任意一個三角形要如何分割成四個彼此相似的組成三角形呢？我們透過嚴謹的數學推理，先對三角形作二、三分割的可能情形進行驗證，並藉由已完成相似二、三分割的三角形，運用「內分」和「外加」的觀念，使相似四分割的討論變得明快，並得以將各式三角形的所有相似四分割的圖示作完整而有系統的呈現。 \r 我們也對「比例四分割」的作圖法與其相關幾何性質，進行猜想與討論，並驗證得出一些結果。尤其對「黃金三角形」經比例四分割後，組成三角形之對應邊長的比值也是「黃金值」，以及使用五條摺痕線的摺紙方式，可以摺出一張黃金三角形紙張的比例四分割，這些研究結果都令我們感到獲益良多。 How to divide a triangle into four similar little triangles？ Possible situations of dividing a triangle into two or three parts could be testified by strict mathematical inferences, and then the concepts of “internal division” and “external addition” could be applied to make our discussion clearly and briefly. With above discussions, figures about four similar divisions of all kinds of triangles could be presented completely and systematically. Some results were come up after making some conjectures and discussions about the geometric constructions and geometric properties of “four proportional divisions”. We learn a lot by these researches especially on the discoveries that the ratio of those corresponding sides in each four similar triangles which form a golden triangle, is also golden ratio; and that we could divide a golden triangle into four similar triangles by using five folding lines.

近年來，隨著癌症人口的激增，及一些食物中天然存在或加工過程中衍生出的致突變物質之陸續發現，人們開始注意到含黃樟素， Pyrrolizidine 生物鹼， alkaloid 生物鹼等食物的致癌性和致突變性。而可可鹼( theo bromine, 3 , 7 -dimethylxanthine )，咖啡因( caffeine )，茶葉素( theophylline )，為 alkaloid 生物鹼的三種主要化合物。只要是嗜好可樂或巧克力甜食的人，就免不了和可可鹼有長時間且高頻率的接觸，這不禁令人對可可鹼是否造成遺傳物質的傷害，感到好奇。

我們發現 l+ 2+…+n=n(n+l)/2這個公式可用下列這種積木堆積方式證明：我們先將其式子看成如下的積木排列數：如〔 圖(一)〕 這時，我們將另一塊形狀大小完全相同的積木組合，與圖(一)疊合如圖(二)。 ∴很明頭地，疊合成的積木組合為一矩形，積木數 2S=n(n+l) ∴S=n(n+1)/2 即 l+2+…+n＝n(n+l)/2

In our experiment, the novel hydrothermal-galvanic couple method is used to produce nanostructured TiO2 thin film. Compared with the traditional hydrothermal method, whose process is conducted under high temperature and high pressure, the hydrothermal-galvanic couple method is a thermally and electrochemically driven process. The titanium atom is gradually oxidized on the surface driven by potential difference, and eventually become nanostructured TiO2. The advantages of the hydrothermal-galvanic couple method are numerous： they are simple, environment-friendly and energy-saving. Experimental parameters include time, concentration and types of solution. The hydrothermal method is used for comparison. By the cross-section and surface pictures of Field-emission scanning electron microscopy (FE-SEM), we can clearly observe that there is obvious change on the titanium surface, along with increased thickness and altered surface structure. The film of hydrothermal-galvanic couple method is thicker than that of hydrothermal method. Thickness increases with time and concentration as well. Both the hydrophile and decomposition of methylene blue examination indicate that the product on the surface contains photocatalyst-like feature.我們利用新穎水熱-化學電池法製備奈米級二氧化鈦薄膜。相較於一般傳統水熱法高溫高壓的製程，水熱-化學電池法結合了熱能與化學電能，讓鈦原子在電位差的驅動下於表面逐步氧化，最終形成奈米級二氧化鈦粒子，具備簡易、環保、省能的優點。實驗參數包括時間、濃度、溶液種類，並以水熱法作為對照組。由FE-SEM 橫截面圖及表面圖可清楚看到鈦的表面有明顯變化，膜厚增加、表面結構改變；以水熱-化學電池法所得的薄膜明顯較水熱法厚，而其厚度隨著濃度及時間的增加也有增加的趨勢，由試片親水性測試與亞甲基藍吸光度測試，皆顯示試片的表面產物具有類似光觸媒的性質。

當海底發生地震，或海底山崩塌，海水便被抬升或崩塌，因此在短時間內獲得大量位能，轉成為海水的動能向四面八方傳遞，這就是海嘯。我們以基隆港為模型，海底坡度1：10，藉由實驗發現水波在寬闊水域由較深區域進入較淺區域，波高(波峰與波谷的距離)並不會出現太大的不同，然而一旦水波進入狹窄的港區，能量在灣內累積，波高就大幅增加，比例可達55%。當波谷先抵達岸邊時，會造成海水後退、水位大幅下降甚至露出海底的情形。在我們的實驗中，代表海底的斜板露出的距離最大約14 公分(坡度1：10)，佔小水槽長度的28%。若改變斜板與水槽底部的角度，斜板露出的距離也會改變，當θ=10°，即坡度175：1000 時斜板露出距離最長。

修正汽車駕駛喜歡猛踩加油踏板之習慣,把一加油動作分解成多段階級式加油動作,使自動變速箱內扭力降低達到順利變換高速檔o 達到節約能源.減少污染.提高效率之目的。The oil-saving project by adjusting the driving habits To avoid the habit of easily step the pedal to speed up, we divide it into multi-step fuel-filling procedures. Therefore, they decrease the wristing strength of transistor inside auto speed-changing box and reach high-speed brake smoothly. As a result, it can save energy, reduce pollution and increase high efficiency.

路邊停車時，總需要三番兩次的調移車身，過程些許費時，因此，嘗試推算一次順利進出車格之軌跡。我們以開出停車格之軌跡做探討，軌跡建立之後再依循所建軌跡供車輛倒車行駛。為了能順利一次路邊停車，我們設定方向盤轉動量最大，讓前輪達到最大轉向角θ（一般車輛是35度），以取得最小迴轉半徑R，利用車輛基本性質，包括：車前懸a、前後輪軸距b、車後懸c及車寬d，推導計算最小迴轉半徑R，所代出之公式經模擬實驗，其誤差率均小於5％，值得引為後續研究之用。於路邊停車軌跡部分，先探討車輛出車格之軌跡，包括：左轉、直行及右轉軌跡，三個軌跡的反向連續軌跡，即為路邊停車時倒車的應行進軌跡。於倒車入庫軌跡部份，則包含直行及右轉軌跡兩部份。最後，對於誤差修正之探討，我們提出所謂前輪轉動受「軸承」控制之計算觀念，將車輪轉動中心砌合實際狀況轉移，於給定承軸及輪胎外側圓心之距時，將有更精密之數據展現。

A total of 64 nonduplicate isolates of erythromycin-resistant (MIC, >1 μg/ml) Streptococcus pyogenes collected from 1979 to 2003 in Taiwan were evaluated. They were collected from three cohort period: 1979 –1989, 1990-1999 and after 2000. The in vitro activities of 10 antimicrobial agents were determined by the agar dilution method. Penicillin, cephalothin, cefotaxime, vancomycin, and ofloxacin were shown to be active against S. pyogenes isolates (100% sensitive). Erythromycin and azithromycin both had poor activities (MIC50s, 16 and >128 μg/ml, respectively; MIC90s, >512 and >128 μg/ml, respectively). The activities of tetracycline, clindamycin, and chloramphenicol against a significant number of these isolates were also limited. Among the 64 S. pyogenes isolates, 58% had constitutive resistance [cMLS], 40% had an M phenotype and 2% had an iMLS phenotype (inducible resistance [iMLS]). A substantial upsurge in the incidence of M phenotype erythromycin-resistant isolates was found with time for S. pyogenes (10% in 1979–1989, 48% in 1990–1999 and 65% after 2000). The erythromycin resistance genes in 64 isolates of the different cohorts were investigated by PCR. All cMLS phenotype isolates tested had ermB gene. The M phenotype isolates had only the macrolide efflux (mefA) gene. This study shows the secular changes of increasing susceptibility of S. pyogenes isolates to both erythromycin and clindamycin in Taiwan. The mechanisms of erythromycin resistance have changed from the predominance of ermB gene (cMLS) to mefA gene (M phenotype). 本研究是探討台灣自1970 年代末期以來不同世代A群鏈球菌菌株對紅黴素的抗藥性及抗藥基因特徵的演變。研究者收集台灣二十年前(1980 年代前後，第一世代)、十年前(1990 年代，第二世代)、)及最近(2000 年以後，第三世代)之A 群鏈球菌菌株共64 株，利用抗生素圖譜和雙藥錠擴散測試及聚合?連鎖反應(PCR)、和脈衝式膠體電泳研究A 群鏈球菌對紅黴素抗藥性的表現型及基因型特徵。結果發現第一世代的A 群鏈球菌對紅黴素最小抑菌濃度(MIC)值相當高，幾乎都是>512 μg/ml，90%為多重抗藥菌株。第二世代則相對有降低，在第三世代此現象更明顯，多重抗藥菌株為30%。在雙藥錠擴散測試結果，從第一世代來看cMLS 佔大多數(90%)，M 型佔10%；第二世代cMLS 及M 型相當分別佔52%及48%；第三世代主要為M 型佔65%，cMLS 佔30%，iMLS 佔5%。利用PCR研究紅黴素抗藥性基因發現所有cMLS 菌株皆有ermB 基因，所有M 型菌株皆有mefA 基因，iMLS 菌株則有ermTR 基因。由本研究顯示在台灣A 群鏈球菌對紅黴素之抗藥性隨著不同世代有逐年改善之趨勢，由MIC50的降低可看出，菌株對紅黴素的敏感性提高，可為臨床治療之參考。

本研究靈感來自對Brianchon定理「圓外切六邊形的相對頂點的三條對角線共點」及Pascal定理「圓內接六邊形的三組對邊延長線交點共線」這兩個對偶定理的性質探討，進一步研究其在雙心六邊形共點共線的可能情形。研究結果有許多驚人的發現，特別是其三條對角線以及三條對邊切點連線，有六線共點，此點為定點，且與其外接圓圓心、內切圓圓心三點共線，且此線與Pascal Line垂直。據此，更進一步對雙心六邊形退化與延伸情形作深入探討。

The purpose of this research was to investigate the most favourable salt concentration that promotes growth in the Lemna minor plant. Lemna minor, commonly known as lesser duckweed, is found growing among other aquatic plants or massed together in still or slow moving fresh water, such as ponds and lakes, in warmer regions around the world.

-to prove my original hypothesis that colour affects the power that is produced by solar panels. \r \r - that the wavelength of an elctromagnetic wave affects the photon or quanta energy that the wave has.

To compare the habitat and physical\r differences of two burrowing scorpions, Opistophthalmus pugnax and\r the Opistophthalmus glabrifrons to be found in the Gauteng area\r (South Africa). Although these scorpions’ habitat overlaps, they don’t\r co-occur at the same site.