k(2αβ ,α2 ? β2,α2 + β2 )是大家熟悉畢氏定理的通式解，且一般書籍的証明大都採用代數的手法證明。以國中生而言，上述的代數方對國中生來說不夠直接且較無推展的實用性。因此幾何觀點出發發展另一種思考方式，利用角平線的性質給予畢氏定理比例解另一種全新的詮釋，並賦予比例解中的參數α 、β 在幾何的意義。在推理的過程中，我們得到一個相當有用的對應關係：一個有理數對應到一個直角三角形、兩個有理數對應到海倫三角形，再將此對應關係運用到各種幾何圖形上面，即可證明出他們所對應的通式解。最後我的興趣鎖定在海倫三角形、完美海倫多邊形與超完美海倫多邊形上的做圖方法上，善用我們所發展的對應關係，上述的問題皆可迎刃而解。k(2αβ ,α2 ? β2,α2 + β2 ) is a popular formula in Pythagoras Theory, often proved in algebra approach among books. Nevertheless, in light of junior high students, the aforementioned algebra method is neither direct nor practical. Hence, a different thinking method is derived from geometry perspective, using the straight line concept to reinterpret Pythagoras Theory and define the geometric meanings of α andβ . In the process of logical development, a useful correlation emerges: a rational number correlates with a straight-angled triangle, and two rational numbers correlate with Heron Triangle. This correlation can be applied to all kinds of geometrical diagrams to prove the correlated homogenous solution. Ultimately, my interest lies in the diagram methods of Heron Triangle, Perfect Heron Polygon, and Super Perfect Heron Polygon in order to apply our developed correlations to solve the above mentioned problems.

在台灣，冷氣已成為日常生活中不可少的必需品，但冷媒的使用卻破壞了地表的臭氧層。科技如何能與環保相結合，是促使我們製作這台多功能冷暖氣機的動機。

The purpose of this experiment is to determine whether or not wood can be used as an alternative testing method for sunscreens and which species of wood are good for this objective. This will be accomplished by applying varying strengths, or SPFs, of sunscreens onto thin wood veneers. They will then be exposed using a weatherometer, in which real light and sun conditions will be simulated. Using a device called a Pulmac, the samples of wood will be pulled apart from the centre at zero span. Based on the consistency of the strengths, it can be determined how the wood reacts to the sunscreen and whether that species of wood is suitable as a testing medium. Trees are an important commodity which enrich the lives of many people, particularly those who live in British Columbia. They provide the means of living and recreation for numerous people, whether it is employment, business, housing, or camping. Since trees are a renewable resource, they are convenient and realistic to use for testing. There are two possible extensions to this project. If the active ingredients in sunscreens can be determined, then we may be able to use these elements to create a new type of stain for fences and other structures. This could make the necessity for painting less frequent, creating cheaper options for the homeowner. The second possible extension of this project is to use the results to as an initiative to reduce the amount of animal and human testing done by manufacturers. This is important, as animal testing not only causes unnecessary pain, but often the results are not very accurate. Overall, I determined that this method of testing sunscreens would work quite well, especially with the following species, listed in decreasing order. 1) Yellow Cedar 2) Yellow Poplar 3) Maple 4) Hemlock These results were based on how tightly grouped together the means of the strength values were for each species. The closer they were, the more consistent that type of wood and therefore the better they are for testing. Overall, I think this method of testing sunscreens would work quite well, particularly with the yellow cedar, maple, yellow poplar and hemlock, as they resulted in fairly consistent strength values. Generally, the sunscreens with a high SPF, or Sun Protection Factor, resulted in a lower strength loss than the sunscreen with SPF 15. In addition to proving that sunscreen is a good method for preventing UV rays from reaching the skin, this experiment has also confirmed that there are other methods of testing sunscreens, which can be researched further. Along with my main presentation I will be showing various graphs, statistics, and pictures. They will be supplemented by a booklet of “Commonly Asked Questions and Answers” and species descriptions for each type of wood.

This project aims to improve the quality of toilet hygiene. The product designed should fulfill the requirements of being an environmentally friendly, user friendly and economical toilet seat system which guarantees the safety and hygiene of the toilet. This project also aims to discover the efficiency of the toilet seat system in eliminating pathogens through conducting various experiments.\r In this project, the photocatalytic property of titanium dioxide is applied. When titanium dioxide is under exposure to ultraviolet radiation, they generate free radicals, which are efficient oxidizers of organic substances. Also, research has shown that the safest ultraviolet light used will be UVA. Thus, by using titanium dioxide paint under exposure to ultraviolet light to oxidize pathogens and toxins, the aims will be achieved. Other than that, experiments will be conducted to explore the efficiency of titanium dioxide under exposure to UV radiation in eliminating pathogens by counting the number of bacteria on the toilet seat system after different time intervals the seat system has been turned on.\r The procedure of constructing the product includes drafting the product, purchasing the appropriate apparatus and materials, constructing the prototype, and checking if the product fits the goals set. Lastly, improving the design based on the flaws found during the checking procedure, as well as checking the product to see if it fits the original goals set.\r The procedure of the experiments aimed to explore the efficiency of titanium dioxide under exposure to UV radiation in eliminating pathogens conducted includes\r counting the number of bacteria on the toilet seat system after different time intervals by inoculation of bacteria on the agar plates.\r Test results showed that the number of bacteria had a steady and notable decline after different time intervals. Results also showed that bacteria would be thoroughly terminated after the system had been turned on for at most one hour. The information was then used to set the delay timer to restrict the amount of time the ultraviolet lamp was turned on to save energy.\r Moreover, the toilet seat system has also been improved so that it will complete the automatic cleaning procedure even without the user lowering the toilet seat. This improvement was made so that the product could be more convenient to toilet users.\r The system also deodorizes the toilet as the oxidization of bacteria and organic substances reduces the putrid odor released by them when they carry out chemical reactions.\r In conclusion, the project succeeds in accomplishing the goals set and is capable of improving the quality of toilet hygiene, especially in common households. The project is also successful in finding out that the toilet seat system is efficient in eliminating pathogens.

在這次的防霧實驗中，我們調查了家鄉漁民常用的防霧方式、澎湖常見植物的防霧效果與探討日常常見的防霧妙方。從簡易測試與透明度分析儀的結果來看，我們發現天然防霧塗料對「玻璃」能有效的防霧，但是對「壓克力」材質的介面並沒有明顯的防霧效果；日常的化學防霧材料對兩介面都有不錯的防霧功效。

The results of the thermal diffusion experimental show that the separation efficient\r increases with increasing ΔT, but decreases with increasing Q at C0 constant. When\r Q is kept constant, the efficient of change ΔT are small, and the maximum at C0 about\r 545 mg/L. The purification efficient of raw water for thermal diffusion is low.\r And it is high energy consumption, difficult operation, and high costs. So the potential\r of the application is low. Therefore, the vertical circulatory laminar flow apparatus\r was developed in this study. And the separation equation of this apparatus was also\r set up. The results of vertical circulatory laminar flow experimental show that\r the efficient increase with increasing V, and the optimum conditions are at about\r Q= 1.05 L/min, C0=800±50 mg/L, and V=26 cm/min. The separation efficient of the\r vertical circulatory laminar flow apparatus is higher than thermal diffusion apparatus.\r And its energy consumption and costs are low, and easy to operate. Since all interior\r moveable plates have two operation sides, so the multiple channel apparatus is application.\r Therefore, the multiple channel apparatus can treat large amount raw water and has\r low costs. The efficient of the experimental all are better than the theoretical\r values that may due to: (1)the assumed partical diameter is too small,(2)the flow\r is not real laminar flow, and (3)the end-side effect is not considerate. \r 熱擴散實驗結果顯示在固定C0下，分離成效隨ΔT增加而增高，但隨進料流率增加而降低。在固定ΔT下，分離效率亦隨進料流率增加而降低。固定進料流率下，增加ΔT對分離效果的影響不大，以C0=545±10\r mg/L時，顯現出最佳成效。採用熱擴散裝置雖對降低原水中之懸浮微粒含量效果有限，且能源需求高，造成高成本和操作複雜，不具實用潛力。為提高分離原水微粒之成率，以及簡化操作與降低成本，本研究開發垂直旋轉帶裝置來製造出上下循環水流，並導出水流與微粒於其中之流速分布式，以及頂部、底部出口之微粒濃度計算式。垂直循環轉帶實驗結果，顯示提高V值有助於降低Ct/Cb比值；Q=\r 1.05 L/min左右、C0=800±50 mg/L下與V在26 cm/min左右，均有較低之Ct/Cb比值。垂直旋轉帶裝置分離成效明顯優於熱擴散裝置，且設備簡單、能源需求低與操作容易。由於旋轉帶之兩面均可以做為移動平板，因此不僅可以用來處理大量之高濁度原水，也能更具經濟效益。由理論與實驗結果之比較，顯示理論成效較實驗差，探討其原因可能是：(1)平均粒徑之假設值偏低、(2)流場並非全然以層流流動、(3)兩端終端效應未加考慮等。

物體在流體中受到的阻力(Drag force) F=1/2CρAV^2（C 是常數，和物體的形狀有關，ρ是空氣密度，A 是垂直投影面積的大小，V 是速度）。但是我們在實驗室中檢驗降落傘的阻力，得到的結果並不是和垂直投影面積成正比，而是和降落傘面所包住的空氣體積大小成正比。進一步，我們發現體積的高度太高也不好，它存在一個最佳高度，此一高度和底面的邊長有關。此外，我們把降落傘頂端開一小洞並製作兩層的降落傘，希望增加降落傘下降的穩定度和阻力，得到很奇特的結果。希望我們的研究能夠對想要自製降落傘的人，提供氣流流動的基礎認知。

蘿蔓A菜莖部內有白色乳狀液成分為橡膠醣、甘露醇、樹脂和萵苣素，若暴露於自然的環境中1-2日，莖部細胞本身可氧化形成紅色似人類的結痂，乳汁並非變紅的主因，莖部特殊的結痂狀集中在用來運送物質的維管束，而阻止了水分和養分的流失；人體受傷時以血小板用於凝血並透過免疫系統來抵抗外敵，而蘿蔓A菜則在莖部產生鹼性環境用以減緩細菌的生長，儘管其只剩莖的一小節，不施水分三週後，仍會長出莖與葉子最後再長出根變成一個完整的新個體。 蘿蔓A菜的結痂其作用與人的血液凝結是否相同，利用抗凝血劑藥物阿斯匹靈的施給，發現可延緩結痂的生成，也可由抗氧化劑維他命C來抑制結痂，可見得植物雖無血小板，但是卻有類似形成結痂的機制防衛來保護並修復傷口。

在日常生活我們常可看到一些和表面張力有關的一些現象。如：荷葉的水珠成球形，刮鬍刀片小心放在水面上，不會下沈。一顆豆大的鉀粒會在水面起火燃燒，且在水面急速的移動。以上所述這些現象都在在顯示液值表面有所謂「表面張力」存在。然其大小受到某些因素影響。在國中第三冊物理第十四章曾指出，雜質及溫度會使液體表面張力降低。然而對於所有液體是否都是如此呢？實在是殊堪玩味。

利用簡單的濾紙層析法，可從植物葉片中萃取光合色素的成分，而利用紫外光照射以及紫外-可見光電子吸收光譜和放光光譜的測量，可判斷各成分所得結果是否有所差異。另外，我們試著加入純水或數種不同金屬離子配製的溶液來檢測對葉綠素螢光強度的影響。我們也嘗試著將萃取出來之葉綠素汁液製作成趣味隱形墨水，書寫在紙上的筆跡在一般光線下是無法以肉眼觀察到，特別的是，在暗室中經過紫外線照射後，便可清楚的看到所有紙上的筆跡。

布朗寧說：「成功的絆腳石不是缺乏智力，而是沒有創造力。」然而，現今高度競爭的環境下，今日的科技在明日可能就已過時。在國中自然與生活科技領域範籌中，以解決問題策略為中心，透過活動單元或作品，使學生循手腦並用的程序，培養學生創造思考的能力及合作學習的習慣。我們將課程所學融合創造力、想像力的實現。因此我們發明了三大主題：一、 便利垃圾桶其特性與傳統垃圾桶相差甚遠，以抽取式代替傳統作法。二、 便利洗衣刷將洗衣刷與清潔劑加以組合，做〝局部〞的刷洗，因此就不會弄濕整件衣服，是極富創造力的作品。三、 水果切丁器突破傳統的處理方式，利用四片刀片為刀片組並且去籽。使其成效成為原來的四倍。

Skin cancer, including basal cell and squamous cell skin carcinoma, is known to\r be the most common cancer type. Skin cancer is thought to make up half of all known\r cancers. Over one million non-melanoma skin cancers (NMSC) are reported every year. \r Approximately 300,000 of these cases are squamous cell carcinoma (SCC). It is\r estimated that about 2,000 people die from NMSC each year. Of the two skin cancer\r types, SCC tends to be the more clinically aggressive and likely to spread and invade,\r typically by way of blood or lymphatic vessels. Understanding the signaling pathways\r in SCC cells that regulate invasion will be important for developing improved cancer\r treatments. The signal transducer and activator of transcription 3 (Stat3) protein is a\r central regulator of numerous cellular activities, including proliferation, survival, and\r motility. Stat3 also has enhanced activity in many cancers, including skin SCC. This\r study shows that Stat3 regulates several invasive properties in a human skin SCC cell culture model.\r HGF (hepatocyte growth factor)- induced cell schattering was assessed for\r SRB12-p9 cells (p9WT), a human skin SCC cell line, along with SRB12-p9 cells\r engineered to have reduced Stat3 activity. Next, a cell viability-based adhesion assay\r was performed with these cells. Finally, severe combined immunodeficient (SCID)\r mice were injected subcutaneously with P9WT and S3DN cells and tumors were\r measured twice weekly. Extracted tumors were analyzed by immunohistochemistry and Western blotting for expression of the invasion related enzyme, MMP-2 and MMP-9.\r The suppression of Stat3 activity in S3DN cell lines resulted in reduced motility,\r greater adhesion, and a less invasive phenotype in SCID mice. Immunohistochemistry and Western blotting indicated higher levels of MMPs in the P9WT cells with\r expression localization towards the outer perimeter of the tumors. This data suggests\r that Stat3 plays a role in skin SCC invasion and better understanding of Stat3 function\r could lead to improved treatment and prevention of the disease.