At the website “MathLinks EveryOne,” we found a problem “Snakes on a chessboard,” which was raised by Prof. Richard Stanley. The following is the problem. A snake on the m n chessboard is a nonempty subset S of the squares of the board with the following property: Start at one of the squares and continue walking one step up or to the right, stopping at any time. The squares visited are the squares of the snake. Prove that the total number of ways to cover an m × n chessboard with disjoint snakes is a product of Fibonacci numbers. We call the total number of ways to cover a chessboard with disjoint snakes “the snake-covering number.” This problem hasn’t been solved since it was posted on September 18, 2004, so it aroused our interest to study it. First, we used the way in which we added each block to the chessboard, and therefore we discovered some regulations about the snake-covering number of the1 × n , 2 × n and 3 × n chessboard. Through “recursive relation” and “mathematical induction”, we proved the general term of the snake-covering number of the1 × n , 2 × n and 3 × n chessboard. In the following study, we found a key method in which we added a group of blocks to the chessboard. Finally, we proved the general term of the snake-covering number of the m × n chessboard. Also, we discovered the way to figure out the snake-covering number of the nonrectangular chessboard.在網站“ MathLinks EveryOne ”中，我們找到了一個有趣的問題“棋然上的蛇” ( Snakes on a chessboard ) ，這個問題是由教授 Richard Stanley 所提出。問題如下：在m x n棋盤形格子上，蛇由任意一格出發，但蛇的走法只能往右 → ，往上↑，或停住 ‧ 若此蛇已停住，將由另一條蛇來走，且不同蛇走過的格子不可重疊”證明：將 m × n 棋盤形格子完全覆蓋的總方法數為費氐（ Fibonacci ）數列某些項的乘積。我們將把棋盤形格子完全覆蓋的所有方法數稱之為“蛇填充數” 由於這個問題自從 2004年 9 月 18 日被登在網站上後，還沒有人提出解答，於是引發了我們研究的興趣。首先，我們使用了將一個一個格子加到棋盤上的方法，並發現了 l × n 、 2 x n、 3 × n 棋盤形格子蛇填充數的一些規律。我們使用遞迴關係及數學歸納法來證明 l x n 、 2 x n ， 3 × n 棋盤形格子蛇填充數的一般項。在接下來的研究中我們發現一個特別的方法，一次增加數個方塊 ‧ 最後我們證明了，m x n, ，棋然形格子的蛇填充數的一般項 ‧ 而且，我們也找到如何求出不規則棋盤形格子的蛇填充數。

高斯曾經提出八皇后問題：八個皇后在8 × 8 的棋盤上有幾種放法可以使任意兩皇后不會互相攻擊？我們在原來的問題上加上一些條件，改變皇后攻擊規則，使得皇后失去一條對角線的攻擊方向，稱之為「跛腳皇后」。我們稱一個在棋盤上放置最多跛腳皇后使其不互相攻擊的放法為好放法；研究跛腳皇后放置在各類棋盤上其好放法的個數和性質。我們分別在六種棋盤上做討論：（1） 在平面n x n 棋盤上，我們證明了其好放法與完美極致史考倫型數列之間的對應關係，並歸納出相關的性質和定理。（2） 在平面m x n 棋盤上，我們固定一邊長度n，做出n 較小時好放法數的通式；我們也將其好放法對應至廣義史考倫。（3） 在環面n x n 棋盤上，我們說明了其好放法與完全剩餘系排列之間的對應關係，並歸納出相關的性質和定理。（4） 在環面m x n 棋盤上，我們固定gcd（m,n），做出gcd（m,n）較小時好放法數的通式。（5） 在柱面n x n 棋盤上，我們證明其與環面n x n 棋盤等價，說明其好放法具有和環面n x n 棋盤好放法相同的性質和定理。（6） 在柱面m x n 棋盤上，分成左右柱面以及上下柱面來做討論。我們歸納出相關性質和定理；並固定一邊長度n，做出n 較小時好放法數的通式。Gauss had researched about putting eight queens on the chessboard on the way that doesn’t make any queen attacks another one. Thus, we added some rules on the question: the queen loses one diagonal attacking-way and become the “lame queen”. We call a way that doesn’t make any lame queen attacks another one “a good way”. We have been investigating the amount and properties of good ways based on six kinds of chessboard: （1）We found the correspondences between the “good way” on n × n plane chessboard and the Perfect extremal Skolem-type sequence, and concluded some associated properties and theorems. （2） On m× n plane chessboard, we fixed the length n of one side of the chessboard, and accomplished the amount of good ways when n is small. We also correspond the good way to the Generalized Skolem.（3）We found the correspondences between the “good way” on n × n torus chessboard and the arrayal of complete residue system, and concluded some associated properties and theorems.（4）On m× n torus chessboard, we fixed the gcd(m,n) （greatest common divisor of m and n）, and accomplished the amount of good ways when gcd(m,n) is small.（5）On n × n cylinder chessboard, we proved that this kind of chessboard is equal to torus chessboard. So the good ways, characters, and theorems on cylinder chessboard are the same as on the torus one.（6）On m× n cylinder chessboard, we separate it into two cases: left-right cylinder chessboard and up-down cylinder chessboard. We concluded some associated properties and theorems, and we also fixed the length n of one side of the chessboard and accomplished the amount of\r the good ways when n is small.

由於奈米科技進步，奈米材料應用在產業上具有多功能的性質。本研究使用不同波美度的色料餵食家蠶，以找出最佳的彩色蠶繭色澤，並研究其如何影響家蠶所結出的蠶繭及色料附著在蠶繭上的絲。同時對色料附著的蠶繭進行水洗、光照、微結構的觀察，以試圖找出色料與波美度之最佳組合參數。由本實驗結果得知，利用奈米色料溶液60 ml，在紅色：1.048、藍：1.058、黃：1.039 的參數下，混合飼料30g，可獲得最佳的彩色蠶繭結繭成功率、均勻度較佳、耐褪色與耐洗滌等優點，並且可獲得表面結構光滑且較細的絲徑，約為19.87μm。相對的，一般色料粒徑為微米級，色彩度優於奈米色料，但表面結構較奈米色料粗糙且線徑較粗，約為21.51μm，易於褪色及不耐洗滌。 Because of the great progress of nano-technology, it has the quality of multi-functions to make use of nano-materials on industrial property. The purpose of this study is to find the best colored silkworm cocoons by mixing different consistency of pigments to feed silkworms. At the same time, this study wished to explore how the different consistency of pigments influenced the silkworm cocoons that the silkworms produced. Besides, in order to find the better association between pigments and Baume degrees, this study exposed the cocoons under different lights, washed with different detergents and take observations of micro-structure of the cocoons. The results of this study are as follows: using the nano-pigments 60 ml in different density, that is, red:1.048, blue:1.058, and yellow:1.039, then mixed them with silkworms’ forage 30g , in this way, best successful ratio to get colored cocoons, desired high visual effects in color, well distribution, long duration and strong resistance to detergents agents are obtained. In addition, we can still get glossy appearance and fine cocoons; the wire diameter is about the size of 19.87μm. On contrast, feeding with the ordinary pigments, the degree of colored silk is better than feeding with the nano-pigments, but the appearance of cocoons are rough and the wire diameter is about the size of 21.51μm.

此研究著重於機器瓢蟲在不同的操控變因下所走出之路徑是否存在著某些性質。對於轉向次數k→∞且轉向角θ為任意角時，我們計算各收斂點P於坐標平面上恰形成圓C：(x- 1/(1-r2)2+y2=(r/(1-r2))2。將瓢蟲的轉向點P1、P2連線，圓心C與收斂點P連線，則P1P2與CP之交點S的軌跡形成長軸長為圓C半徑(r/(1-r2))的橢圓，且此橢圓的焦點為P1(1, 0)與C(1/(1-r2), 0) 。各轉向點Pn(n∈□)位於一個方程式為R=mrθ-π/α，m=OP=√1/(1-2rcosα+r2)定角為cot-1(㏑r/α)之等角螺線上；同時繪出轉向次數k在不同值時，瓢蟲行進終點之軌跡，以驗證當k愈來愈大時，各終點形成的軌跡會趨近於一個圓。當k=2時，圖形為蚶線並證明其經平移後之極坐標方程式為 R=r+2r2cosθ。最後我們展示行進公比r→1- ，r=1，r→1+時所呈現的終點軌跡，並對此軌跡所呈現出的意象與自然界連結，而其實質關聯性則有待未來研究。

NO.60-01 2021 FEB | 科學研習期刊目錄 本期專題 全國科學教具創意競賽 第三屆全國科學教具創意競賽推廣與省思 | 洪偉清 謎之費西納色彩與貝漢轉盤 | 戴明鳳、高嘉鄖、廖偉翔、葉唐迪、林家賢、李芳瑜、程安瑜、邱彩瑄、張又懿 Arduino色散、折射、全反射實驗創作過程分享 | 張敏娟、吳翼翀 聲波干涉-2020全國科學教具創意競賽 | 吳明德、王立文、陳林志傑 物理實作課程研發平台介紹 | 駱芳鈺 教學現場 創意動手做活動融入自然課程之實作 | 盧俊良 跨域學習探究實作課程之教材教法 | 謝甫宜 發電機教學模組用於探究與實作 | 吳明德、陳林志傑 科學新知 科學闖關的設計與實施 | 謝迺岳 融入文化資產的科普旅遊學習新願景-以屏東二峰圳水故事遊程為例 | 陳正治 北投貴子坑岩壁的形成機制和演進過程 | 陳正改 特約專欄 科學繪本的選用與教學應用 | 劉淑雯、黃明宏 STEAM創新教具設計與教學實踐-恐龍鎖 | 陳彥妃、李雅君、黃琴扉 森棚教官數學題-一點點畢式 | 游森棚 科普活動報導 透過議題式桌遊創造科學對話與互動－從0到100的實戰設計工坊 | 顏慈瑤、黃奕誠、鄭秉漢、蘇萬生、張俊彥 總召集人的話 二十年前國科會科教處的一個大眾科學教育政策的制定，讓許多第一線的老師在多年的計劃滋潤培育之下茁壯，也因此有許多科技部科普活動計畫在教育部108課綱探究與實作上面有許多的貢獻及參與；真該謝謝當初制定此重要政策的主事者，真是高瞻遠矚。 本期專題單元有五篇文章；有參加過全國教具創意競賽的師生一定會想知道當初舉辦的緣由、過程、轉折及成就，也會想知道參賽者投入造成的話題與契機，讓文章說給你知道。轉盤上的線條、段落位置、形貌、全黑區域；從轉動中挑戰人類的視覺反應，讓文章說給你知道。 教學現場單元共有三篇文章；、、；教學現場第一線教師們，將樂趣引入、結合時事、精緻化科普活動教材以及展現開發者的巧思自製教材，透過光學探究實作教材教具的開發來展現跨域學習的教材教法。 科學新知單元的三篇文章：資深老師在一文分享在規劃、設計、舉辦科學園遊會，鉅細靡遺的提醒注意問題；科學含量高的旅遊會有些許壓力，融入在地文化及故事的屏東二峰圳水故事遊程會是不錯的想法；看完會讓你想到貴子坑水土保持教學園區走走，感受岩壁的美麗與哀愁以及聽他述說台灣島的前世與今生。 特約專欄單元的三篇文章，如何透過實作教材開發，讓學生在原理釐清、動手組裝與拆解的過程，能綜整STEAM跨域自主學習，請看；你喜歡看繪本嗎?結合STEM的科學繪本對科學學習的吸引力及鏈結歸納、在選用資料及教學應用方面在文章中有詳細描述。除了畢氏定理還加了質數的限制，等你來挑戰及找尋規律。 科普活動報導單元以第一屆台灣科學節的活動為例，讓讀者知道從問卷調查到工作坊的實施進而設計出具可操作、有議題內容的桌遊。 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：吳仲卿 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

本研究針對利吉惡地進行探討，研究此區之泥岩含水量、有機質含量、pH值、比重、可溶性陽離子含量、滲水特性和該區之植物種類，並探討坡度、水量對沖蝕率、山脊密度和溝痕形成之影響。 研究結果發現： 一、表層泥岩之含水率較高，深層泥岩最低。中層泥岩之有機質含量較高，表層與深層泥岩較低。各層泥岩pH值約8.1；無植被採樣點之 pH較高，有植被採樣點偏中性。有植被採樣點，其 Ca2+含量較高。 二、此區共發現十九種植物，其中銀合歡、相思樹屬優勢種。 三、坡度增加時，沖蝕率亦增加；水量增加時，沖蝕率、溝痕寬度也隨之增加，兩者呈高度正相關。第一區坡度較緩，山脊密度較大，第二區坡度較陡，山脊密度小，表面較平坦，溝痕較淺。Our research discusses with the contents of water in mudstone, the organic content, pH, the specific weight, the contents of dissoluble cation, dankness and the category of plants in Ligiligi Badland. Dissecting it`s slope, the abrasion of water, the density of mountain ridge and the formation of scuff mark. Outcome of our research： 1.Solum of mudstone is the dampest. Intermediate of mudstone has more organic content than others. Every bed of mudstone`s PH is 8.1. Having plants area is indifferent and having more Ca2+.2.We found nineteen categories of plants. For example Leucaena glauca and Taiwan acacia. 3.The more augmentation of gradient,the more increase of the abrasion of water and the breadth of the density and the abrasion of water too.

To measure the air quality of the city of Prince George by using lichen as bio-indicators of pollution.

受應力拉伸時，橡膠溫度明顯上升；縮放回原長，橡膠溫度驟降。由文獻得知橡膠內部具有特殊的鍵鍊結構，在一般的情況下，交鏈分子糾結成一團，狀態複雜；受外力拉伸時，交鏈分子依橡膠長度之增加而伸展，排列較為整齊，狀態之複雜度減小。根據熱力學第一定律，當內能變化為零，則外力作功會造成能量變化。在定溫之下，橡膠內能變化為零，當其受應力拉伸，使其內部交鏈分子排列複雜度降低，造成橡膠熵值減小，而有能量（dQ=TdS）的釋出。測量此一能量dQ 變化，即可計算出熵與狀態數之變化The temperature of rubber rises as it is stretched, its temperature comes back again while it restores to its original length. It is known that the rubber is consisted of long-chain molecules, the long-chain molecules strangle each other at normal state, however, they become more order when the rubber is stretched. Based on the 1st law of thermodynamics dU=dQ+dW, The deformation caused by applied force supplies energy to the rubber and reduce its entropy, the heat dQ (=TΔS) released by the reduction of entropy causes the temperature rise of rubber as dU=0. We report the study on the correlation of thermal properties and the molecular network in rubber, from the measurements of temperature change, the changes of entropy and the changes of states’ number were estimated.

This scientific research project “Tharn Din - Alternative Energy Source of the Future” is directed toward producing a new type of soil charcoal. Tharn Din, with excellent combustibility. The experiments were divided into six steps. First, we selected soils of exceptional adhesion property Next, we looked into many different combustible materials for soil admixtures. Many different formulas of soils and admixtures were tested. The most promising formulas were then optimized for maximum combustibility. After which, the best formula was chosen and we further optimized its combustibility. Combustion and ignition rate and characteristics of this formula were investigated. And lastly the effect of surface area on combustible rate was examined. It was found that mud was the best adhesive and wood chip was the best admixture. Tharn Din made of one part of mud and 3 parts of wood chips released higher thermal energy than normal charcoals. We found that a special type of Thai soil, Din See-eaw, when mixed with wood chips created Tharn Din of exceptional combustibi1it Ignition and combustible rates are proportional to the surface area of Tharn Din.

The main purpose of this study is to explore whether fruit flies (Drosophila melanogasters which background is 2U) can distinguish and memorize different colors and smells by learning. Futhermore, to find out the relation between age and learning ability, and analyze the influence of repeated training on how long the memory would last. According to our experiment, in smell training, the fruit flies are able to distinguish and memorize different smells, and young fruit flies have better memory than old flies. In color training, the fruit flies can distinguish and memorize different colors, but the effect was less than that of smell training. In intensive learning, proper times of learning increased the memory ability, but excessive learning exhibited an opposite effect. In the labyrinth experiment, we select and nurture the fruit flies having the best color memory in order to further understand the gene correlated with the memory learning. In addition, in one-time training, fruit flies are able to remember the smells and colors in four minutes, and young ones have the better ability. In six-time training, fruit flies have the ability to remember the smells and colors in twelve minutes. In the end, we hope you can know more about the learning and memory ability of fruit flies through our report. 本實驗主要探討果蠅是否可經由學習分辨、記憶顏色與氣味，並探討年齡與學習能力的相關性、分析多次訓練對記憶時間的影響。由實驗結果得知，氣味方面，果蠅有辨識記憶氣味的能力，以年輕果蠅的效果較佳；顏色訓練方面，果蠅亦可分辨記憶顏色；密集學習方面，適當學習次數內，有助於增加果蠅的記憶能力，但過度的學習刺激會降低學習效果。並且，我們選顏色訓練中記憶較佳的一組進行迷宮實驗，經三次的岔路選擇，選出對顏色記憶最佳的果蠅，希望能探討訓練過的果蠅子代能否有較優良的記憶。至於記憶時間方面，一次氣味學習，果蠅在四分鐘內皆有記憶，且年輕果蠅記憶效果較強，達六分鐘；另外，多次氣味學習，果蠅於第四次訓練效果最佳，且記憶能力可達十二分鐘。希望藉本實驗報告，以期更瞭解果蠅學習與記憶的資料。

It is used by pigeon owners, farmers and squatters. The machine peels thesunflower seeds and leaves them separate from each other. The seeds can be used for pigeons,birds and making of flour. The shells of the seeds can be used as compost and ferilizer. This is an eco-friendly system.

This study analyzed how short-term solar activities interact with the earth atmosphere, by using two statistic methods: Diffusion Entropy Analysis (DEA), and Standard Deviation Analysis (SDA). Since solar activities influence the Earth atmosphere in its radiating heat and magnetic field, we use DEA and SDA to calculate the exponents, H and δ, of the scaling law in three time series: “the intensity of solar flare” (representing by SOLAR H-alpha flare index), “magnetic anomaly of magnetosphere” and “sea surface temperature anomaly”. The values of H and δ show the time memory and correlative relationship between the event and next event happening in time series. When H = δ = 0.5, events occur in random. When 0.5