里曼球面在高中數學只是大略提過，上課時談到里曼球面投影，過北極的大圓投影為一直線，那麼不經北極的大圓投影後圖形為何？任一小圓的投影又為何？前幾章講二次曲線，觀察里曼球面上，北極與圓上點的連線掃出的形狀不應稱圓錐，而應稱為橢圓錐，而此橢圓錐與複數平面相交的圖形又為何？問幾位同學，有的說橢圓，有的說不成圖形，有的說成雞蛋形，（一邊曲率半徑較大，另一邊曲率半徑較小），因沒有實際式子，實也難以決定何者正確，隨即著手求證。

整體而言，今年之水準較去年高出甚多，尤其高中組，取材也相當生活化，但是，仍有些 缺點宜待改進： 一、國小組： 二、有些作品之結論，祗展示數據，沒有作簡略說明。

小黑蚊又稱黑金剛，被叮咬後的癢痛使大家都深受其苦。小黑蚊不同於蚊子，是\r 屬於雙翅目蛺蠓科之衛生昆蟲。為了找出大戰黑金剛的策略，先利用問卷調查後\r 找出不同方式來對抗小黑蚊。校園中小黑蚊密度調查比較各區域之地理環境結果\r 為：下過雨後出太陽有微風加上著生青苔之壤土處小黑蚊出現數量最多；創意的\r 戰鬥型、炮彈型吸蚊瓶，內裝有糖水加酵母、尿液且加熱至37℃（味道、溫度），\r 有較好的誘捕效果（物理防治）。窄域油，一種安全無毒之礦物油，在稀釋100\r 倍的濃度中會造成蘚苔物理性窒息，有抑制生長之效果（化學防治）。蔓花生是\r 保水力佳、貼地性夠的植物，除了利用它作為校園中水土保持之作物外，也能達\r 到小黑蚊生物防治之效果。

去年我們發現洋菜在理化實瞼上有許多妙用，經過研究後，所提出的報告，「洋菜的妙用」獲得全國科展佳作獎，一年來我們又陸續發現洋菜製成的活塞還可以有很多廣泛的用途，所以今年我們的作品是「洋菜活塞與氣體的P.V.n.T.及O2、呼出氣體、CO2 含量的探討」。

This study was to explore the nature of two basic constitutes of the regular pentagon,With these two constitutes, the regular pentagon could be multiplied into any times. We used four multiplication methods (m2 = 2m1 + n1 、n2 = m1 + n1 、m2= k2m1 、n2= k2n1、a2 = a1 + 1、a2 = a1 + ) to show how the regular pentagon could enlarge and to verify that the enlarged regular pentagons derived from computer did exist. By integrating these four multiplication methods, we were able to arrange regular pentagon of any length of side, and evidenced the equation was ( If the side length of a regular pentagon is a form of m,n is the number of A,B respectively ) We further proved that the first multiplication method could be developed into a new modified method, which could divide a regular pentagon with a given side length into a combination of A and B. But only when the x and y of side length of a regular pentagon could be divided by a natural number, k, and made x/k into an item of the Fibonacci Sequence and y/k a successive item. When we tried to verify if any regular pentagon could be constituted by other smaller regular pentagons, we also found that it was un-dividable only if the length of pentagon side were ( the number of A, B were the 2n and 2n-1 item of Lucas Sequence). Otherwise, any regular pentagon might be able to be constituted by other smaller regular pentagons. 本研究是以正五邊形的兩個基本組成元素(B)作為討論對象，利用此二元素可以將正五邊形做任意倍數的放大。我們共使用4種繁殖法則(m2 = 2m1 + n1 、n2 = m1 + n1 、m2= k2m1 、n2= k2n1、a2 = a1 + 1、a2 = a1 + ) 來說明正五邊形的放大情形，並利用此4 種繁殖法驗證電腦運算出的放大圖形確實存在。利用這4 種繁殖法則的改良與整合，已達到能排出任意邊長之正五邊形的目標，並能計算並證明出其通式為。 (若正五邊形的邊長為形式,m、n代表、的個數) 更特別的是，我們能用第一繁殖法反推出一種方法，將給定邊長的正五邊形利用簡單的切割方式分成由A、B 組合成的形式，但只有正五邊形邊長之x、y 值可同除以任一自然數k 而使 x/k 為費波那契數列之一項且 y/k 為其後一項者才可以使用。 將此想法推廣至一個正五邊形能否由比他小的其他五邊形組合而成時，我們也發現當正五邊形之邊長為時（其A、B 個數為盧卡斯數列之第2n,2n-1 項），不可分解，否則應該皆可將一個正五邊形分解成比它小的其他五邊形組合（我們也可以利用這些質形檢驗出其他正五邊形是否也為質形）。但其分解形式，不只一種，而我們推測只用兩種較小的正五邊形就能達成，我們期待能找出一或多種分解方法，能將正五邊形分解成標準的分解形式。

本研究針對疏散星團NGC2099的年齡與視直徑來進行探討，利用冷卻CCD進行恆星的UBV光度觀測，藉由拍攝到的照片進行雜訊移除、測量儀器星等及視星等修正等步驟後，繪出NGC2099星色-星等圖(CMD)並分析之，求得NGC2099的年齡約在108.5~108.6年之間，紅化值為0.1 ± 0.02，並利用距離模數公式求得該星團的距離為5433.21 ± 499.00pc，再以數星與統計方法求得該星團在赤經方向之視直徑為21 ± 0.5角分、赤緯方向之視直徑為13 ± 0.5角分後，再藉由弧長公式計算得到星團直徑在赤經方向為33.26 ± 3.84ly，赤緯方向為22.43 ±0.86ly。

本實驗中採用自製的甲殼素吸附金屬離子，發現在0.04M、pH4、25℃、45分鐘時添加了戊二醛的甲殼素對銅離子有最好吸附效果。其中甲殼素在不同濃度的銅離子中，濃度越低對銅離子的吸附量會越少。而在添加戊二醛改質甲殼素以形成網絡型結構方面，隨著戊二醛添加量的增加，甲殼素對銅離子吸附量隨之增加。時間對銅離子吸附量的影響發現，GA2在10到40分時吸附最快速，約在45分時達平衡。在甲殼素克數對銅離子的吸附量影響發現，大約在0.8克時吸附可達平衡。甲殼素在不同pH對銅離子吸附量的影響方面在越偏酸性的環境下吸附效果最佳。

1. Purpose of Research / Project The purpose of this research was to find out whether clay has any diagnostic value as a three-dimensional medium compare to drawing which is two dimensional medium and to determine if learners would prefer to work with clay or to rather draw a picture when depicting their ″feeling-stories″. Furthermore to do research on the effect that different coloured clay has on the emotions and behavior of learners during therapy. 2. Procedure A number of learners from different backgrounds, ages and cultures were used in this empirical research. They were asked to draw a ″feeling-story″ with a two-dimensional medium and then depict a ″feeling-story″ with different coloured clay which is a three-dimensional medium. Afterwards they had to describe their stories. They also had to choose what they liked best-the two-dimensional medium (drawing) or the three-dimensional medium (clay). 3. Data From the results it was clear that clay projections have diagnostic value. The learners were able to communicate their ″feeling-story″ better by using the three-dimensional figures in a verbal and non-verbal way. Through actions and the choice of coloured clay they used, they could portray and describe their emotions and symbolic messages. This indicated that they enjoyed the clay projections more than the drawings they made. 4. Conclusion From my research I found that clay as a three-dimensional medium has diagnostic value and can be applied as a supplementary projection medium. Different coloured clay can be associated with different emotions and behaviours in children. More learners preferred to work with clay (three-dimensional) as a medium in depicting their ″feeling-story″ rather than drawing two-dimensional pictures.

運動讓緊張忙碌的生活壓力得到快速的紓解，而排汗衣的發明，讓許多熱愛運動的人們在大量排汗的同時，能夠迅速有效的將汗水吸收，再排到衣服的外層蒸散，阻隔溼答答的衣服直接附著在皮膚上，免除身體的不舒適感，而達到舒爽的最佳效果，因此排汗衣成為運動員趨之若鶩的好夥伴。然而排汗衣究竟是何方神聖，有何種了不起的法術能夠成為今日運動界的當紅炸子雞席捲全球呢？我們為了揭開它神秘的面紗，特別追蹤研究，並且設計了三個實驗，藉由測試比較各種布料的吸水、擴散及蒸發能力，透過實驗的過程與結果，最後就知道排汗布料是由何種材質所製成及它的特殊性質為何了。

The highly water-absorbing polymers were prepared by the reaction of acrylic acid as a graft\r monomer and natural starch (eg. rice starch, sticky rice starch or corn starch) as the backbone\r using water hydrogen peroxide and vitamin C as solvent, initiator and catalyst, respectively. The\r reaction was carried out by mixing of starch in distilling water and stirring at 60-70 ℃ for 3\r hours and then cooled to 30℃ Acrylic acid was added and the pH was adjusted to 6-9 by the\r addition of limestone powder. To the stirred mixture were then added hydrogen peroxide (30%\r v/v) and vitamin C and continued stirring for 3 hours until the solution became viscous The\r viscous solution was neutralized with potassium hydroxide (30%v/v) to give the pH for 6.5-7\r and allowed to cool to room temperature overnight. The resulting solution was spread on\r winnowing baskets and allowed to dry under the sun to yield a continuous absorbent polymer\r film. The absorbent polymer film was ground and yield of white powder, The above procedure\r was repeated by using another types of starch. The ability of starch slurry to swell on heating, by\r absorption of water, is it’s most important practical property. Rice starch has very low swelling\r capacity in aqueous media compare with sticky rice starch and corn starch. The capacities of\r water-absorbing polymer were tested by placing polymer powder in the beaker and adding of\r water until it swell and cannot absorb more water. The polymers were found to be an excellent\r water absorbent, which absorbed water about 248, 245 and 167 times in weight of polymer for\r corn starch, sticky rice starch and rice starch, respectively. The water retention was calculated by\r measuring the amount of water releasing after every week for 10 weeks. They have also good\r water retention capacity. The swollen polymers were mixed with soil in ratio 1:3 and the\r increasing water holding capacity of soils which promotes more efficient plant growth in pot were\r test. It was found that the soil could be absorbed water for 10 weeks. It is possible to use highly\r water-absorbing polymers from natural starch in agriculture because they are low in cost and the\r polysaccharide main portion of the product is biodegradable

從國中開始，我們做過許多電解實驗。我們發現一些電解質水熔液電解僅靠電解質導電致使水電解；而有的卻能連電解質本身都氣化還原，而水亦電解。 然草酸水熔液電解又會產生什麼呢？於是便自行動手做；又發現以鋁為電極電解會發光，更值得加以研究探討。 人才、知識、技術、設備的缺乏，使此次研究分外艱辛，不過仍希望藉科學展覽達到研究相互交流的目的。

本研究是利用「熱聲效應」來探討聲波冷卻的原理，並製作一個簡單的聲波冷卻裝置，而此裝置分別由揚聲器、共振管、片堆及熱交換器等四個主要部分所構成，並利用聲音編輯軟體讓揚聲器產生所需的頻率之聲波，讓共振管內產生共振駐波使工作氣體能作壓縮及膨脹，並且在片堆內能將聲能轉換成熱能以達到降溫的效果。本研究針對不同的聲波頻率、片堆間隙及熱交換器高度來探討聲波冷卻的效率。研究後發現下列幾點：一、聲波頻率愈高並不能提升冷卻的效率根據聲波冷卻的原理發現工作氣體在進行熱交換循環時有一定的週期時間，當聲波的頻率愈高則工作氣體進行熱交換的週期時間愈短，反而無法有效的進行熱交換使得冷卻的效果降低。二、片堆的間隙大小與共振管內的工作氣體性質及聲波頻率有關本研究的片堆間隙是以 357 Hz 的聲波頻率計算而得，並根據聲波冷卻的原理將片堆的間隙的大小設計成接近四倍的熱滲透深度。經實驗的結果發現在 357 Hz 的頻率下，片堆間隙愈接近四倍的熱滲透深度時所得之冷卻效果愈佳。三、熱交換銅片的高度愈高其冷卻效果愈好本研究在加裝熱交換器的實驗結果發現，於相同的片堆間隙及聲波頻率的條件下，高度較高的熱交換器之冷卻效果確實會比高度較低者佳。