In this project, the stem of the banana tree is innovated into the absorbent substance in the baby’s diapers. A water proof material too has been innovated . In the study carried out, several changes has been identified in the production of an environment friendly disposable diapers.The structure of water molecules and cellulose as well as charges in both materials will enable cellulose present in all green plants to absorb water easily and effectively. Cellulose is also insoluble in water or solvent. This project uses the banana stem due to its high cellulose content and furthermore the cellulose present has a very fine structure which will increase its absorbency rate. Baby’s urine will be absorb into the absorbent material through capillary actions due to surface tension that develops between the cellulose and baby’s urine. The absorbent substance in baby’s diapers available today in the market is made up of Polyacrilate (SAP) and cellulose which are extracted from hardwoods, particularly pine trees. The production of the absorbent substance from the cellulose will help to reduce the logging of hardwoods.

1. Purpose of the research: Recovering bioethanol from fruit wastes by using brewing yeast and enzyme Viscozyme L\r 2. Procedures: Four different experiments were conducted in our project.\r Experiment-1: Samples in RM by the addition of only S.Cerevisia.\r Experiment-2: Samples in RM broth meduim by the addtion of 100 μl/g ViscozymeL and S. Cerevisiae\r Experiment-3 : ViscozymeL with different concentration\r Experiment-4: to determenine whether the enzyme with high concentration inhibited the fermentation.\r Analysis of ethanol: HPLC method was used for the analysis;\r HPLC method: (high performance liquid chromatography)\r 3. Data\r HPLC measured initial and final concentrations of glucose and ethanol by the addtion of S. Cerevisiae.\r Initial glucose concentration and final ethanol concentration was the highest in Grape pulp 12 and 9 g/L respectively. Despite the glucose concentration was the lowest, the ethanol concentration was quite high (7 g/L) in the mixture with orange. The lowest ethanol was produced in the mixture with pomegranate.\r Concentrations of ethanol and glucose from the samples in RM broth meduim by the addtion of 100 μl/g ViscozymeL and S. Cerevisiae\r After the 24 hour incubation by the addition of enzyme glucose concentration incresed by 1, 4 and 2 respectively in sample 1, 2 and 3. The ethanol concentrations in comparison to first experiment were higher especially in the sample1 (grape pulp).\r Effect of ViscozymeL with different concentration on glucose production.\r The glucose concentration generally increased by the addition of 200 micro L of enzyme as the time proceeded. In grape pulp sample glucose concentartion didnt increased by the addition of 500 micro L enzyme.\r The remaning glucose and produced ethanol concentrations by the addition of viscozyme L with two different concentartion and S. Cerevisiae\r As the concentartion of enzyme added incresed the amout of ethanol also inreased in sample 2 and 3 but in the sample 3 the fermentation was inhibited.\r 4. Conclusions\r In this study sugars in fruit wastes that are regularly not recylecled were fermented successfully into ethanol by using S. Cerevisiae.\r Generally we get more ethanol from the samples when the enzyme was used. As the graph5 shows the ethanol concentration generally increased as the enzyme concentration increased. But especially in the sample1 (mixture with pomegranate) at 200 and 500 micro liter concentrations, ethanol production were 2 and 0 g/L respectively. In the light of this daha we conluded that the enzyme with high concentartion might inhibit the fermentation. When the activity of enzyme was inhibited by keeping the pretreated enzyme in boiling water, the fermentation restarted and recovered more ethanol; 8 and 12 g/L at the enzyme concentration of 200 and 500 microliter respectively.

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.

We study the effect of dark energy on the evolution of cosmic structure in a scenario where the dark energy is treated as free particles and thus can be localized. By theoretical derivation and numerical simulations, we found that: 1. The dark energy particles gain kinetic energy from a moving dark matter particle through gravitational interaction. Due to energy conservation, the dark matter particle will slow down with time Ek(t) = Ek0 - 9 × 10-5[|1+3w|ρDE]1.92t where Ek(t) is the kinetic energy of the dark matter particle,Ek0 is its initial kinetic energy, w is the coefficient of equation of state for dark energy, ρDE is the mean energy density of dark energy, and t is the time. 2. The formation history and structure of galaxy clusters are different in the presence of localized dark energy. The more the localized dark energy, the earlier the formation of the cluster core. In addition, the kinetic energy Ek(R) as a function of R will be different if the ρDE is different. Thus we can compare the observed Ek(R) of clusters with our results to deduce the ρDE in our universe. The results here can be applied to the observations in the near future. 我們探討宇宙結構演化受到可局部叢集之黑暗能量粒子的影響。藉由理論推導及電腦模擬，我們發現： 一、黑暗能量粒子會透過重力交互作而從運動中的黑暗物質粒子獲得力學能。因力學能守恆，黑暗物質粒子的速率會減慢，滿足 Ek(t) = Ek0 - 9 × 10-5[|1+3w|ρDE]1.92t 其中Ek(t) 為黑暗物質粒子的動能，Ek0 為其初始動能，w 為狀態方程式係數，ρDE 為黑暗能量的平均密度，t 為時間。 二、星系團的形成過程及結構，會因可局部叢集之黑暗能量的存在而改變。黑暗能量越多時，星系團的核心會越早形成。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，因此可以將量測到的 Ek(R) 和這裡的結果比對，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。

Adducin蛋白在細胞骨架的調節上扮演著重要的角色。然而，近來有許多研究指出，骨架蛋白也會出現在細胞核並參與轉錄調控，因此本研究的目的即在探討adducin蛋白是否會進入細胞核中，並參與轉錄調控或具有其他功能。在本研究中，我們將綠色螢光蛋白(GFP)標示的adducin質體DNA，利用轉染技術送入老鼠纖維母細胞株NIH3T3中表現。NIH3T3細胞原本並無adducin蛋白的表現，在共軛焦顯微鏡下觀察，野生型的GFP-adducin蛋白會表現於細胞核與細胞質中。由於adducin蛋白尾端序列攜有可能往核內運輸的訊號，於是將位在此一訊號中的離胺酸718及離胺酸719進行突變，結果發現此一突變株只能在細胞質中表現。此外，蛋白磷酸脢C(protein kinase C)已知能磷酸化adducin蛋白在絲胺酸716及絲胺酸726的位置，於是假設其磷酸化是否與其在細胞內的分布有關。將adducin的絲胺酸726置換成丙胺酸，並不影響其在細胞內的分布。然而將絲胺酸716置換成丙胺酸後，則完全只在細胞核中表現。由於adducin可分布於細胞核，因此我們懷疑adducin蛋白可能與細胞分裂有關，於是本研究利用流式細胞儀分析adducin轉染後NIH3T3細胞的細胞週期。流式細胞儀的分析結果顯示，攜有GFP-adducin或其突變株的細胞與未經轉染的NIH3T3細胞的細胞週期並沒有顯著差異。其次，為了避免因轉染的效率不高而造成統計上的誤差，我們利用顯微鏡追蹤技術觀察攜有GFP-adducin的細胞株，結果顯示攜有adducin突變株的NIH3T3細胞株仍能正常分裂。再者，因為adducin能與細胞骨架中的肌動蛋白結合，所以adducin不同的分布位置可能影響細胞附著與細胞展延的效率。細胞展延試驗的結果顯示，adducin及其突變株對細胞附著與細胞展延的效率並無明顯的影響。本研究的結果證明，adducin的確帶有往核內運輸的訊號，其在細胞質中的分布可能也同時受到絲胺酸716磷酸化的影響。然而adducin的功用似乎與纖維母細胞的分裂與展延無明顯的關聯性。Adducin, an actin binding protein, is known to play an important role in the regulation of the membrane cortical cytoskeleton. More and more evidence indicates that proteins involved in the cytoskeletal regulation could also reside in the nucleus and participate in gene regulation. Thus, the goal of this study is to examine whether adducin is expressed in the nucleus and involved in certain nuclear events. In this study, adducin and its various mutants were fused with green fluorescent protein (GFP) and transfected into mouse NIH3T3 fibroblasts which do not have endogenous adducin for monitoring their subcellular distribution under a laser scanning confocal microscope. The wild-type GFP-adducin was found to be present both in the nucleus and in the cytoplasm. The COOH-tail of adducin contains a motif analogous to the nuclear localization signal (NLS). Mutation of two lysine residues (lysine 718 and lysine 719) located within this motif abolished the nuclear localization of adducin. Moreover, adducin is known to be phosphorylated by protein kinase C at serine 716 and 726. Substitution of adducin serine 726 with alanine had no effect on its subcellular localization. In contrast, substitution of adducin serine 716 with alanine led to only nuclear expression. Nuclear localization of adducin renders it possible that adducin may be involved in the regulation of cell division cycle. For cell cycle analysis, flow cytometry was applied. The results of flow cytometry indicated that expression of adducin and its mutants in NIH3T3 fibroblasts did not affect their cell cycle progression. To further examine the effect of adducin on cell division, NIH3T3 cells transiently transfected by adducin were monitored by time lapse video microscopy. The video clearly showed that the cells with GFP-adducin underwent cell division to generate two daughter cells. Since adducin is well known to bind to actin and thereby regulate microfilaments, we wondered that expression of adducin in NIH3T3 cells might affect their adhesion and spreading onto extracellular matrix proteins. The results of cell spreading assays showed that adducin appeared not to affect cell spreading. In conclusion, our results demonstrate that the subcellular distribution of adducin is likely regulated by two signals, one is the nuclear localization signal and the other is the phosphorylation status of the serine 716. However, enforced expression of exogenous adducin in fibroblasts such as NIH3T3 cells does not alter their cell cycle or cell spreading on fibronectin.

Purpose of research. Microbial fuel cells (MFCs) are bioelectrochemical systems that generate electrical energy by exploiting the extracellular electron transport (EET) capabilities of electrochemically active bacteria (EAB) (Logan 2009). This investigation aims to identify genes involved in driving bacterial EET with a new procedure that enables rapid screening of a side array of genes. These insights may lead to improved MFC performance through enhancing reactor design or genetic engineering EABs (Alfonta 2009). Procedures. MFC metagenomic analysis. Twelve MFCs incubated with four different bacterial samples were operated for approximately one year. The bacterial DNA from before and after incubation was extracted and the 16S rRNA regions were PCR amplified and sequenced. The bacterial community changes were analyzed using the QIIME program to identify bacteria that were being selected. Fosmid Clone Isolation. An E. coli fosmid library (Mewis et al. 2013) that contained genes from EAB inferred in the previous step was incubated in three MFCs. After a 48 hour enrichment period, biofilm samples from the MFCs were extracted and individual clones were isolated and screened in the MFCs individually. An E. coli DH5α strain with no insert DNA was incubated separately as the control. DNA sequencing. Fosmid insert DNA from high-performing clones were extracted, purified using gel electrophoresis, constructed into sequencing libraries and sequenced. Bioinformatics Analysis. The sequences were constructed into larger contigs using the Velvet algorithm package. The open reading frames (ORFs) were inferred and translated into amino acid sequences and annotated with proteins identified from the KEGG, and SEEDs databases using Metapathways 2.5. Results. The changes in bacterial communities from the metagenomic analysis revealed increases in relative abundance in numerous genera from Firmicutes and Bacteroidetes. The MFCs incubated with the fosmid clones generated about 4 times more peak power than the MFCs incubated with the E. coli DH5α. Polarization curves generated for the MFCs demonstrated that the fosmid clones were able to sustain a higher current. Incubation of pure cultures of individual clones yielded four clones with significant performance improvements over the control strain. Protein data from Metapathways outputs reveled both novel and previously reported EET genes encoding for Type IV pilus structures, c-type cytochromes, soluble cytochromes, flavoproteins, and porins. Taxonomy inferences of the gene inserts by the Green Genes database reveal the genes most likely came from the same EABs that were inferred from the metagenomic analysis. Conclusions. The increased performance of the fosmid clone-powered MFCs suggest that the clones carried genes that enhanced their performance in the MFCs. This is further confirmed by polarization curves generated for the MFCs. The results of the taxonomy inferences suggest that the bacteria being selected for in the environmental samples carried genes that enhanced their performance in the MFCs, and that these genes were successfully identified in the subsequent steps. The results of this study demonstrate that using a gain of function approach to rapidly screen a wide array of genes in a gene library may be an efficient method to identify genes that enhance power generation of EABs in MFCs.

(a) Purpose of Research To investigate the wave conditions offshore along the South African coast to determine wave heights, intervals, and patterns. These results have demonstrated the power potential of ocean waves and identified sites for offshore power stations. The waves off of the South African coast are the most viable, as they have wave heights of between 2.7m (9ft) and 14.6m (48ft). It is also to assist in the development of my power station design, through research into offshore wave composition, principles, periods and characteristics. (b) Procedures I have used various calculations including the surface pressure of salt water per square meter to calculate the potential power produced by a buoy. These figures have been expressed in Kilowatt Hours, and are then able to be divided by the known consumption of a single USA household in 1 year. A figure of the amount of households that can be supplied by a single generator will then be reached. An approximate power output for a single buoy is between 200 and 300 homes per year (Dependant on wave height) A concept for a maintenance free electrical generator suitable for marine use has been investigated. The design will be made as: ● A working demonstration model capable of producing electricity, which consists of a Rotary Induction Generator, ● a scale model to show the appearance of one such generator & ● A large scale model to show how generators can be congregated to form a power station offshore. (c) Data Utilising the calculations of potential power output and the wave data, the financial viability of the generator has been calculated, in relation to current fossil fuel power stations, down to a cost per Kilowatt. Wave data from international marine monitoring websites that provide real time wave condition graphs, have been tracked by myself daily for over 1 month and recorded to provide a large data resource. This provides wave heights of multiple weather systems as well as averages. Costs have been investigated from Internet sources for electrical integration to the national power grid, as well as the generator manufacture. These are estimates, as the exact specifications of my device cannot be finalised without further prototypical research. (d) Conclusion With conclusions reached by thorough research into wave dynamics, weather patterns and their effects on wave heights, Rotary induction power generation and costs related to multiple power systems, I intend to demonstrate fully to the International Electrical Producers, that coal fired power plants are more costly and environmentally damaging than my revolutionary concept for a truly economically viable, ocean based generator system.

本文我們研究下列問題： 1. 何時心律會成穩定的狀態呢？ 2. 是否能建立出心律穩定的數學模型？ 3. 什麼樣的函數會使得心律趨於穩定？我們以xmp+i 表示第p+1 個訊息傳到第i 個細胞之前，第i 個細胞的舒張時間，而且xk 和 xk−m, xk−m+1,..., xk−1的關係為 In this paper we study the problems as follows: When will the rhythm of heart beats approach to a steady state? Can we set up the mathematics model with steady rhythm of heart beats? What kind of function will make the rhythm of the heart beating tend to be stable? The result of our study is as follows:

本研究針對台灣產水生植物，蓴菜之構造與生長環境、蓴菜對腸胃道常見致病細菌之抑菌效果以及主要成分暨化合物分析。由本研究結果得知，崙埤湖內之稀有浮葉型水生植物蓴菜，其生長環境為無汙染之乾淨偏酸性水源，最適合生長之生深為50-160 ㎝；水溫則為22-25℃；而蓴菜之地下根莖對表皮金黃葡萄球菌（Staphylococcus aureus）具有輕度之抑菌效果，經由分離純化得知為BS-1：沒食子酸（Gallic acid）；另外，由蓴菜之葉片分離出十種成分分別為BS-2 （Kaempferol-7-O-Glucosids）、BS-3 （Quercetin-7-O-glucosids）、BS-4（5,8,4’-Trihydroxyflavone-7-O-glucosids）、BS-5 （3,5,8,3’4’-Pentahydroxy flavone）、BS-6（Vitamin E: d-Tocopherol）、BS-7 （Glyceride）、BS-8 （Phenolic A）、BS-9（Quercetin）、BS-10（Kaempferol）、BS-11（Phenolic B）。其中發現BS-8 對神經膠腫瘤細胞株有18.42%之抑癌效果，另外，BS-2、BS-3、BS-5、BS-10、BS-11 等成分，呈現良好之美白作用。This investigation is to analyze Brasenia schreberi Gmel., a native rare floating water plant in Taiwan, focusing on the plant’ s structure, its growth environment and, most importantly, the effect of chemical compounds it produces on restraining the common pathogenic bacteria in human stomach. The result indicates that the most suitable growth environment for Brasenia schreberi Gmel. is in slightly acid, pollution-free water such as that in the lake Lung Pi in northern Taiwan. The ideal water depth for its growth is 50-160 cm, and the water temperature is 22-25°C. The impractical BS-1 (Gallic acid) extracted from the izome of Brasenia schreberi Gmel. by separation and purification has a light effect on restraining Staphylococcus aureus, a bacteria in the stomach. From the epidermis of the blade of Brasenia schreberi Gmel., ten other ingredients are also isolated, including BS-2 (Kaempferol-7-O-glucosids), BS-3 (Quercetin-7-O-glucosids), BS-4 (5,8,4’-Trihydroxyflavone-7-O-glucosids), BS-5 (3,5,8,3’,4’-Pentahydroxyflavone), BS-6 (Vitamin E: d-Tocopherol ), BS-7 ( Glyceride ), BS-8 (Phenolic A ), BS-9 (Quercetin), BS-10 (Kaempferol),and BS-11 (Phenolic B). BS-8 is found to resist cancer C6 ( Glioma ) by 18.42%, while BS-2,BS-3, BS-5, BS-10, and BS-11 show an outstanding effect on skin-whitening.

NO.60-02 2021 APR | 科學研習期刊目錄 本期專題 文化與數學數養 以數學建模在STEAM教育中創價數學文化 | 楊凱琳 從數學史談核心素養之涵育：以「畢氏定理」為例 | 蘇意雯 怎識數學真面目？談數學文化與素養 | 劉柏宏 數學建模—操作實務與建構理論的橋樑 | 蕭志如 數學素養導向評量簡介 | 吳正新 談數學素養－生活中的數學記憶 | 李宗祐 教學現場 有數學感的分數教學：半條蛋糕平分給四個人 | 李源順、林旭霓 素養導向的數學課室樣貌―以國小三年級「小數」概念啟蒙教學為例 | 溫世展 素養導向的國小數學課室樣貌―以高年級「分數除法」為例 | 陳玉珊 「數戰棋」奠基模組融入數學教學之設計 | 孫德蘭 科學新知 看見格子點－高中數學的探究與實作 | 張宮明 朝三暮四－談Haberdasher問題的摺紙解 | 李政憲 特約專欄 繪本跨領域創造力探究學習活動 | 劉淑雯、楊紹圓 「今天飛不飛？」－金門高中生活議題之探究實作課程分析 | 丁于真、李育賢、黃琴扉 森棚教官數學題-圓形軌道碰碰車 (配合3/14國際數學日Pi Day) | 游森棚 大氣河長江水 | 盧孟明 科普活動報導 臺灣科學節創意實作科學營推廣與省思 | 洪偉清 女孩們，FUN科學! | 黃真瑱、呂玉環、林琦峯、蘇萬生 科教館GO好玩 「點實成今」-中小學科展一甲子特展紀實 | 蘇珮婷 總召集人的話 最近在看「好音樂的科學」，這是一本同時從科學理性及音樂感性的角度讓我們理解聽眾跟音樂產生共鳴的機制—情感連結，當然還有很多好東西要深究此書才能享用到。科學如同音樂般，透過多層次的轉譯，透過不簡單的語言，讓受眾在情感上受到挑戰、啟發，才有機會與情感對準頻率產生共振，才有主動探究的力道。試想一條琴弦，琴弦的材料、鎖緊的張力以及固定的方式都會對於彈奏的效果有所影響；這時需要數學建模把弦的振動方程式推導出來，再來就是有系統的求解，從不同的振動模態跟音樂之間的關係開始有了連結。 數學建模需要豐富的生活經驗作為後盾，數學建模歷程對於問題解決是個很好的學習典範，又數學建模與STEAM相關學科的整合是實踐數學文化多種價值的很好策略。「文化中的數學」與「數學中的文化」交錯互動耦合成為「數學文化」，您知道多少種畢氏定理的證明方法?人類發展過程中的數學扮演的角色可以透過「柏拉圖多面體」的美與「七橋問題」的趣味來說明。結合數學史的脈絡，展現不同時空文明間的問題解決方法，可以協助學習者將抽象觀念具體化，在學習數學過程中，也能認識這些問題在我們人類文化中代表的意涵。 想知道如何建立「帶著走」的數學能力嗎?如何建立素養導向評量工具?這些目標都是讓學生從真實情境中，學習思考、提問以及建立問題解決的能力，進而產生學習遷移，達到終身學習的目標。生活中的數學記憶則透過生活中的許多實例，如鉛筆工廠的倒三角形容器、酒杯堆疊的二階等差數列、祈福摺紙、牛奶盒的堆疊，讓學生理解生活中的數學應用；有空時也該搜尋自然界中無所不在的數學元素，讓數學之美提升對數學的相關概念及精神並內化到自己的所學。 熟悉代數運算的大人們遇見算術問題的解釋，就突然間發現需要回到童年時期的思考。國小的數學教育是很具挑戰性的，如何在先備知識不多的情境之下逐步建構學生的知識體系?半條蛋糕平分給四個人，要如何表達有感的分數教學?如何透過生活情境、學習需求及操作有感的學習啟動小學三年級的小數啟蒙教學?還有高年級的分數除法，結合數感理論的讓學生說、讓學生畫圖、讓學生舉例等教學策略，引導學生有感的數學學習。 課堂上要吸引學生的目光需要好的任務設計，如何透過活動及遊戲在競爭中增加挑戰性，還要從玩樂中增強學生數學的準備度?看見格子點---高中數學的探究與實作是思考與探究的很好例子，很值得讀者拿起鉛筆，跟著做一遍，動腦歸納動手畫。切割及拼布問題--朝三暮四，是講縫紉商透過適當切割正三角形拼布，再重新拼組為正方形的問題；透過討論四種不盡相同的正方形切割重拚為正三角的組法，並比較不同切割方式的差異性，非常有趣，看了好想跟著動手裁切拼裝。 繪本跨領域創造力探究學習活動透過第一線教師的學習活動分享，讓讀者有典範學習之效。「今天飛不飛？」一文讓讀者理解使用航空站公開資訊結合生活議題，做出不同條件的估算，以達探究與實作之效。森鵬教官照例給了趣味有挑戰性的圓形軌道碰碰車，三輛車從十二等分圓周上的指定出發點及指定方向出發，在特定條件及設定的規則下，這三部車要經過多久才能同時回到原來的出發點。 地上的河流、空中水氣形成的大氣河是全球水循環的基本現象，值此久旱不雨的今天，讀此文章特別有感；對於大氣河的發生及地點的氣象預報準確度提升，有助於因應變動加劇的未來。舉辦活動是需樣樣兼顧、統籌運轉且勞心勞力的工作，臺灣科學節創意實作科學營的舉辦，綿密的合作夥伴以及各方資源的投入都值得參考學習。科教館透過執行科技部女性科技人才培育計畫，入校推廣科學實作的課程以及推動高年級女學生探究與實作課程的教學實況。中小學科展六十年了，有許多好作品值得學習，「點實成今」-中小學科展一甲子特展紀實呈現整個策展的理念以及所欲表達的探究、好奇及融入生活；展現創新思考、解決問題與合作學習的科展精神。 這一期的科學研習月刊是數學含量很高的一期，讓我們跟著動手玩玩、動腦想想，也趁機省思數學文化及數學學習的各個面向。 總召編輯委員 - 李旺龍 關於本刊 出版單位：國立臺灣科學教育館 發行人：劉火欽 總召集人：李旺龍 編輯委員： 物理科吳仲卿/陳耀榮/李柏翰/盧玉玲 | 化學科古建國/許良榮/王伯昌/林如章/周金城 | 生物科王美芬/蕭世輝/陳建志/郭淑妙 | 地球科學許民陽/王郁軒/李文禮/謝隆欽 科技科張玉山/汪殿杰/林育沖/趙珩宇 | 數學科李源順/鄧家駿/溫世展/張宮明 | 跨領域學科李名揚/連信仲 | 特約專欄 游森棚/黃琴扉/陳正改/劉淑雯 策劃：曾聰邦 主編：吳中益 本月專題特約主編：李源順 編輯：佟冠誼 網頁設計編輯：施曉恬 投稿規範請來信詢問：article@mail.ntsec.gov.tw

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.

對4 × 4 方格表中計數問題的二個解題方法(1..解方程式的方法， 2.分割圖形的方法)作分析和研究後，首先我推廣分割圖形的方法來証明 : “好的n × n 方格表” 存在若且惟若n 為偶數。同時証明這種“好的n × n 方格表”內所有n2 個數的總和f(n) 為n(n+2)/4。當討論一般的n×m 方格表時，發現分割圖形的方法盲點，無法繼續推廣來証明。再經過深入分析與推廣解方程式的方法，藉由n×m 變數方格表，我們終於找到構造所有“好的n × m方格表”的方法。同時計算“好的n × m 方格表” (n≦m)內所有mn 個數的總和f(n,m), n≦7和証明好的nxm 方格表會有2(n+1)行一個循環的現象。We first studied two solution methods (1.solving equations,2.dissecting diagrams.) for calculations on 4x4 checkboard. Using the method of dissecting diagrams, we proved that``good nxn checkboard'' exists if and only if n is even. Furthermore, the sum f(n) of those n2 numbers in a ``good'' nxn checkboard is equal to n(n+2)/4.In studying the more general nx m checkboards, we found that the method of dissecting diagrams does not work, However, by extending the method of solving equations, and by considering nx m variable checkboards, we obtained a way of obtaining all ``good nxm checkboards.'' By way of computing the sum f(n,m) (n≦7) of those mn numbers in a ``good nxm checkboards,'' periodicity in every 2(n+1) rows is observed.