈6.03 ∠EFG=∠FGH=∠GHE=∠HEF=90∘