全國中小學科展

2024年

多面體滾漆問題

本研究探討了柏拉圖多面體滾漆問題,並且延伸至半正多面體進行研究。正多面體中分別為正四面體、正六面體、正八面體、正十二面體、正二十面 體。研究中證明柏拉圖多面體滾漆問題中的地圖限制以及有解充要條件。為了簡化問題難度,我們先簡化遊戲規則使「掉落」情況不被討論,再轉換回原規則的問題。在研究中我們於正四、六、八、二十面體使用原本的遊戲地圖,而其他延伸研究則自創地圖進行討論。

使用蓋亞資料庫探討球狀星團中天琴座RR型變星的組成

球狀星團是星體分布緊密、金屬豐度低的星團。天琴座 RR 型變星經常出現在球狀星團中, 且在恆星演化上有重要意義。僅管目前對此類型變星的其週期、亮度等研究十分完備,分析其組成比例的研究仍略為缺乏。使用 GAIADR3資料庫,首先根據目標星團周圍星體數量繪製熱點圖,求出星團視半徑後,分析二十個球狀星團的天琴座 RR 型變星組成百萬分率,發現影響的主要參數依序為星團年齡、星團半徑與金屬豐度,並分別提出假說解釋 其原理。透過調整三個參數的係數,定義出能代表三者或其中二者共同影響的參數,使變星組成比例成為輔助判斷星團相關參數的依據。另外討論偏離主要趨勢星團的原因,且亦探討以熱點圖概念求出的視半徑和文獻之出入之處。

Anti-forma Chitogel

Formaldehyde is an air-borne, carcinogenic indoor pollutant. It may cause adverse effects on human health such as irritation of eyes and respiratory system. Shells of hermetia illucens, Black Soldier Flies (BSF) are leftovers when the insects mature from pupae to adults. BSF shells are rich in chitin which can be converted into chitosan by demineralisation and deacetylation. Chitosan and its ammonium salt (chitogel) can remove formaldehyde via condensation of water. In this investigation, the efficiency of removal of formaldehyde by different substrates were compared including shells of BSF before and after demineralization, deacetylation and action of vinegar; and common commercial products and Anti-Forma Chitogels made from shells of BSF and some crustaceans. Anti-Forma Chitogel of BSF was found to be effective in removing (91.2%) formaldehyde (1:20 by mass) among shells of BSF with different treatments and its efficiency was better than all commercial products tested. Concentration of formaldehyde in the container with deacetylated Anti-Forma Chitogel is 0.54 mg/m3. It removed 74.8% of formaldehyde compared to the control (2.14 mg/m3). Concentration of formaldehyde in the container with Anti-Forma Chitogel without deacetylation is 0.76 mg/m3 . It removed 64.5% of formaldehyde compared to the control (2.14 mg/m3). The Anti-forma Chitogel of BSF was found to be eco-friendly with high formaldehyde removal efficiency when placed in a drawer (removal of 54.8% of in 24 hours), the chamber of a newly renovated room (removal of 84.9% in 30 minutes reducing the conc. of formaldehyde from 0.53 mg/m3 to 0.08 mg/m3; cf. the safety limit of formaldehyde <0.125mg/m3) and drawers of a new wardrobe (removal of 83.7% at 20.2oC in 1 day reducing the conc. of formaldehyde from 0.49 mg/m3 to 0.08 mg/m3 & kept the conc. of drawers below 0.125mg/m3 most of the time over a month when temperature was below 21oC). Conc. of formaldehyde in air-tight boxes (5g of construction adhesive in 9.3 dm3) with air purifiers with and without Anti-forma Chitogel as filter before and after 3 hours was reduced by 44.5% (from 6.25mg/m3 to 3.47mg/m3 ) and 27.7% respectively showing that Anti-forma Chitogel as filter in air purifier outperformed that without by 160%. Besides, anti-forma Chitogel is antibacterial, so it would also kill bacteria when used in air purifiers. [1] proving that Anti-forma Chitogel is effective in removal of formaldehyde on the spot and can be applied to households. It can also help achieve Target 3.9 and 12.5 of the Sustainable Development Goals of the United Nations.

攻角對水漂跳動行為的力學分析

此研究是以實驗方式,驗證理論模擬中指出水漂在不同入水模式下,入水攻角為 20 度時皆可產生最佳的彈跳效果。因此我以壓克力板作為模擬水漂的模型,設計了以下四組操作變因,分別是入水攻角、水的流速、水漂邊界形狀以及接觸面的粗糙程度,接著透過Tracker 分析壓克力板的質心彈跳高度及運動軌跡,再利用 Excel 分析數據,找出其中的運動相關性。最後透過座標轉換,可以利用此實驗來分析打水漂的運動行為,成功發現入水攻角在 20 度時的確有最佳的彈跳效果,並以此實驗結果來優化打水漂的運動行為。

雙層式水平軸風力渦輪機葉片結合尾流之探究

本研究主要目的為改變風力渦輪機的結構,將原始的單層葉片設計改為雙層葉片,當風流過第一層葉片時將產生尾流效應,使葉片後氣流產生偏轉,若將第二層葉片更具此氣流偏轉區域調整,將能有效的提升發電效率。根據實驗結果顯示,葉片後的尾流造成氣流偏轉的角度約為 15 度,因此當渦輪機的兩層葉片位於理論最高的相位夾角時,應再減去 15 度的尾流偏轉角,該夾角才為最大的發電效率配置,基於此結果所設計的渦輪機,儘管與單層葉片渦輪機具有相同的葉片數量,卻能提升發電效率約 40%,同時相關文獻指出,葉片的成本約佔整體發電機總成本之 14%,因此透過使用本研究之作法,預估可降低約 18%的成本,整體而言,本研究之設計不僅能提高風能發電效率,同時將有效的減少成本,未來具高度前瞻性。

Beyond Limits: An Intelligent Wheelchair for Inclusive Living

The aim of this project is to enhance the mobility of individuals with disabilities, particularly aiding them in navigating stairs and challenging terrains. Across the world, powered wheelchair employ various methods, primarily categorized into two: 1) tracked mechanisms and 2) robotic wheelchair utilizing intricate robotic systems. The design presented by our team belongs to the latter category, which is recognized for its lighter build when contrasted with the former. However, despite its lightweight structure, this wheelchair design incorporates equipment that renders it more cost-effective and practical than conventional designs within the same category. Our design integrates three distinct mechanisms to adjust the height and center of mass of the passenger during stair climbing and maintain balance and surface contact. Utilizing an array of sensors, it continuously monitors the position of the person on the wheelchair and the wheelchair on the surface. This data guides adjustments in the mechanisms, ensuring stability. This innovation harbors the potential for enhancing various functionalities, including: GPS integration for user navigation. Real-time monitoring of vital signs (e.g., heart rate, blood pressure, body temperature). In an emergency, this data can be transmitted to ambulance centers to pinpoint the individual's location and immediate assistance. A simplified ambulance request system, accessible via a single button press. Overall, this innovative wheelchair prototypes aims to revolutionize accessibility, granting enhanced mobility and independence to individuals with disabilities.

Straw manufacturing for epidemic prevention

Recently,thefeedpricesforlivestockfarmshavebeencontinuouslyincreasing, while the prices of calves have been declining, leading to many livestock and dairy farms facing financial losses. If livestock farms are affected by diseases such as foot-and-mouth disease, they suffer significant losses. This is because reducedproductivityinlivestocknotonlyaffectstheirproductionbutalsoentails substantial costs for vaccines and treatments. Therefore, there is a need to explore how to effectively prevent diseases, focusing on common diseases in cattle such as subclinical mastitis and mastitis, and alleviate the burden on farms economically and environmentally. This study aims to investigate the production of bacterial growth-inhibiting straw bedding using substances such as illite and charcoal to contribute to disease prevention.

智慧車的「 聲」存之道

本研究探討聲源的追蹤方法,開發出一輛能自動轉向聲源方向的智慧車。首先,我們先理論推導出聲源方向的演算法,主要是透過兩個麥克風接收聲源訊號的時間延遲差,來求出聲源方向。然而音源訊號有大小聲的問題,我們採用單範互相關函數,能準確估算出兩個麥克風接收聲源訊號的時間延遲差。然後,我們在 ESP32的平台上開發演算法程式,結合麥克風和車體,利用單頻 1kHz 單頻訊號進行參數最佳化調整。從量測結果發現,智慧車能準確的估算出音源方向,並在動態展示影片連接中,智慧車展現快速追蹤音源,並讓輪胎準確的轉向音源方向。

Strict Inequalities for the n-crossing Inequality

In2013,Adamsintroducedthen-crossingnumberofaknotK,denoted by cn(K).Inequalities between the 2-, 3-, 4-, and 5-crossing numbers have been previously established.We prove c9(K)≤c3(K)−2 for all knots Kthat are not the trivial, trefoil, or figure-eightknot.Weshowthisinequalityisoptimalandobtainpreviouslyunknownvalues for c9(K).

兩組直線所構造的三角形外心軌跡性質與推廣

本研究源於 2022年數學雜誌《CruxMathematicorum》的一道四邊形動態幾何問題,我們先將此問題設定為三角形,利用綜合幾何方法給出了兩種構圖條件下的三角形外心軌跡皆為圓弧,並且發現兩種圓弧的變換關係以及豐富有趣的性質。值得一提的是,分別對三角形的三個頂點輪換進行第一種構圖得出三個圓弧,這些圓弧恰可組合成三角形的九點圓。回到原始問題的四邊形,我們構造了兩個三角形,透過巧妙轉換頂角與直徑圓變換而給出外心軌跡所在圓弧的兩個定點而解決此問題。 最後探討三角形的形心之軌跡為圓或橢圓的幾何結構是什麼?先考慮具有定角的形心切入,結果發現垂心的軌跡是橢圓,但內心與旁心的軌跡並非二次曲線。再從外心與垂心思考,我們進而給出了該軌跡的內在的幾何結構是歐拉線。值得注意的是,歐拉線上的任意點之軌跡恆為橢圓,並無拋物線或雙曲線。