在高中數學第三冊中我們剛了解圓與球的性質，再加上國中常接觸到許多正多邊形其內切圓及外接圓的問題。這令我們聯想到：是否所有多面體都有內切球與外接球？若有，它們間的關係又是什麼？恰巧，化學老師在課堂上提到了由六十個碳原子構成的C-60 模型，而我們發現，以數學的角度來看，“C-60 ” 是由數個正五邊形與正六邊形所構成的立體圖形。在我們與數學老師討論後得知這種由十二個正五邊形與二十個正六邊形所構成的立體圖形就是所謂的”巴克球”，且從數學刊物上看到”巴克球為最接近球體的多面體”。這引發了我們的興趣，因此我們決定就這方面的問題展開討論。

自工業革命至今，人類對環境的迫害早已超過人類有文明以來的程度，石化燃料的使用甚至到達氾濫的地步，而石化能源的蘊存量日漸減少，科學家估計再 40 年人類會將所蘊存的石油耗盡，沒有了能源，難道所有的動力都將停擺？答案是否定的！生質柴油，顧名思義為來自生物性的柴油，它源自於自然的油脂，如：家庭廚餘所剩的油以及一些植物脂肪、動物脂肪、及其它脂肪酸…等。因此，生質柴油沒有能源危機，更是取之不盡，用之不竭，來自於天然。生質柴油（甲基酯）的反應原理是根據有機化學課本 12－1 酯類，當酸與醇在強酸或強鹼當催化劑下加熱，即生成酯類。本實驗是以油脂與甲醇、乙醇，利用氫氧化鈉作為催化劑反應製成「生質柴油」，當油酯/醇之莫耳比為 1/6，而氫氧化鈉的量控制在 0.5～1％為最佳結果。另外我們發現：高純度的米酒不但可以作為製作生質柴油的原料，還可以直接添加至生質柴油中製成「米酒生質柴油」，這便是一個可自然再生的新能源。

液體中之球體運動與液體的黏滯性有關，本實驗找出球體半徑與終端速度之間的關係。利用攝錄機作為紀錄工具，拍攝三種材質（壓克力、玻璃、水晶）的球體在沙拉油中的自由落體過程。使用電腦影像處理軟體將影像分解成幅影像，時間的解析度為1/30秒。測量球體的高度與時間，分析高度與時間的變化情形，發現終端速度與球體半徑之間的關係。 流體中之運動方程Fdrag = -k1V，無法符合實驗結果。我們的實驗結果顯示油中的自由落體的運動方程應該是Fdrag = -（k1V+ k2V2）。由不同材質的壓克力球（~1.18g/cm3）、玻璃珠（~2.47g/cm3）與水晶球（~2.66g/cm3）所獲得的終端速度（Vt）與球體半徑（a）的關係為a3(ρ-ρ') = 0.00003（a Vt）2 + 0.00021（a Vt） + 0.00575，其中ρ與ρ'分別為球體密度與沙拉油密度（0.90 g/cm3）。 再者，在相同半徑的條件下，密度越大的球體終端速度越大，在靜止下落後，越久達到終端速度。 The motion of a sphere which is falling through a fluid is subject to the fluid viscosity. In this study, we find out the relation between the radius of a sphere and the terminal velocity. We used a digital camera to record the sphere's descent in the oil. The three kinds of sphere we choose are acrylic（~1.18g/cm3）, glass （~2.47g/cm3）and crystal （~2.66g/cm3）. Frame-by-frame analysis of the video footage yielded rough estimates of the sphere's location within 1/30 seconds accuracy for statistically consistent results. By measuring the location and time and analyzing them, we find out the relation between the radius of a sphere and the terminal velocity. The expression of the drag force,Fdrag = -k1V, is not cosistent with our results. The study indicates the expression of the drag force should be Fdrag = -（k1V+ k2V2）. The expression for the terminal velocities of the three kinds of sphere is of the form：a3(ρ-ρ') = 0.00003（a Vt）2 + 0.00021（a Vt）+ 0.00575, where a is the radius, ρ is the sphere density and ρ' is the oil density（0.90 g/cm3）. In addition, if the radius is the same, the terminal velocity of a denser sphere is higher and the time to approches the terminal velocity is longer.

能源危機日益嚴重，開發再生能源成為當務之急。在諸多的再生能源之中，太陽能最易於使用，且可源源不絕的不斷取得利用。但目前太陽能電池的效率始終不高。其中重要的原因是太陽本身的頻譜多為短波長，並不適合絕大部分頻譜響應較佳，多為長波長的太陽能電池。目前改善效率方式，多為改變太陽能電池的頻譜響應以配合太陽之頻譜。本研究提出反向思考的概念，藉由頻譜轉換的方法，改變照射在太陽能電池上的太陽光頻譜，以提升太陽能電池的效率。本研究利用一種珊瑚礁的螢光蛋白質（DsRed）以及人工合成的螢光染料（Cy-5）最為本研究的頻譜轉換的材料，加於低成本，目前市場佔有率較大的單晶矽太陽能電池上，經由理論與實驗的結果顯示，增加的發電效率約為3~5%，證實利用頻譜轉換的概念確實可以提升太陽能電池的效率。Energy crisis has become more and more serious in recent years, which makes recycled-energy development is a must. Among different recycled energies, solar power has two advantages, that is, easy-to-use and endless supply. However, the conventional solar cell makes poor use of the solar spectrum because the solar spectrum is mainly composed of short-wavelength, which can’t fit to most of solar cells which is more sensitive to long-wavelength. Currently, the major method to improve the efficiency is change the function of spectral response, such as concentration lens, tracking devices, and antireflection coating. Up to now, no one notices the possibility of changing solar spectrum yet. This research provides an insight into this issue. Instead of changing the function of spectral response, I changed the solar spectrum, which irradiates solar cells through spectrum conversion to improve solar cells’ efficiency. This research uses one kind of coral fluorescence proteins (DsRed) and one kind of artificial fluorescence dyes (Cy-5) as the materials of spectrum conversion. Then coat them on the low-cost and high-market-share mono-crystal-Si. According to the theories I researched and my experiments, the improvement of the efficiency is about 3~5%, which proves it is actually useful to elevate the efficiency of solar cells through spectrum conversion.

從國中理化課本陸續學到物質密度求法、溶液濃度求法、比熱測定法、物質分離法、液體蒸發以及熱量計算法後，使我們很想利用這些科學知識和方法進行對國產酒的試驗，以達學而致用的願望。

那一種昆蟲是惡作劇的最佳材料呢？無疑地就是蟑螂──存活達三億年之久的活化石──；億萬載來，環境的變遷不可不謂之巨大，而這些指頭般大的生物，竟能在物競天擇下生存，引發我們許多的遐想；就在好奇心的驅使下，展開了一連串別開生面的實驗研究。

The Online Course Management system was developed in 2012 by George Moon to address the issue of creating course books at Burnside High School in Christchurch, New Zealand. The course books are designed to inform students, staff and parents of the many courses that are available for students to choose for their next year of study. In the past, the system that the school used consisted of large amounts of paperwork and duplication. Not only did this system require a lot of effort from staff, but the course book cost the school thousands of dollars to produce, as it had to be sent off to be published into a large book that would be read by students for a week, then likely thrown out. This year the school decided to digitise the course book, so that students would look at their courses online. Earlier this year, the school believed that the new School Management System (SMS) ‘KAMAR’ would be able to handle all of the necessary information, however this was not the case. Because of this, they needed a simple solution that would collate all of the course data, and then output it as a course book. I developed my project to do this. It is a web based program that is accessible by staff on their computers which enables them to enter in all of the course and assessment data for their departments. As it is all securely stored on a central database, it reduces duplication and staff workload, as well as the added environmental bonus of less paper being used. The program also outputs data in a number of ways including as a coursebook PDF (digital document which can be uploaded or printed), an Excel spreadsheet and a webpage for easy viewing. It can be sorted or printed by different categories (such as level, faculty, department), which proved to be a very useful feature. Following some research on areas such as design principles, browser compatibility and screen resolution (computer screen size), the program was designed to make best use of this this information. For example, most of the computers that staff would access the website on were of a similar size screen, so I made sure that my website worked well for them. I also used my research on design principles to try and create a simple, clean interface that users with limited computer skills would easily be able to navigate around. The outcome was real, as it was used by the school to generate their coursebook this year. Following a 95% student completion rate of course selection many months earlier than previous years, the system (although it had some issues) was pronounced a success, and the school is looking to use it in the years to come. There are a number of steps I am looking to take in the future with this program including the potential sale to other schools, so they can take advantage of the features it has to offer.

「點積」這個名詞，是為了稱呼上的方便，由作者自定的名詞。顧名思義也就是：「集點求積」的意思。在求算一例圖形的積( 包括：線長、面積、體積) 時，「點積法」與過去的求積方法有很大的不同，它只計算圖形裏的「等距點（即方格點）有多少，就可求得其積。

線性計劃在數學中是一支新起的部門，它主要的基礎是受193年J.von Ncumann與W.Lcntief 之經濟理論影響，而於1940年為F.L.Hitihcoch與 L.Kantorovitch 等人所建立，而今日在工程學上與經濟學上都廣泛的應用。所謂線性計劃乃在求定義於有界多面凸集合之線性函數；f( x1)C1X1+C2X2＋……＋CnXn＋d 之極大值與極小值的問題。本文主要將高中數學程度所提及之二維空間中線性計劃的理論推廣到 n 維空間。

某日偶而看到由天花板懸掛下來的日光燈在振動，連想其振動該為週期性，但其週期到底與那些因素有關？於是引起探求的興趣，乃完成如下的實驗。

香蕉弄蝶是危害香（芭）蕉樹的害蟲之一，屬外來物種，一年約有4~5 個世代，以蛹期越冬。成蟲在清晨及傍晚出沒覓食，母蝶有產單顆卵於葉背、面以引開寄生蜂寄生達到保護群聚卵的行為。幼蟲有築巢行為，對食草有相當的專一性。由於築巢位置有特別的選擇特徵，我們認為利用此特點，可發展出對香蕉弄蝶的防治方法。

這份科學探究，最早是想要為那些在停電狀況下需要與外界聯繫的人們，趕緊取得電力為手機充電。電力的取得條件是，完全沒有外界能源支持，必須自力生電。我們上網搜尋了好多可用的發電設備，風力、太陽能都有體積大、需要看天候的不利因素。因此我們決定自力研發，設計了這部利用人們走動時的能量，經由傘齒輪輕易轉動發電的「漫步發電機」。它能穩定的送出5V的電力，經過測試，不管是傳統手機或智慧手機都能順利充電。這部發電機以USB介面輸出電力，因此所有以USB為介面的設備都能使用，像是MP3、LED燈甚至3號4號電池都可以應用得上。將來還要將這發電機安裝在滑板車上、嬰兒推車上、買菜推車上，一定可以給人們帶來更多的便利。