漩渦也有形
流體旋轉時，外圍及底部流體，因槽壁及槽底摩擦力的影響，流速較慢，相對的壓力也較大，導致外圍的水流會轉入中心。發現本實驗的渦流為強迫與自由漩渦組成。實驗中，探討f(轉動器的頻率)、H(總水深)、y(?入深度)、R(轉盤半徑)四者與角形數間的關係。若y、R 愈大、H 越小，隨著f 的增大，可觀察到的形狀邊數越多；反之，若y、R 愈小、H 越大，則f 愈高，所形成的圖形半徑愈大，易超過轉盤，不易觀察。依白努利方程式，外層水流的流速較慢，而內層水流的流速較快，故外層壓力大而內層壓力小，水會由外往內流，而此渦動流於轉動液面產生的剪力，可能為產生N 邊形漩渦的主要原因之一。流體旋轉系統中，因轉動而產生流體離心力與內外層壓力差交互作用下，於某特定相關的因素條件下，形成特定角形數漩渦，是本實驗的重要發現。When fluids are in rotation, fictitious force given by the container brings about the relative decrease of speed of the bottom and outer layer of water, which causes its pressure to increase, and water to spin inward, resulting in a vortex motion with N-corner polygons formed at the surface of the rotating plate. During this experiment, we discover that the vortices consisted of free and forced vortex and the polygons vary as control parameters f(rotation frequency), H(height of fluid), y(depth of the plate), and R(radius of the plate) change. The larger y and R are,the smaller H is, the more corners show up as f increases. On the contrary, the smaller y and R are,the larger H is, few polygons are identified since the rotating radius of polygons are larger than the plate. According to Bernoulli’s principle, smaller velocity of the outer-layer water causes water pressure to increase and water to spin inward. During this process, shear force is developed at the surface of the rotating fluid, which we believe is the main cause of N-corner polygons. In a rotating system, the interaction of centrifugal force and differential pressure causing a certain Ncorner polygon to be formed under different controlled parameters is our main discovery.
黑棘蟻聚落的生物時鐘
This study is to investigate whether colony of the spiny-weaver ant, Polyrhachis dives, have biological clock so as to observe the locomotion activities of the ants in the nest and find out if the Light period will interfere the rhythm. The conclusion is the colony of the ants get the rhythm is 23.8 hours during in L:D=12:12.There are ants not significant difference between large colonies and small colonies. While in Dark (D:D)the ants appears free running with 23.1 hours as the rhythm, so, the colony of the ants has obvious light-rhythm movement, showing that the biological clock will act on group and being controlled by light period. 本研究是在探討黑棘蟻 (polyrhachis dives) 聚落是否有生物時鐘(biological clock)，以觀察黑棘蟻在巢裡的活動情形，找出週期並探討光是否會影響週期。結果觀察出黑棘蟻 的聚落在有光的時候(L:D=12:12)以23.8 小時為週期，沒有光的時候(D:D)黑棘蟻仍呈現自由律動(free running)，以23.1 小時為週期，所以黑棘蟻的聚落有明顯的日週律動，顯示生物時鐘能作用在聚落上，且受光週期之調控。
魔術猜牌
本研究是藉由數學手法探討；如何由一疊36 張四種花色的撲克牌中，尋找出保證可猜中最多張花色的方法。研究過程是以在適當的猜牌時機，以鴿籠原理、邏輯推理、二進位、分析與歸納……等數學原理與方法，搭配巧妙的策略運用而達到目的。猜牌方法：先約定好猜牌規則，助手將36 張牌背圖樣相同但非對稱的撲克牌，以旋轉牌背的方向傳達訊息。在本研究中得出利用數學原理與方法可「經由巧妙的猜牌方法保證可以猜中26 張花色」，並提供後續研究者利用本研究之結果繼續深入探討與研究。 The study is mathematically based with reasonable explanations behind it. We are to correctly guess as many cards as possible from a deck of 36 cards, with random numbers and four different suits. We will apply mathematical methods, such as pigeonhole principle, logic inference, binary system, and analytical reduction, upon right timing. Using careful arrangement of the principles and reasoning, we can reach our ultimate goal. To state guessing: Conference between the guesser and the assistant about the guessing rules, the assistant will have 36 cards with the same exact pattern on the back but not symmetrical. The pattern of the cards will be different when rotated 180o. The only communication between the two is by rotating cards. In the process we will obtain mathematical theory and methods assuring 26 cards correctly guessed, and the study is for further and deeper discussion.
完美長方形
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.
磁剎車系統探討
本研究探討運用磁場來達到非接觸煞車的功能，本實驗採用兩種方式來探討磁煞車力，分別為馬達有外加電流及沒有外加電流的情況。首先本實驗提供一穩定的電源使鋁盤轉動，觀察加上磁場及把電源切掉後鋁盤轉速的變化。實驗發現，當馬達沒有外加電流時，磁煞車力與轉速及磁場平方皆成正比；馬達有外加電流時，電流差會與轉速平方差成正比。探討磁煞車力與厚度及介質的關係，實驗結果發現，渦電流常數與厚度成正相關，且當兩片鋁片中夾有介質時，渦電流常數較小。 This experiment is based on the magnetic brake’s practical uses and braking forces. We want to calculate the braking force, and also examine the factors that cause the braking force to differ.We attached a metal disk to a motor to make the disk rotate, then we control the distance between the magnet and the metal disk, therefore measuring the relativity of the distance and the rotational speed. We discovered that when the metal disk received a large quantity of the magnetic field (close distance), the breaking force and the rotational speed increased. On the other hand, when the metal disk received a small amount of the magnetic field (far distance), the breaking force and the rotational speed decreased. The magnetic braking force will convert into kinetic energy, thus, by using this connection and also by increasing the electric current to measure the resistance, we calculated the magnitude of the magnetic braking force. Hence we perceived an inverse ratio between distance and the braking force, that is to say, the closer the distance, the stronger the magnetic braking force; the further the distance, the weaker the magnetic braking force.
幽靈雷劈數的推廣及其性質研究
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！
「蓮」「環」密碼--環境因子對蓮花效應的影響
蓮花效應是指蓮葉表面具有奈米纖毛結構，因此只要葉面稍微傾斜，水珠就會滾離葉面，在我們生活週遭，許多植物具有蓮花效應。本實驗選擇彩葉山漆莖作為研究材料，因為我們發現在同一植株上，嫩葉的蓮花效應最佳，而老葉幾乎無蓮花效應。當彩葉山漆莖的新葉轉為老葉，蓮花效應會減弱，甚至消失。我們以不同水量、土壤酸鹼值及光照作為變因，來探討蓮花效應改變的原因，結果發現水量並非主要影響蓮花效應改變的變因；土壤過酸或過鹼，會減弱新葉及嫩葉的蓮花效應；置於暗室則使整株彩葉山漆莖所有葉面皆無蓮花效應。許多植物的性狀，在老化或面臨環境改變時，會將控制性狀的基因開啟或關閉。因此，我們推論，當環境因子改變時，植物的蓮花效應可能是經由基因層次的調控，藉以增強或減弱此性狀的表現。如果不是基因的開啟或關閉，則有可能僅是葉表面的結構發生些微的改變，真正詳細的機制仍有待進一步的確認。;We choose Breynia nivosa (Bull ex W. G. Smith) Small as a model plant to study the lotus effect on the leaves for the reason that on the same chosen plant the new-born leaves have the best lotus effect while the elder ones have little lotus effect. When the new leaves turns into elder ones, the lotus effect also turns weaker or even vanishes. To explore the exact mechanisms, we take water quantity、soil pH、and light density as the experimental factors. The results show that water quantity cannot affect the lotus effect on all leaves, change in soil pH can decrease the lotus effect on the new and new-born leaves, and dark treatments can eliminate the lotus effect on all leaves. When the environments change, the phenotypes of plants could also be changed to adapt to the new conditions by turning on or off genes. Therefore, we suggest that the lotus effect on the leaves is also controlled by genes to increase or decrease its phentype so as to adapt to the changing environments. If not, it may simply be a little change of the surface structure of the leaves. The detailed mechanism remains to be confirmed further.
有毛!沒毛!哪個好!?探討石田螺及其螺殼上附生藻類與環境因子之關係
This research is about two ponds in the Ｂ park’s and the Ｄ park’s snail(Square Mystery Snail：Sinotaia quadrata) in Taipei city of Nei-hu District for research object, carry out the study of the following research proceed: 1.Discriminate the algae species that are growth on the snail shell and which is a kind of interaction with the snail; 2.The influence of the snail and algae with difference of temperature, salinity, pH value and dark ; 3. The factors affect algae growth on snail shell; 4.Use the variation of snail and algae to be a biological incator. The result manifestation: the algae that are growth on snail shell have two kinds, one is Cyanophyta and the other is Cladophora sp. The interaction between algae and snail belong to communalism, but under the condition of lacking of food, the snail then will eat the Cladophora sp. which grow on the shell of other snails. The temperature adapts aspect, upper limit of the feat existence of the snail should be low in 28℃. When over than 28℃, Cladophora sp. as the most strong, Cyanophyta is secondly, and the snail then is most poor. For the maximum tolerance of the salinity, the snail is about 4.375?, Cyanophyta is about 5.0?, Cladophora sp is then about 7.0?; Under the different salinity for the tolerance , the Cladophora sp. still the most strong, Cyanophyta is secondly, and the snail then is most poor. Under the dark environment, the speed of Cyanophyta begin to be bleaching is very fast than the Cladophora sp.. In the tolerance of pH value range: The snail is about pH=5～10, Cyanophyta is about pH=7～8, Cladophora sp. is about pH=6～8; When the pH value range is in the pH=5～8, the speed of the Cyanophyta occur changing is very fast than Cladophora sp.. The algae are growing on snail shell very different between two ponds, the main reason is water pH value dissimilarly: When pH value over than 8.5, there is no Cladophora sp. to grow on the snail shell, after the pH value to decrease, Cyanophyta then will compare early than Cladophora sp. to grow on the snail shell. Calculate by the classification of the freshwater biological incator : Two organic pollution degree of the ponds may be lain in theβ-mesosaprobic to theα-mesosaprobic, and the polluting degree of the Ｄ pond is more seriously. As for two ponds, have already faced what level of eutrophication? Belong to actually which stage of pollution grade? Not only added the classification data of floating and fixative algea in two ponds, and also according to the parts of chemistry analysis method measure of the data makes the substantial evidence, then could carry out the more accurate and thorough study in the days to come steadily studying process.本研究是以臺北市內湖區兩個綠地公園(Ｂ公園與Ｄ公園)池塘內的石田螺(Sinotaia quadrata)為研究對象，進行以下研究目的之探討：1.鑑別石田螺螺殼上藻類的種類及其與石田螺的互動關係；2.溫度、鹽度、酸鹼值及黑暗等環境因子的差異，對石田螺及螺殼上附生藻類的影響；3.影響藻類附生於石田螺螺殼上的因素；4.將石田螺及螺殼上附生藻類的變化作為監測環境因子或水質變異的指標現象。結果顯示：附生於石田螺螺殼上的藻類有藍綠藻(Cyanophyta)與剛毛藻(Cladophora sp.)兩類；與石田螺的互動關係應屬於片利共生(communalism)，但在缺乏食物的情況下，石田螺則會採食同伴殼上的剛毛藻。溫度適應方面，石田螺適宜生存的溫度上限應低於28℃，超過28℃水溫環境的耐受程度，是以剛毛藻為最強，其次是藍綠藻，而石田螺則為最差。對於環境鹽度最大耐受度方面：石田螺約為4.375??，藍綠藻約為5.0??，剛毛藻則約為7.0?；在不同鹽度環境下，鹽度的耐受程度，仍以剛毛藻為最強，其次是藍綠藻，而石田螺則是最差。在黑暗環境下，藍綠藻褪色產生白化現象的速度明顯地比剛毛藻要快了許多。在環境酸鹼值耐受的範圍方面：石田螺約在ｐＨ＝5～10 之間，藍綠藻約在ｐＨ＝7～8 之間，剛毛藻則約在ｐＨ＝6～8 之間；而酸鹼值範圍在ｐＨ＝5～8 時，藍綠藻產生變化的速度明顯地比剛毛藻還要快。而兩樣區池塘水體酸鹼值的不同，應是造成石田螺螺殼藻類附生現象差異的主要原因：當酸鹼值超過8.5 時，螺殼上就無剛毛藻附生，當酸鹼值降下後，藍綠藻則會比剛毛藻早出現在螺殼上。藉由淡水生物指標的分類推測：兩樣區池塘水體有機污染程度，可能介於β-中腐水性(β-mesosaprobic,βm)至α-中腐水性(α-mesosaprobic,αm)的範圍之間，而Ｄ池塘受污染的程度應會比Ｂ池塘還要更嚴重些。至於兩樣區池塘水體，已面臨了何種優養化的程度？究竟是屬於哪一個階段的污染等級呢？除須補充水體中浮游性及附著性藻類分類的詳細觀察資料外，仍必須參照部分水質化學分析法所測得的數據作佐證，才能在日後持續地研究過程中進行更精確及深入的探討。
台灣地區冷泉成因的實驗室模擬
本實驗是以實際探勘的地質及泉水資料和文獻為基礎，對於幾個可能造成冷泉降溫的原因(岩石種類、泉水pH值、流通氣體之壓力、流速)進行實驗。我們製作了一個模擬地下泉水流動的實驗管路，此管路並可同時觀察紀錄氣壓、氣體流速，以及實驗前後模擬管路的溫度變化。透過對實驗管路的熱容量校正，我們可以找出各變因對泉水降溫的關係，以建立出一個模型，期望可套用於實際冷泉的狀況，進而推論出更多冷泉的性質。This experiment uses data and bibliography from real exploration as bases to find the possibilities of why the cool spring drops in temperature. (Mineral types, spring water's pH value, air flow pressure, and movement flow.) We created a model of underground spring water for the simulation. From this model, we could observe the air pressure, movement, and the spring's change of temperature before and after the tests. By adjusting the thermal capacity in the model, we could find the direct cause of the spring's temperature drop. And hopefully be able to adopt this model to the realistic problem, increase the effort of analyzing the natural cool spring's properties.