壹、研究目的：培養建構式思考方式，提高解決問題的能力。 貳、研究過程：一先查數學辭典，確定F.S.之定義。二以文字敘述替代數字敘述F.S.，並分析歸納規律性。三將發表過的有關關係式，挑選適合以代數分析研究者，研究採逆命題角度處理，共有下列七種關係式採論之。 壹、Motivation and Purpose In this study, we expect to know something about Fibonacci Sequence (F.S.) that we can understand and enjoy as a high school student. 貳、Procedure 一.Make sure the definition of F.S. 二.Use algebra instead of numerical to state F.S. 三.Select the related formulas and discuss by fundamental algebra. We get 7 types as follows

My project ‘Avert’ (To avert and vertebrae combined) involves research into posture related back problems and a solution to help prevent back pain by maintaining correct posture. My solution is a chain-like structure fitted with 24 sensors that is sewn into a Skins compression top. When worn the chain is aligned with the user’s spine from the lower back to the base of the neck and moulds to the spine as it moves. As everybody’s back is slightly different it is important that the device can recognise the difference between what may be bad posture for one person, yet relatively normal for another. To solve this the device takes an initial reading of the user’s spine in correct posture and saves it as a reference measurement. Bad posture is defined by the device as angles that exceed the natural movement of individual vertebrae and their platelets. While in use the 24 sensors are continually measuring the shape of the user’s spine and comparing it with the original reference measurement taken earlier. If any measurement links to unhealthy posture a light will flash and an alarm will sound either aloud or through headphones until the posture is corrected. This device can be worn during light activity and non contact sports to encourage the user to maintain correct and healthy posture. The device can also record and save poor posture measurements that can be uploaded later to a software program I designed to draw the shape of the spine as a vector diagram. The device can also be plugged directly into a computer so that the user can see the shape of their spine as it moves in real time. I, along with others, tested my solution with many activities and found Avert to be a beneficial and reliable product as it successfully detects slouching and many potentially problematic spine shapes. Throughout my research I gained a thorough understanding about the potential damage bad posture can cause and the endless number of activities it occurs in. With further development I feel there is a huge potential for Avert to become a marketable product used not only for posture correction in everyday activity, but for many other purposes such as physiotherapy, biomechanics and athletic performance. Many people have approached me with praise and requests for the Avert system which is extremely exciting and also rewarding to know that my research has the potential to help people.

During the biology classes from junior to senior high, we have learned many interesting instance of different animal behavior. Most people paid more attention on the Vertebrates as their experimental subjects. The other species around us, although with simple body structures, may behave rather complicated and versatile reactions. In particular, one of the most common insects with simple body structure in our neighborhood is the American cockroach (Periplaneta americana). The aim of this study is to investigate the different swing motion modes of antennae of American cockroach by computer-aided Imaging Analysis. The parameters of each swing motion mode were calculated in order to analyze how light (including light stimulation and light adaptation) and vibration may affect the antennae behavior of American cockroach. It was found that the antennae swing motion modes were significantly different under different types of stimulus. If two types of stimulus occurred at the same time, the reactions of antennae motion may become conformable. In conclusion, antennae behavior has shown to significantly affect the survivability and environmental adaptation of American cockroach. Not only the antennae are considered as the sensitive receivers; but also they are the important transmitters to reflect physiological status and environmental condition.從國中到高中的生物課堂上，我們學到許多有趣的動物行為例子，但前人多以脊椎動物作為研究對象，而我們身旁的許多生物，身體構造雖較為簡單，但行為表現卻豐富多樣，尤其是常見的美洲蟑螂(Periplaneta americana)，可說是最親近我們的昆蟲之一。本研究以攝影紀錄的方式，透過電腦進行影像分析，記錄不同刺激下蟑螂的觸角擺動模式，並計算出各項觸角運動的參數，以瞭解光線(照光刺激或照光適應)與震動刺激對其觸角行為的影響。我們發現在不同因子的刺激下，觸角擺動的模式具有差異，若兩種刺激同時發生，蟑螂觸角的行為亦具有整合性的反應，證明蟑螂觸角的行為模式，對其生存與適應具有重要意義。這也代表觸角除了為敏感的受器，亦為能反映出生理與環境狀態的重要動器。

(一)內錐孔傳統之量測方法： 利用兩直徑不同之鋼球置於錐孔內而測出兩球之中心距離，計算出半角(Sinθ/2)之值再求正切(Tanθ/2)函數乘以2即得： 兩球中心距 c=h-d1/2+d2/2=[2h-(d1-d2)]/2 兩球半徑差 a=d1/2-d2/2=(d1-d2)/2 Sinθ/2=a/c=[(d1-d2)/2]/{[2-(d1-d2)]/2}=(d1-d2)/[2h-(d1-d2)] (二)以上測量時須使用l.平板 2.鋼球 3.高度規 4.深度分厘卡等綜合如下。 1. 需較多之量具。 2. 測量手續繁多費時。 3. 須經計算。 且在工作進行中無怯量測須待工作完成時才能量測。

1. Purpose of the research While studying about insects for school club activity, we found that there are differences in several anatomical characters of the insects according their habitats. Especially, the unguis was different as whether the insect lives in water or on land. So we observed the structure of unguis of some insects by microscope, and physically analyze to relate with the habitat of each insect. 2. Procedures First, we read papers and books about insect morphology to study about insect's unguis. Then, we collected samples of Chironomus plumosus(larva), Neuronia regina(larva), and Carbula humerigera. After pretreatment of samples, we put them in the SEM (Scanning Electron Microscope), observed the unguis of each insect and took pictures. 3. Data First, the larva of Chironomus plumosus has prolegs with numberless hooks that has a certain arrangement and the same angle of 90º. They also has several tiny swellings around the hook. Next, the larva of Neuronia regina has pincer-like unguis which were sharp and bend, reminding the shape of a quadratic curve. Lastly, Carbula humerigera has two large, thick pincer unguis, its form same as the of Neuronia regina. The unguis are very sharp and faced towards the land. 4. Conclusions Both the aquatic insects and the terrestrial insects have structures in unguis developed to increase precision on land. Especially, the angle of unguis were all close to 90º. In addition, aquatic insects like the larvas of Chironomus plumosus or Neuronia regina have particular characters increasing friction force according to resist the flow of water.

Steel slag, is received from iron and steel production facilities in Turkey, and is up to 25-30% from steel production. These couldn’t have been reclamation for any field of use and free stored in nature. When the structure of this slag examined, it was contained metallic formation (Fe2O3, Al2O3, MnO2, MgO2 etc.) and oxide compositions (SiO2, CaO2 etc.). The aim of this project is investigate metallic content of steel slag used as fertilizer in plants. For this purpose, slag is used to determine the physical and chemical characterization. Then, it is separated from metallic content by using shaking table and multi gravity separative (MGS) method. After these procedures, there are determinate 6 groups with different densities and different grit size. Element analysis was made of these groups by atomic absorption spectrophotometer (AAS) and ICP-OES system. In addition, mineral analysis was determined by XRD device. Thus, within each group minerals have been identified. Slag-soil mixture was prepared for determination the highest yield of using six different slag groups as fertilizer in the plant. Thus, corn crops were grown in different combinations. Then harvested corn plants and done soil analysis of the plants. As a result of experiments, percentage of the most effective slag-soil composition for corn was determined. The highest yield in the slag pot was determined the rate of %12.5 and coarse-grained. Ideally, the slag content found to be chinerals such as merwinite (3CaO-MgO-2SiO2), akermanite (2CaO-MgO-2SiO2), gehlenite (2CaO-Al2O3-SiO2). Thus, it was detected the steel slags can be used as feed material for plants. Hence by maintaining the ecological balance economic contribution to the country was achieved.

The experiment was primarily focused on studying whether the enzymes from different bacterial species collected in various hot spring areas still exhibited activities at high temperatures. A further study would be conducted on analyzing the unique characteristics universally found in the genes of selected bacteria. First, hot spring samples were collected form Peitou and Wulai, and then cultured on the PY, PTG, MFB, and TS media in the laboratory. After the broth media growing with thermophilic bacteria, a series of continuous dilution method and solid-plate spreading were applied to separate these bacterial clones. The genomic DNA of the selected bacteria was extracted and used to analyze subtilisin-like gene by polymerase chain reaction (PCR) and electrophoresis. Finally, we examined the six selected thermophilic bacteria with the enzymatic activities of fibrin- and milk-protein degradation. We successfully concluded the experiment by proving that these thermophilic bacteria still exhibited significant enzymatic activitives in the high-temperature environments. The results of this experiment can be applied in numerous fields, for example, thrombus treatment and food processing, and a more in-depth study shall warrant the due consideration. 這次的實驗，主要是研究在不同的溫泉區中所採集不同種類細菌，是否酵素在高溫下仍具活性，如果有，再進而研究它們的基因有何特別的共同之處。首先，我分別自北投和烏來採集水樣，到實驗室後再以PY、PTG、MFB 和TS 四種培養基做細菌的培養，接著再利用連續稀釋和固態塗抹來做細菌的分離。經過挑選和培養之高溫菌直接進行DNA 的抽取，並利用「聚合?鏈反應」和「電泳跑膠」技術分析其類似蛋白質分解酵素subtilisin 基因。另外，本研究同時針對所選定之6 株高溫細菌利用血栓和牛奶蛋白來測試其蛋白質分解酵素的活性。由以上實驗結果可以證明某些細菌在高溫的環境下酵素仍具活性。這次在高溫菌的實驗結論，可應用在很多地方，例如：血栓的治療、在高溫下食品處理‧‧‧等，應用相當廣泛。

本研究目的主要在瞭解昆蟲的複眼(compound eyes)結構，比較晝行性與夜行性昆蟲複眼之差異，探討其視覺遠近和複眼結構的關連，及進一步觀察其對不同波長光源反應的差異。本實驗使用反射式及倒立式顯微鏡來觀察複眼及其小眼的結構，及觀察其成像情形，並使用攝影式接觸分析儀與放大管來探討視覺遠近和小眼表面曲率之關連，另外在暗室利用不同波長的光源照射蝴蝶以觀察其反應。實驗結果顯示複眼是由數千至數萬個小眼組成，小眼表面曲率半徑隨選用物種在25.3μm 至117.6μm 之間，蜻蜓複眼上半部和下半部小眼曲率半徑分別為30.6μm、117.6μm，印證了蜻蜓複眼上看遠下看近的說法，也發現蝦子小眼是正方形，其他實驗物種則皆為六邊形，而蝴蝶對光的反應程度則是隨波長漸增而遞減。The main purpose of this study is to understand the structure of the compound eye of insects, to compare the difference between the diurnal insect’s compound eye (apposition eye) and that of the nocturnal insect (superposition eye), to explore the relationship between the vision and the structure of the compound eye, and to observe the eye’s reaction to the different light wave length. In this study, a microscope (OLYMPUS BX51M) and an inverted microscope (OLYMPUS 1X71) were used to observe the structure of the compound eye and its ommatidia, as well as the resulting image. A contact angle measuring instrument (Dataphyscis OCA 20) and a microscope (Mitutoyo NAVITAR) were used to determine the connection between the vision distance and the facet curvature of ommatidia. The butterfly’s reaction to the light source with different wave length was also observed in a darkroom. It was observed that the compound eye of insects is composed of more than a thousand ommatidia. Among the subject insects, the facet curvature radius of their ommatidia ranged from 25.3μm to 117.6μm. The radius of the top and bottom half of a dragonfly is 30.6μm and 117.6μm. It confirms a scientific finding that dragonfly’s top compound eye focuses farther than the bottom half. The facet of each ommatidium observed is hexagonal in insects compared with the square shape found in the eye structure of shrimp. Regarding the reaction to light of the butterfly eye; the reaction decreased when the light wave length increased.

Water is very vital in our lives as we cannot live without it. However our world is now facing a serious problem. Owing to the increasing population, water resources are scarce. In recent years, we can see that droughts have been affecting millions of people around the globe. In the meantime, people in developed countries have been wasting huge amount of water for flushing the toilet. According to the US Environmental Protection Agency, 30% of household water goes toward flushing the toilet. Countries like China, US, Canada and UK are still using fresh water in flushing, consuming 190 million L of fresh water every day, not to mention the energy needed in pumping the water. In fact, it is not necessary to use so much water to flush away substances like tissue, hair, urine etc. The water we used is far more than we need. However, as we cannot control how much water is used when we flush, all water in the cistern is flushed away. Realizing the seriousness of water shortage and wastage in flushing, we tried to invent a device to conserve water by controlling the amount of flushing water used. Firstly, we study the principle of normal flushing system so as to understand why flushing cannot be controlled. Then, we tried to think of ways to control flushing. We have tried various methods and materials. After the 6-month testing and modification, we successfully invented Fast Fabulous Flush. It is a device which can be fit into existing cistern to conserve water. With our invention, users can control the amount of water flushed according to needs, so as not to waste unnecessary water. Our invention costs a low price which is no more than 2 US dollar. Also, it can be fit into existing cistern within 3 minutes with simple installation process. Most importantly, flushing water can be conserved effectively. It is estimated that around 200L of water can be saved per household every day.

We study the magic power of dark energy and dark matter by using theoretical derivation and numerical simulations. We found that: 1. The dark energy will gain kinetic energy from the moving dark matter through gravitational interaction. Due to the law of energy conservation, the motion of the dark matter will slow down and satisfy Ek(t)−Ek0 ∝ρDE1.92 t, where Ek(t) is the kinetic energy of the dark matter, Ek0 is its initial kinetic energy, ρDE is the energy density of the dark energy, and t is the time. 2. The formation history and the structure of galaxies will be different due to the existence of dark energy. The more the dark energy, the earlier the formation of the galaxy core. In addition, the kinetic energy Ek(R) as a function of R will be different if the ρDE is different. Thus we can observationally measure the Ek(R) of galaxies, compare it will our results here, and then deduce the ρDE in our universe. The results here can be applied to the observations in the near future. 我們藉由理論的推導，配合電腦模擬的手段，來探討宇宙中黑暗物質和黑暗能量的神祕力量。我們發現：一、黑暗能量會透過重力交互作用而從運動中的黑暗物質獲得力學能，而且因力學能守恆，致使黑暗物質的速率減慢，滿足 Ek(t)−Ek0 ∝ρDE1.92 t, 其中 Ek(t) 為黑暗物質的動能， Ek0 為其初始動能， ρDE 為黑暗能量的密度，t 為時間。二、星系的形成過程及結構，會因黑暗能量的存在而改變。黑暗能量越多時，星系的核心會越早形成。而且動能 Ek(R) 隨著至星系中心距離 R 的變化，會因 ρDE 的不同而不同，因此可以試圖量測宇宙中星系的 Ek(R) ，然後和這裡的結果比對，即可推導出宇宙中的 ρDE 。這些研究成果，將可直接應用在未來的觀測結果上。

Tic tac toe (井字棋)是大家童年時期常玩的小遊戲，本研究希望能以人工智慧的概念編寫出能在遊戲中立於不敗之地的程式，並將程式寫入LEGO EV3主機，利用LEGO積木打造出一台能與人對下井字棋的機器人。在研究的過程中先將井字棋遊戲可能出現的棋路一一列出，再從中找出中最適合的應對棋路，並在遊戲過程中利用顏色辨識零件去偵測對手下棋的位置。經過測試，它的確能夠在遊戲過程中立於不敗之地。未來希望能針對更加複雜的賽局，例如象棋、五子棋或4*4、5*5的方格等，設計出能從人手中輕易取勝的機器人。

Our research is connected with the problem of the mercurious wasre products (MWP) recycling, luminescent lamps take a great part among them. The problem of recycling MWP is topical not only in Yakutsk, but also in other cities of Russia because of its toxic influence on the human’s body. Mercury is the top among eight the most dangerous metals. I have analyzed the conditions of recycling of luminescent lamps in Yakutsk schools. I have got data on the problem. There is a great amount of the fused luminescent lamps is stored in the territory of schools, it produces danger for the pupils’ health. On the research work I have proposed some ways of solution of the problem.