正方形和長方形是每一個人都非常熟悉的圖形，但其中卻隱藏了非常多奇妙的“數學之謎”。 所謂「完美長方形」是：在一個長方形中 (長、寬不等)，能否分割出最少大小相異的正方形。 這個研究中，首先用「草圖」的解題方法研究完美長方形，接下來利用「平面圖形」的解題方法可簡化計算的過程，最後利用「對偶關係」證明出：完美長方形的最少階數為 9 階。 進而，我們將這個問題擴展至三維空間，思索在一個長方體中（長、寬、高都不等長） ，能否仿照二維空間，分割出最少大小相異的正方體，而完成這個研究。 Square and the rectangle are figures that everyone knows well very much, but what a wonderful " mystery of mathematics " is hidden among them. What is called the perfect rectangle is whether in a rectangle (its length and width is different ) could cut apart two squares as the least difference in size . In this research, the solution approach of "the sketch map" is used to study the perfect rectangle at first, then the solution approach of "the level figure" to simplify the complicatied calculation of the solving course , and "the dual relation" is finally used to prove 9 orders are the least orders for a perfect rectangle . And then, we expand this question to three-dimensional space, considering in a cuboid (its length, width, and height is different) whether could follow the two-dimensional space model to cut apart two squares as the least difference in size, and finish this research.

在2003 年台灣國際科展之作品說明書「Concatenating Squares」中【9】與2004第三屆旺宏科學獎「SA3-119 ：與特殊型質數之倒數關聯的兩平方總和的整數分解」成果報告書中【10】，就已有令人驚訝的結果。在2005 第四屆旺宏科學獎「SA4-298 ：分和累乘再現數產生的方法及其性質探討之推廣與應用」成果報告書中【11】，更是以逆向思維進行研究推廣，創造出許多新穎且引人注意的美麗數式，由原創性的觀點來進行逆向思維的研究。正由於這些再現數充滿奇巧，且與不定方程（代數）、簡單的數整除性分析（數論）以及同餘式理論都有所關聯，我們要發展前所未有的同步關聯與研究分歧， 且是最新的發現，更以豐富的想像力、創造力與推理能力提出令人耳目一新的重要結果，得到許多從未見過世面的美麗數式，回眸觀賞時內心充滿了數學之美！;Number which when chopped into two（three）parts, added / subtracted and squared（cubed） result in the same number. Consider an n -digit number k , square it and add / subtract the right n or n .1 digits. If the resultant sum is k , then k is called a Kaprekar number. The set of n -Kaprekar integers is in one-to-one correspondence with the set of unitary divisors of 10 n m1. If instead we work in binary, it turns out that every even perfect number is n - Kaprekar for some n . We wish to find a general pattern for numbers these numbers cubed or 3-D Kaprekar. We also investigate some 3-D Kaprekar of special forms. In addition, some results relating to the properties of the Kaprekar numbers also presented. This study indicates the “interesting” and “pragmatic” natures of the research project. We have developed the original results based upon his initiatives and has thus created a new horizon through the research project. This is the proudest achievement for this study. Generalization of Some Curiously Fascinating Integer Sequences：Various Recurrent Numbers！

為了瞭解黃斑黑蟋蟀叫聲和溫度之間的關係，我應用物理熱平衡原理，自製水浴槽控制環境溫度，以電腦錄音程式分別錄製15℃、20℃、25℃、30℃、35℃時的蟋蟀叫聲，利用Sound Forge軟體分析並比較不同溫度下的各種特性。結果發現所分析的chirp、chirp period、syllable period、pause均和溫度呈負相關，而單位時間內的叫聲次數則與溫度成正相關，並推導出15~35℃範圍內蟋蟀叫聲次數與溫度成正相關的公式。最佳直線為：﹙15秒內叫聲次數＋19.385﹚÷2.483=當時溫度﹙℃﹚，呈高度正相關﹙相關係數：0.9398﹚。本實驗也比較母蟋蟀對不同溫度下雄蟋蟀叫聲的偏好程度，發現母蟋蟀較偏愛25℃時的雄蟋蟀叫聲，此結果可能與雄蟋蟀在25℃時叫聲的波形最為穩定有關。為探測蟋蟀觸角上的溫度感受器位置，我們曾將不同部位的觸角加以剪除，結果顯示觸角剪除面積越大的雄蟋蟀越不傾向鳴叫，但無法證實是否為溫度偵測異常所導致。本實驗除供學術研究外，因黃斑黑蟋蟀在世界各地均有分布，所以希望能藉由分析溫度與蟋蟀叫聲的相關性實驗，未來嘗試能探討其在不同環境的適應行為亦或種化的可能性。另外，全球暖化問題日益嚴重，也希望能藉由相關實驗探討暖化對蟋蟀生態上的影響。最後，我們的實驗證明了蟋蟀叫聲和環境溫度確實有極大的關聯性，未來或許能參考蟋蟀感覺溫度的機制，製作出一個天然零污染的溫度計。 To find out the relationship of cricket’s calling and temperature, we use a hand-made water-bath tank to control the temperature and record the callings with microphone and software, Sound Forge. After analyzing the collected data, we’ve found that cricket’s chirp, chirp period, syllable period, and pause are indeed affected by temperature (15 degrees - 35 degrees C). Moreover, we also compare female cricket’s preference to the callings, and the result indicates that female cricket’s preference is changing with temperature. In the last, we tried to find out where the thermoreceptors are by cutting out the antennae. After cutting, crickets tend to not to make any calls at all, so we conclude the antennae might play an important role in sensing and calling. The experiment proves that this communication system is temperature coupled. Because the cricket, Gryllus bimaculatus, is a worldwide species, we may learn the accommodation or the possibility of performing a new species by researching the relationship of temperature and cricket’s callings. By the way, the Green House Effect is getting more and more serious, so we want to search for the influences on crickets that are caused by Green House Effect. The last but not the least, according to the report, maybe we can investigate the mechanism of sensing temperature and then make a natural thermometer that is no pollution in the future.

想像一下，原來固定的一個黑色大正方形(以下我們簡稱S1)四個角經過較小之正方形(以下簡稱S2)遮蓋後旋轉，為什麼會有放大縮小的感覺呢?(圖一) 我們猜測這是因為未被遮蓋部分(以下簡稱S3)的面積改變了，所造成的結果。令S1的邊長為 r，S2的一個小正方形邊長為n，k=r-n，θ為旋轉角度，我們實際算出了旋轉角度θ對S3的面積函數，

根據我們找到的資料，視覺是植食性昆蟲覓食的重要工具。資料指出：果蠅的視覺對於 380nm（紫外光）、420nm（靛色）、500nm（綠色）這三種光線的波長較為敏感，又由於市售黏蠅板皆為黃色，因此，我們就針對果蠅視覺的辨色記憶、顏色偏好、不同色光的趨光性做探討，發現：一、辨色記憶：由實驗結果，我們認為果蠅應能記憶顏色，如此可間接證明果蠅能夠分辨顏色，果蠅可能是有彩色視覺的。二、顏色偏好：利用五種顏色的黏蠅板，發現在黑色背景下，亮度最高、反射波長範圍介於 500nm 至 700nm 而從 580nm 又趨於平穩的高反射率的黃色黏板最為果蠅所偏好的。由此顯示：背景、亮度、反射波長皆可能影響果蠅的顏色偏好。三、在不同色光的趨光性方面：果蠅對於不同波長的色光並不具有特殊喜好。原因可能為實驗所使用的 LED 燈泡波長涵蓋範圍太少，另一個原因則是，果蠅的趨光行為影響實驗結果。綜合實驗結果，我們認為：以植物為食的果蠅，對於不同的顏色，可能有能力區別並加以記憶，如此彩色視覺在果蠅的生理機能與行為上，可能佔有重要的地位。

白華是生長於混凝土中孔隙的鹽類晶體，但確切影響其生成量及速率的機制仍未可知。為探討及分析不同因素影響晶析與實際上壁癌的晶體結構，我們以混凝土試片浸泡於漆料中常含的有機溶劑中，並測試市面上販售之多種防壁癌之漆料塗抹於混凝土試片上之效果。除此之外，更蒐集現實生活中所產生之壁癌，且針對上述有鹽類晶體生長之試片採集之壁癌進行顯微照相以及成分分析。結果發現，水泥比例造成的裂隙大小、有機溶劑的黏性會影響毛細作用與水泥析出，而防水漆料則能在短時間內抑制水分滲入。顯微照相顯示，在各種鹽類中，硫酸鹽的小顆粒較易析出至表面，是現實生活中的主要成分。我們期望將控制上述有利於白華生長之因素，應用於有效抑止壁癌的生長。

在能源日漸耗竭的今日，開發環保新能源是重要的課題。本研究中使用的藻類電池，係藉著藻類照光會行光合作用而發電。藻類可以吸收空氣中的二氧化碳，因此更符合「節能減碳」的概念，藻類電池又被稱為「活的太陽能電池」。從研究結果發現製作藻類電池時，以藍綠藻與小球藻的組合為最佳，其中藍綠藻擔任負極，而小球藻擔任正極。藻類電池在光照強的環境，有較佳的發電效率，而且添加營養劑在藻類電池中，不僅可以提高發電率並可以延長藻類的生命。在不同色光的照射中，藍光與紅光對於刺激藻類電池發電效率最佳；綠光則是最差。藻類電池也可以進行串聯，藉此提高電壓與電功率。我們期待藻類電池在未來可以成為一種新的能源。

抗生素是由細菌、黴菌或其他微生物在生活過程中所產生具有抗病原體或其他活性的一類物質，功效是殺菌。主要是從微生物的培養液中提取的或者用合成、半合成方法製造。抗生素作用，是抑制細菌中蛋白質與核酸的合成，干擾新陳代謝與繁殖，已達消滅細菌功效。但是因為病毒沒有新陳代謝的路徑，所以抗生素對病毒一點用都沒有。寄生蟲的細胞結構與細菌也有很大的不同，因此抗生素可以抑制細菌的生長或殺死細菌，但卻不會對病毒或寄生蟲造成很大的作用。

本文旨在研究螢光棒內的物質對於生物的影響；選擇以蝦的胰臟細胞、B.cereus,S.aureus, V.damsela, Streptococcus, E.coli, V.alginolytious, A.hydrophia 等七種細菌及三斑鯛魚、斑馬魚等作為生物的代表，在實驗室內培養細胞及細菌並觀察螢光棒的內含物是否會抑制細菌的生長、細胞及生物個體的生存．當我們每每在電視上看到無數隨歌手節奏舞動的螢光棒，在一場大型演唱會後被隨意丟棄，我們便不禁自問，它們是否有被適當的分類及處理呢？在對七株不同的菌株進行不同濃度的抑菌圈實驗以及將不同量的螢光棒內含物加入蝦胰臟細胞培養液共同培養後得知，僅要微量的螢光棒內含物質，便可以對上述兩種對象產生相當的損害以及影響；接下來，我們還將以三鯛斑魚及斑馬魚的魚苗來進行生物個體的實驗．然而以目前的結果可初步得知，以一般的掩埋及焚燒法來處理螢光棒，可能不是一項明智的舉動，有待政府相關機構來深入研究，並提出更好的解決之道．

機械加工過程中往往遇到形狀複雜工件，無法用一般虎鉗夾持進行加工。若需加工複雜工件時，需使用V 形槽、壓枕……等等夾具加以輔助，但有些夾具根本無法夾持。若用特殊夾具需拆除原有之虎鉗，而且還必須校正，工作繁雜又浪費很多時間。 本設計之優點為不需更換虎鉗，直接放在虎鉗鉗口即可夾持不規則的物體，利用正向力的作用夾持而不打滑，輕易達到夾持時之穩定和足夠之夾持力，以達迅速、不需使用特殊夾具、不需再校正、可當平行塊之多功能夾具，使複雜形狀之工件加工簡單化、迅速化之設計。;When handling workpieces in complicated and irregular shape in the mechanical process, users are unable to make it with ordinary vises. V-block and clamping block might help, while some others do not work at all. In such cases, the user has to tear the vise apart and then do some correction, which is complicated and time-wasting. The strength of this design is that there is no need to replace the vise. The user just puts this device on the vise clamp to clamp the irregular object. The vertical clamping force makes the piece at work stable and allows no slipping. With this device, no special fixture or further correction is needed. It can also be used for a parallel block if necessary. In other words, as a fixture of multiple functions, the device makes the processing work simpler and more efficient than ever.

This Project is inspired by the situation incurred by pedestrians, which for the most part are students who need a crossway in order to obtain public transportation or to get to the school; the difficulties that are faced by the personnel to exit the parking lot as well as the students who have a vehicle and to help those parents who drop and pick up their children at the school. At the same time, we would like to reduce the amount of contaminated gas emissions that are emanated into our environment. As consequence of the emission of toxic substances, the air contamination can cause side effects such as the burning of eyes or ears, throat irritation and itching and or respiratory problems. Under determined circumstances, some chemical substances that are found in the contaminated air can produce cancer, congenital malformation, brain damage and disorders to the nervous system, as well as, pulmonary damage and harm to the respiratory tract. For the present investigation it has been suggested as a primary goal: The development of a device, in this case a traffic light, which has the objective to reduce the previously mentioned traffic/security problems that arise upon entering and exiting the institution. The secondary goal is to have a friendly ecological impact within our community. This device was built and tested during a month to obtain figures and demonstrate benefits reported. The device should be low maintenance, it should have a long lifetime and, be simple enough to be operated by those who use it. Among the benefits found, the safety of the students, the prevention of accidents such as: car crashes and run overs, etc. Our studies indicate that per week it is consumed an average of 2,020.16 liters of gasoline, in schedules of 13 hours (from 7:00 AM to 8:00 PM) to lessen this figure would have a good ecological impact since all the hydrocarbon emission are harmful to health.