任意等角六邊形𝐴𝐵𝐶𝐷𝐸𝐹之6邊的延長線，即會得到兩個正三角形Δ𝐼𝐽𝐾、Δ𝐼′𝐽′𝐾′，其中三組對邊以[(𝑎,𝑏,𝑐),(𝑎′,𝑏′,𝑐′)]表示，則三組對邊均相互平行，任兩相鄰邊長的和必等於其對邊長的和(𝑎+𝑏′=𝑎′+𝑏）（𝑏+𝑐′=𝑏′+𝑐）（𝑐+𝑎′=𝑐′+𝑎)，則有以下成果： 1.若已知四邊長度，且其中三邊相鄰，即可決定唯一之等角六邊形。 2.三組對邊都相等或都不相等，才能決定一個等角六邊形。 3.兩組有相同公差的數列，各取連續三個正數為邊長，則可決定唯一的等角六邊形。 4.一組等差數列中，任取6個連續正數(𝑎1,𝑎2,𝑎3,𝑎4,𝑎5,𝑎6)為邊長，可形成兩個相異的等角 六邊形([(𝑎1,𝑎2,𝑎3),( 𝑎4,𝑎5,𝑎6)]、[(𝑎1,𝑎3,𝑎5),( 𝑎2,𝑎4,𝑎6)])。 5.當等角六邊形邊長為完全平方數時，可以求出一些特列。 6.討論等角六邊形的面積與用相同大小正三角內鑲崁的個數。

Agro-guard aims to revolutionize disease identification and community-based projects in the field of agriculture. Integrating Machine learning, Computer vision, clustering, and community-based technology, this project helped farmers to detect their plant disease with their solution and for early warning of plant disease which was spreading in their community which helped in crop management. The research project is divided into three parts.First,Integrating Machine learning to detect and classify plant disease with their solutions.Second,Integrating Density-Based Spatial Clustering of Applications with Noise (DBSCAN),to identify disease and analyze the pattern within agricultural regions.Third,Establishing notification system to notify real-time alerts to farmers about disease spreading in particular region.The research is crucial because it solve one of the crucial problem of our community which is untimely detection of disease.The finding of the research highlight the effectiveness of Agro-Guard framework in early disease detection and community detection.The machine learning models achieved high accuracy in identifying common plant disease and clustering results the pattern in diseases that were very important for notifying the community.The significance of these findings is that it can build powerful system which will overall grow the production of crops and plants due to timely update of the disease prevailing in the community.It contributes in sustainability production of crops and plants which ultimately ensure the good livelihood of farmer.

本研究希望能找出一種能使多邊形車輪平穩前進的曲線方程式。由於車輪之中心高度不變時即可達成平穩前進的目標，本研究先是追蹤正多邊形的中心正下方與該圖形的交點所形成的曲線，得出此曲線圖形的方程式。接著因圓內接多邊形可切割成多個直角三角形，利用畢氏定理與三角函數推導，得出圓內接 n 邊形車輪的中心在同高度下滾動時，中心正下方與該圖形的交點之曲線恰為懸鏈線方程式。 在刻劃完正n邊形的情況後，進而推廣至一般圓內接 多邊形以及勒洛多邊形的相關特性。在未來，將可以為多邊形車輪的設計與運行提供新的思路，並可能在交通、機械設計及自動化設備中發揮重要作用，了解懸鏈線的特性將促進相關技術的創新與發展。

本研究觀察臭巨山蟻（Camponotus obscuripes）處理同伴屍體的特殊行為。我們在三年間注意到，螞蟻基於巢穴衛生有「屍體清除行為」（necrophoresis），但在特殊狀況下 臭巨山蟻還會搶奪同伴屍體和搬屍繞行行為。我們進行一系列的實驗觀察，嘗試證明一些假設，最後得到以下結論： 一、臭巨山蟻在搬屍繞行同伴屍體時的行為與「屍體清除行為」有所不同，繞行行為通常在探索新環境時出現。牠們會將同伴屍體從棄屍場所搬出、舉起屍體在新環境四處移動，還會將屍體散佈在新的環境中，最後再將屍體移回棄屍場所 。 二、螞蟻在搶奪屍體的選擇上，可能與死亡時間有關。 三、螞蟻與其搬運的屍體之間不存在特定的配對關係。

Problem • Rice is the primary cereal crop consumed by nearly half the population worldwide • By 2050, there will be a 50% increase in demand for rice • The world’s poor populations depend more on rice, both for income and consumption, than any other food. Rice is the single-largest source of employment and income for rural people • Worldwide, 51–82% of agricultural crop yield is lost annually due to abiotic stress due to climate change • Climate change causes extreme temperatures, erratic rainfall, dangerous droughts, and increased salinity from rising sea levels Solution • To adapt to abiotic stress, rice has intricate signaling pathways, particularly those mediated by the phytohormone abscisic acid (ABA), that cause an increase in stress tolerance • Clade A genes of the Protein Phosphatase 2C (PP2C) gene family are known to be negative regulators of the ABA signaling pathway. • “Deleting” these genes activates the ABA pathway and increases stress tolerance in rice without inducing stress CRISPR gene editing technology is the ideal solution Research Goal • While the role of PP2C genes in stress response is recognized, there is a gap in understanding the specific genes within this family that contribute significantly to stress signaling. Furthermore, there is a need for a detailed investigation into the effects of targeted CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) genome editing on rice stress response pathways.

According to the 印尼n Association of Olefin Aromatic and Plastic Industries/INAPLAS, 2019 national plastic consumption still relies on plastic packaging at 65% and surprisingly, around 60% of plastic waste is absorbed by the food and beverage industry. The waste has been widely sought to be environmentally friendly, one of which is by developing biodegradable packaging. The purpose of this research is to make durian peel cellulose nanocomposites impregnated with TiO2 NPs, to form antibacterial properties against E. coli wild type and resistance. In this research, there are research methods consisting of nanocomposite synthesis, PSA test, FTIR, physical characteristics test and resistance test. The results analyzed that the nanocomposite nanocellulose-TiO2 NPs was successfully made using a 1:1 ratio and had a particle size of 458.7 nm based on the PSA test, which is classified as a nano size. The success of nanocomposite synthesis was proven by the results of FTIR analysis, which showed the formation of 698.65cm-1 and 1633.99cm-1 spectra, indicating the peak of TiO2 NPs and O-H functional groups on TiO2 NPs, as well as 1028.98cm-1 and 1158.42cm-1 showing C-O and C-O-C bonds in cellulose. The antibacterial test performed showed no significant activity in disc diffusion and well diffusion tests against E. coli wild type and resistance. This is potentially caused by inhomogeneous particle size variation. Physical characteristics test showed that the tensile strength test (0.075 > 0.0125 MPa) Durio Nano-Pack is superior to styrofoam, but the compressive strength test (0.125 > 0.875 MPa) shows the opposite. In this study, nanocomposite has a potential innovation that provides good mechanical properties and has a dual function mechanically as bio-based food packaging and chemically as antibacterial. Further research is needed to improve the particle size homogeneity of nanocomposites, modify the impregnation method, so that it has the potential to develop multifunctional materials that excel in various applications.

Due to widespread water shortages, there is an increasing need for innovative water conservation strategies, such as reusing greywater from laundry. The World Health Organization (WHO) recognizes greywater as suitable for plant irrigation, but commercial laundry detergents contain synthetic chemicals that can harm both the environment and plant health. Soap nuts, derived from the Sapindus mukorossi tree, offer a natural alternative. Their pericarp is rich in triterpenoid saponins, amphiphilic compounds, composed of hydrophilic sugar group and hydrophobic triterpenoid sapogenins. These saponins mimic the chemical structure of surfactants in detergents, allowing soap nuts to act as natural foaming and surface-active agents in water. As a result, soap nuts have long been used as a sustainable option for shampoo and laundry detergent in many Asian countries (Sochacki & Vogt, 2022). Greywater, an often overlooked resource, is generated from household activities like laundry, showers, and basins. Unlike blackwater, it contains lower levels of pathogens and bacteria. However, due to a lack of awareness, greywater is frequently mixed with blackwater and directed to the same sewage treatment systems (Greywater Systems: From Recycling to Filtration, n.d.). Greywater accounts for 50-80% of a household’s daily wastewater (Wong, 2011). Repurposing greywater offers a promising and sustainable solution to address water conservation challenges.

本研究透過探討發現高齡化族群在肢體靈活度逐漸下降的問題，且在人們的生活中是不可或缺的需求就是「照護」，卻沒有非接觸式的工具能幫助到高齡化族群及協助照護者，如果將這樣工具放置在桌面、輪椅及病床，加上人臉追蹤鏡頭及人體工學的尺度，搭配自動調整符合每個人適合的角度並且隨時守護長者，因此我們設計出能隨時可以守護的「非接觸救星」。在研究中設計非接觸救星左右及仰角、人臉追蹤、LED燈光及外加功能等實驗，為最終設計之參考依據。透過研究之結果未來依照現階段科技及智能互連應用進行創意發想，並且時現在更多不同辨識下之情境進行守護及通知照護者，讓高齡化社會所面臨之問題可以得到更完善的解決。

The billiard table is a cuboid with integer side lengths. A point-wise ball moves with constant speed along segments making a 45◦ angle with the sides and bounces on these. We allow the ball to start from any of the 8 corners, resulting in a periodic trajectory known as a corner path. The geometry of the path depends on the artihmetic properties of the side lengths (for example if these are pairwise coprime). Points of contact between the ball and edges, known as edge points, are inves- tigated and their characteristics like distribution explicitly described. This generalizes a previous work by Perucca, Reguengo da Sousa and Tronto of University of Luxembourg.

隨著全球咖啡市場擴大，永續的咖啡生產成為必須探討的議題。咖啡生產過程中會產生大量富含蛋白質與抑菌成分的副產物和廢棄物，有潛力可做為膠膜和塗層的原料。本研究從生咖啡豆中萃取出粗蛋白質，將其與海藻酸鈉混合烘乾成膠膜，再進行抑菌與水果保鮮和水蒸氣阻隔測試。 由結果得知：咖啡豆蛋白膠膜液對大腸桿菌有抑制生長的效果。沒封膜的蘋果切片失水率 12.72%，有膠膜封口的失水率在 6.84%~8.47%，比沒封膜的失水率降低 46.5%~33.1%，顯示膠膜保水性佳，可提高保鮮效果。微波加熱試驗沒封膜的水蒸氣散失率為 2.45%，膠膜試驗組中最 低為 0.15%，比沒封膜的散失率降低 93%，顯示具有良好的水蒸氣阻隔性。 本研究結果顯示咖啡豆蛋白質膠膜有抑制大腸桿菌生長的效果和良好的氣體阻隔性，可作為可生物降解的食品包裝材料，以替代傳統保鮮膜，有助於減少環境污染。

本研究從一道科學班入學考題出發，突破傳統代數解法限制，提出創新的幾何作法，並系統性推廣至更廣泛的圖形。透過將內接三角形分為【點邊邊】，與【邊邊邊】的兩種類型。結合使用 GeoGebra 進行作圖與輔助推理。使用正弦定理、餘弦定理與相似形等幾何原理進行推導。探討其內接三角形與周圍多邊形的面積關係。從長方形開始，逐步推廣與觀察，歸納出面積公式的形式，並進一步應用至其他凸多邊形，建立更普遍性的面積關係公式與解題策略。

本研究研發出最適植物萃取液配方：洛神花3滴、黑豆1滴、紫莢長豆2滴、紫色高麗菜2滴與蝶豆花7滴。建構出具穩定性、連續性與高辨識度的天然酸鹼色階圖卡，於pH1～14範圍內產生自然清晰的協同變色反應，顯色漸層分明，辨識度高，成功取代市售指示劑。 探究初期以水萃法提取植物色素，觀察其顏色與稀釋後的色彩變化；接續將各萃取液滴於 pH2～13標準溶液中，運用電腦影像軟體分析RGB色彩參數，量化其變色趨勢。 探究發現，市售指示劑於全pH範圍內的顯色反應缺乏連續性與辨識度。因此更進一步評估植物色素間的協同效應，調整配方比例，提升色階表現整體性。最終優化配方具清晰的變色反應，整體效能優於市售指示劑，展現教學與綠色化學之應用潛力。