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| 几何学 |
几何学几何学是研究空间关系的数学分支，有时简称为几何。中文“几何”一词，为明代徐光启所创，希腊语原意为“测地术”。
簡史
几何学有悠久的历史。最古老的欧氏几何基于一组公设和定义，人们在公设的基础上运用基本的逻辑推理构做出一系列的命题。可以说，《几何原本》是公理化系统的第一个范例，对西方数学思想的发展影响深远。
一千年后，笛卡儿在《方法论》的附錄《几何》中，将坐标引入几何，帶來革命性进步。从此几何问题能以代数的形式来表达。实际上，几何问题的代数化在中国数学史上是显著的方法。笛卡儿的创造，是否有东方数学的影响在里面，由于东西方数学交流史研究的欠缺，尚不得而知。
欧几里得几何学的第五公设，由于并不自明，引起了历代数学家的关注。最终，由罗巴切夫斯基和黎曼建立起两种非欧几何。
几何学的现代化则归功于克莱因、希尔伯特等人。克莱因在普吕克的影响下，应用群论的观点将几何变换视为特定不变量约束下的变换群。而希尔比特为几何奠定了真正的科学的公理化基础。应该指出几何学的公理化，影响是极其深远的，它对整个数学的严密化具有极其重要的先导作用。它对数理逻辑学家的启发也是相当深刻的。
分支学科
- 平面几何
- 立体几何
- 非欧几何
- 罗氏几何
- 黎曼几何
- 解析几何
- 射影几何
- 仿射几何
- 代数几何
- 微分几何
- 计算几何
- 拓扑学
Category:几何学
ja:幾何学
ko:기하학
simple:Geometry
zh-min-nan:Kí-hô-ha̍k
空间
ja:空間
ko:공간
simple:Space
徐光启和徐光启]]
徐光启（），中国明末科学家，农学家，政治家。字子先，号玄扈。南直隶松江府上海县（今上海市）人。是天主教徒並且被稱為「聖教三柱石」之首。
徐光启万历三十二年（1604年）进士及第，任翰林院庶吉士，迁左春坊赞善。官至礼部尚书兼东阁大学士、文渊阁大学士，赐谥文定。现有徐光启墓在上海市徐汇区南丹路光启公园内。
他在农学、数学和天文学方面都有重要贡献。他晚年还亲自练兵，主张使用西洋大炮防卫。
他和利玛窦等意大利传教士合作翻译了欧几里得的《几何原本》前6卷，以及《测量法义》、《简单仪说》和《泰西水法》，又主编了《崇祯历书》。
徐光启对农事注重亲身实践和经验总结，一生中曾数度归田，从事栽培实验和撰写农学著作，著有《甘薯疏》、《吉贝疏》、《芜菁疏》、《代园种竹图说》、《北耕录》、《农遗杂疏》。
徐光启于天启五年（1625年）开始撰著《农政全书》，1632年入阁参与政务后仍不停止，不断补充，甚至在病中还执笔不休。遗稿经陈子龙修订，编成60卷，于崇祯十二年（1639年）刊行。
X徐
X徐
X徐
X徐
X徐
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几何原本
]]
《几何原本》（希臘文Euclidis Elementa）是古希腊数学家欧几里德所著的一部数学著作，共13卷。这本著作是现代数学的基础，在西方是仅次于《圣经》而流传最广的书籍。
- 1-6卷：平面几何
- 7-9卷：数论
- 10卷：无理数
- 11-13卷：立体几何
歷史
歐幾里德約於前300年寫成《几何原本》。
它翻譯成阿拉伯文，然後再二手翻譯成拉丁文。最先的印制本出現於1482年。希臘文版的文字仍然存在於各地，例如牛津大學的Vatican圖書館和Bodlean圖書館。遺憾的是這些現存手抄本品質參差而不完整。
有人認為，第13卷很有可能是後人加上去的。
中国最早的译本是1607年意大利传教士利玛窦和徐光启根据德国人克拉维乌斯校订增补的拉丁文本《欧几里德原本》（15卷）合译的，定名为《几何原本》，几何的中文名称就是由此而得来的。他们只翻译了前6卷，后9卷由英国人伟烈亚力和中国科学家李善兰在1857年译出。
相关条目
- 欧氏几何
外部链接
- [http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Euclid's Elements] (《原本》的在线英文版@美国克拉克大学)
Category:數學書籍
ja:ユークリッド原論
方法论方法论是笛卡儿在1637年出版的著名哲学论著，对西方人的思维方式，思想观念和科学研究方法有极大的影响，有人曾说：欧洲人在某种意义上都是笛卡儿主义者，就是指的受方法论的影响，而不是指笛卡儿的二元论哲学。
笛卡儿在方法论中指出，研究问题的方法分四个步骤：
#永远不接受任何我自己不清楚的真理，就是说要尽量避免鲁莽和偏见，只能是根据自己的判断非常清楚和确定，没有任何值得怀疑的地方的真理。就是说只要没有经过自己切身体会的问题，不管有什麽权威的结论，都可以怀疑。这就是著名的“怀疑一切”理论。例如亚里士多德曾下结论说，女人比男人少两颗牙齿。但事实并非如此。
#可以将要研究的复杂问题，尽量分解为多个比较简单的小问题，一个一个地分开解决。
#将这些小问题从简单到复杂排列，先从容易解决的问题着手。
#将所有问题解决后，再综合起来检验，看是否完全，是否将问题彻底解决了。
在1960年代以前，西方科学研究的方法，从机械到人体解剖的研究，基本是按照笛卡儿的方法论进行的，对西方近代科学的飞速发展，起了相当大的促进作用。但也有其一定的缺陷，如人体功能，只是各部位机械的综合，而对其互相之间的作用则研究不透。直到阿波罗号登月工程的出现，科学家们才发现，有的复杂问题无法分解，必须以复杂的方法来对待，因此导致系统工程的出现，方法论的方法才第一次被综合性的方法所取代。系统工程的出现对许多大规模的西方传统科学起了相当大的促进作用，如环境科学，气象学，生物学，人工智能等等。
笛卡儿在方法论中还第一次提出“我思，故我在”的名言，第一次引入笛卡儿坐标系。对牛顿和莱布尼茨发明微积分理论有很大的作用。
Category:哲学著作
ja:方法序説
ko:방법서설
代数代数是数学的一个分支。它是算術的概括和延伸。在现代数学中，代数主要研究各種代数结构，与中学所教的代数有极大不同。
历史
代数的起源可以追溯到3000多年前的古埃及人和古巴比伦人。他们用一种早期的代数解决线形的、二次方程和不定方程。
大约公元前300年的希腊数学家欧几里德在他的《几何原本》第二卷中论述了二次方程，尽管使用了严格的几何方法。
大约公元前100年，中国的《九章算术》一书中有论述代数方程。
Around 150 AD Greek mathematician Hero of Alexandria treats algebraic equations in three volumes of mathematics.
Around 200 AD Greek mathematician Diophantus, often referred to as the "father of algebra", writes his famous Arithmetica, a work featuring solutions of algebraic equations and on the theory of numbers.
Indian mathematician, Aryabhatta (476 AD) obtained whole number solutions to linear equations by a method equivalent to the modern one. Bhaskara II (1114 AD), who wrote bijaganita (algebra), was the first to recognize that a positive number has 2 square roots. The Hindus recognized that quadratic equations have two roots, and included negative as well as irrational roots. They treated indeterminate quadratic equations.
The word algebra itself is derived from the name of the treatise first written by Persian mathematician Al-Khwarizmi in 820 AD titled: Kitab al-mukhtasar fi Hisab Al-Jabr wa-al-Moghabalah meaning The book of summary concerning calculating by transposition and reduction. The word al-jabr (from which algebra is derived) means "reunion", "connection" or "completion".
Algebra was introduced to Europe largely through the work of Leonardo Fibonacci of Pisa in his work Liber Abaci in 1202.
分类
代数大致分为以下几类：
- 基础代数：讨论实数或複数系中基本运算，是中学数学的一部分。例如多項式因式分解、求解一次或二次代数方程式等。
- 抽象代数：讨论代数结构的性质，例如群、环、域等。这些代数结构是在集合上定义运算而来，而集合上的运算则适合某些公理。
- 线性代数：专冂讨论矢量空间，包括矩阵的理论。
- 泛代数, 讨论所有代数结构的共有性质。
- 计算代数：讨论在电脑上迸行数学的符號运算的演算法。
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代數是一種特殊的代數結構。給出環 R（其元素稱為標量），另一個環 A配以標量乘法 (r,a) → ra 適合
#r(a+b)=ra+rb，r∈R，a,b∈A
#(r+s)a=ra+sa，r,s∈R，a∈A
#(rs)a=r(sa)，r,s∈R，a∈A
#r(ab)=(ra)b，r∈R，a,b∈A
則A是一個 R-代數。實際上A亦同時是 R-模，而R亦是A-代數。
Category:代数
ja:代数学
ko:대수학
ms:Algebra
simple:Algebra
希尔伯特
希尔伯特（David Hilbert，1862年1月23日—1943年2月14日）是德国著名数学家，生于哥尼斯堡，在格丁根逝世。1900年，希尔伯特在巴黎的国际数学家大会上提出了著名的“希尔伯特的23个问题”。
希尔伯特的著作有《希尔伯特全集》《几何基础》《线性积分方程一般理论基础》等。
相关内容
外部链接
- [http://www.ebookcn.net/bbs/read.php?fid=29&tid=593 希尔伯特的数学生涯]
- [http://www.scxxt.com.cn/ziyuan/mdv/seniormath/mathstory/hilbert/hilbert.htm 希尔伯特介绍] [http://www.oursci.org/ency/people/020.htm] - [http://211.153.80.12/RESOURCE/CZ/CZSX/SXBL/SXTS1007/655_SR.HTM 大数学家希尔伯特]
- [http://www.nhyz.org/hef/maths/readnews.asp?NewsID=166 希尔伯特的两个小故事] - [http://blogs.ustcers.com/edwinhu/articles/537.aspx 数学历史的启示(龚昇)] - [http://www.lytu.edu.cn/math/wenzhang/mathematician/mathematics_sub/mathematics_theory.htm 近现代科学家透视]
category:德國数学家
X
X
ja:ダフィット・ヒルベルト
ko:다비드 힐베르트
th:ดาฟิด ฮิลแบร์ท
立体几何数学上，立体几何(solid geometry)是3维欧氏空间的几何的传统名称— 因为实践上这大致上就是我们生活的空间。一般作为平面几何的后续课程。立体测绘(Stereometry)处理不同形体的体积的测量问题：圆柱,圆锥, 锥台, 球, 棱柱, 楔, 瓶盖等等.
毕达哥拉斯学派就处理过球和正多面体，但是棱锥，棱柱，圆锥和圆柱在柏拉图学派着手处理之前人们所知甚少。尤得塞斯(Eudoxus)建立了它们的测量法，证明锥是等底等高的柱体积的三分之一，可能也是第一个证明球体积和其半径的立方成正比的。
令见: 阿基米德, Demiurge, 开普勒, 平面测绘, 柏拉图, Timaeus (dialogue)
...部分来自1911 Encyclopaedia Britannica
立体几何基本课题
包括:
- 面和线的重合
- 两面角和立体角
- 方块, 长方体, 平行六面体
- 四面体和其他棱锥
- 棱柱
- 八面体, 十二面体, 二十面体
- 圆锥，圆柱
- 球
- 其他二次曲面: 回转椭球, 椭球, 抛物面 ，双曲面.
其它课题
较高级的研究有
- 三维的射影几何导出了
- 用增加一个维度的方法的笛沙格定理的证明
- 更多的多面体
- 描述几何.
解析几何和向量技术通过允许系统的使用线性方程组和矩阵代数带来了重大的冲击；这在高维变得更为重要。研究这个主题的一个重要应用是计算机图形学，这意味着算法变得重要起来。
Category:欧几里德几何
罗氏几何
双曲几何又名罗氏几何（罗巴切夫斯基几何），是非欧几里德几何的一种特例，专门研究当平面变成鞍马型之后，平面几何倒底还有几多可以适用，以及会有甚麼特別的现象產生。在双曲几何的环境裡，平面的曲率是負数。
罗式几何
罗式几何学的公理系统和欧式几何学不同的地方仅仅是把欧式一对分散直线在其唯一公垂线两侧无限远离几何平行公理用“从直线外一点，至少可以做两条直线和这条直线平行”来代替，其他公理基本相同。由于平行公理不同，经过演绎推理却引出了一连串和欧式几何内容不同的新的几何命题。
我们知道，罗式几何除了一个平行公理之外采用了欧式几何的一切公理。因此，凡是不涉及到平行公理的几何命题，在欧式几何中如果是正确的，在罗式几何中也同样是正确的。在欧式几何中，凡涉及到平行公理的命题，再罗式几何中都不成立，他们都相应地含有新的意义。下面举几个例子加以说明：
- 欧式几何:
- 同一直线的垂线和斜线相交。
- 垂直于同一直线的两条直线或向平行。
- 存在相似的多边形。
- 过不在同一直线上的三点可以做且仅能做一个圆。
- 罗式几何
- 同一直线的垂线和斜线不一定相交。
- 垂直于同一直线的两条直线，当两端延长的时候，离散到无穷。
- 不存在相似的多边形。
- 过不在同一直线上的三点，不一定能做一个圆。
从上面所列举得罗式几何的一些命题可以看到，这些命题和我们所习惯的直观形象有矛盾。所以罗式几何中的一些几何事实没有象欧式几何那样容易被接受。但是，数学家们经过研究，提出可以用我们习惯的欧式几何中的事实作一个直观“模型”来解释罗式几何是正确的。
1868年，意大利数学家贝特拉米发表了一篇著名论文《非欧几何解释的尝试》，证明非欧几何可以在欧几里得空间的曲面（例如拟球曲面）上实现。这就是说，非欧几何命题可以“翻译”成相应的欧几里得几何命题，如果欧几里得几何没有矛盾，非欧几何也就自然没有矛盾。
人们既然承认欧几里是没有矛盾的，所以也就自然承认非欧几何没有矛盾了。直到这时，长期无人问津的非欧几何才开始获得学术界的普遍注意和深入研究，罗巴切夫斯基的独创性研究也就由此得到学术界的高度评价和一致赞美，他本人则被人们赞誉为“几何学中的哥白尼”。
category:几何学
解析几何解析几何，又叫做 坐标几何 ，早先也被称作 笛卡尔几何，是使用代数方法进行研究的几何学。通常，使用二维或三维的直角坐标系来研究平面、直线、曲面和圆的方程。有人认为，解析几何的提出是现代数学的开端。
在中学课本中，解析几何被简单地解释为：采用数值的方法来定义几何形状，并从中提取数值的信息。然而，这种数值的输出也可能是一个向量或者是一种几何形状。
1637年，笛卡尔在《方法论》的附录“几何”中提出了解析几何的基本方法。以法语和哲学观点写成的这部著作为后来牛顿和莱布尼茨各自提出微积分学提供了基础。
解析几何中的重要问题：
- 向量空间
- 平面的定义
- 距离问题
- 点积求两个向量的角度
- 叉积求一向量垂直于两个已知向量 (and also their spatial volume)
- 交集问题
这些问题中很多都牵涉到线性代数。
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对代数几何学者来说，解析几何也指（实或者）复流形，或者更广义地通过一些复变量（或实变量）的解析函数为零而定义的解析空间的理论。这一理论非常接近代数几何，特别是通过 Serre 在代数几何和解析几何领域的工作。这是一个比代数几何更大的领域，不过也可以使用项类似的方法。
Category:幾何學
category:代数几何
ja:解析幾何学
微分几何微分拓撲是一個处理在微分流形上的可微函数的数学领域。很自然地，它是在研究微分方程理論的过程中被提出來的。微分幾何是用微積分來研究幾何的学问。这些领域非常接近，在物理学，特别在相对论方面有许多的应用。他们合在一起还建立了可从动力系统观点直接研究的、可微流形的几何理论。
微分几何：
- 古典微分几何起源于微积分，主要内容为曲线论和曲面论。歐拉，蒙日，高斯被公认为古典微分几何的奠基人。
- 近代微分几何的创始人是黎曼
，他在1854年创立了黎曼几何(实际上黎曼提出的是Finsler几何)，这成为近代微分几何的主要内容，并在相对论有极为重要的作用。E.Cartan和陈省身等人曾在微分几何领域作出极为杰出的贡献。
內在對外在
从一开始到19世紀中葉, 微分幾何是從外在觀點来进行研究的: 曲線和曲面是被放在更高維歐幾里德空間中来考虑的(譬如曲面被放在三维的背景空间中)。其中的最简单的成果就是曲线微分几何中的结果。内在观点开始于黎曼的工作，在那里因为几何对象被认为是独立的给出的，所以不能说移到外面来考虑这个对象。
内在的观点更加灵活，例如在相对论中时空不能很自然的用外在形式表示。但用内在的观点，曲率和联络这样的结构比较难定义一些，所以采用内在的观点也不是没有代价的。
这两种观点也是可以融通的，即外在几何可以被看作是附加于内在几何上的结构。(见纳什嵌入定理)
技术要求
微分几何的工具也就是流形上的微积分：包括对于流形，切丛，余切丛，微分形式，外微分，-形式在维子流形上的积分以及斯托克斯定理，楔积，和李导数的研究。这些都和多变量微积分相关；但对于几何上的应用来讲，必须发展一种在某种意义上和特定坐标系无关的方法。微分几何的特殊概念可以说是那些体现几何本质的二阶导数：曲率的很多表现方式。
可微流形是一个拓扑空间，它有一个开覆盖，其中的每个开集同胚于中的一个开单位球。并且，如果,是其中两个同胚映射，则函数无限可微。我们称一个函数无限可微，如果它和每个同胚的复合是从开球到的无限可微函数。
在流形的每一点，有一个该点的切空间，它由每个从该点离开进行运动的所有可能的速度(方向和大小)所组成。对一个n维流形，每点的切空间是一个n维向量空间，或者说是一个Rn。切空间有多种定义。其中一个是作为所有在该点取值为0的函数组成的线性空间的对偶空间，除以
所有取值为0 并且一阶导数为0的函数空间(所得到的余空间)。导数为0可以定义为“和任何可微的从实数到该流形的函数的复合的导数为0”，因而只需要用到可微性。
向量场是从流形到它的切空间的并集(切丛)的函数，在每一点所取的值是该点的切空间的一个元素。这样的映射称为纤维丛的截面。
向量场可微，如果该向量场应用到每个可微函数都得到一个可微函数。向量场可以看作是时不变的微分方程组。从实数到流形的可微函数是流形上的曲线。这给了一个从实数到切空间的函数:曲线上每点的速度。一条曲线称为一个向量场的一个解，如果曲线每点的速度和向量场在该点的值相等。
交错k维线性形式是向量空间V的对偶空间V
- 的反对称k阶向量积的一个元素。k微分形式就是在流形的每一点选取一个这样的交错k形式--V在这里就是该点的切空间。如果它作用在k个可微向量场上的结果是流形上的一个可微函数，则称它可微。体积形式是维数和流形相同的微分形式。
分支
- 切触几何
这是辛几何在奇数维上的对应物。大致来说，在(2n+1)微流形上的切触结构是一个1-形式使得处处非退化。
- 芬斯勒几何
芬斯勒几何以芬斯勒流形为主要研究对象— 这是一个有芬斯勒度量的微分流形，也就是切空间被赋予了巴拿赫范数。芬斯勒度量是比黎曼度量一般得多的结构。
- 黎曼幾何
黎曼几何以黎曼流形为主要研究对象— 有额外结构的光滑流形，他们因此无穷小的看起来像欧氏空间。这使得欧氏几何的诸如函数的梯度，散度，曲线的长度等概念得到了推广；而无须假设空间整体上有这么对称。
- 辛拓撲
这是研究辛流形的学科。一个辛流形是带有辛形式(也就是，一个闭的非退化2-形式)的微分流形。
外部連結
[http://rsp.math.brandeis.edu/3D-XplorMath/Surface/a/bk/curves_surfaces_palais.pdf A Modern Course on Curves and Surface, Richard S Palais, 2003]
[http://rsp.math.brandeis.edu/3D-XplorMath/Surface/gallery.html Richard Palais's 3DXM Surfaces Gallery]
參考書
1. Michael Spivak (1999)， A Comprehensive Introduction to Differential Geometry，(5 Volumes),3rd Edition.
2. Manfredo Do Carmo (1976), Differential Geometry of Curves and Surfaces. Prentice Hall.
3. Manfredo Perdigao do Carmo, Francis Flaherty (1994), Riemannian Geometry.
4. John McCleary (1994), Geometry from a Differentiable Viewpoint
5. Ethan D. Bloch (1996), A First Course in Geometric Topology and Differential Geometry
6. Alfred Gray (1998), Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed.
Category:几何学
Category:微分几何
category:微積分
ja:微分幾何学
拓扑学
- 此條目談的是數學上的拓扑，其他含義請見消歧義頁面拓扑。
----
拓扑学，台灣叫拓樸學，是近代发展起来的一个研究连续性现象的数学分支。中文名称起源于希腊语Topology的音译。Topology原意为地志学，于19世纪中期由科学家引入，当时主要研究的是出于数学分析的需要而产生的一些几何问题。发展至今，拓扑学主要研究拓扑空间在拓扑变换下的不变性质和不变量。
分支学科
- 点集拓扑学又称为一般拓扑学
- 组合拓扑学
- 代数拓扑学
- 微分拓扑学
- 几何拓扑学
ja:位相幾何学
ko:위상수학
simple:Topology
Category:几何学Category:数学
ja:Category:幾何学
ko:분류:기하학
zh-min-nan:Category:Kí-hô-ha̍k Yakkity YakYakkity Yak was a television program that ran on Nickelodeon from 2003 to 2004. It was known for its extreme silliness, and featured a style of animation which broke with past Nickelodeon tradition. Created by Mark Garvas, the show was cancelled just months after it first aired because of generally low ratings. The show's slogan, "It's Just Plain Stupid," may have turned potential viewers away. Reruns are currently shown regularly on Nicktoons TV.
Yakkity Yak is a 12-year-old yak who dreams of being a famous comedian. While at school, Yakkity is doing the groundwork by playing “gigs”, including occasional kids’ birthday parties, impromptu school performances and anything else he or his semi-committed agent Trilo can get!
Yakkity’s two best pals are pineapple-headed Keo and Lemony. They are always by Yakkity’s side helping him through his mishaps.
Characters
- Yakkity Yak - Yakkity is a student at Onion Falls High - class clown and undervalued mascot for all of Onion Falls sporting teams including the rugby team. Yakkity got the job because his grandfather was mascot when the football team won the state championship in 1925. Much to Yakkity’s dislike, it’s the football team not the mascot who gets all the glory (well, not really, they haven’t won since 1925).
::Yakkity now lives with his Granny and her boarder Professor Crazyhair. His closest friends are Keo (whom lives next door) and Lemony. Yakkity and Keo’s relationship is a strong buddy relationship that is ever-evolving and has its difficulties but ultimately these are two best friends who need each other. Yakkity needs Keo as he’s grounded – Keo needs Yakkity as he needs to be pushed.
::Yakkity has his dream of comedic fame. Yakkity has his outlet through small gigs landed by the Trilo Entertainment Agency. From kids birthday parties to ‘Yakstravaganza’s, Yakkity is keen for experience. Even when encouraged by Trilo to fill in for Fairy Yakkity, which entails him dressing up as a ‘female fairy’, Yakkity takes it in his stride as he knows part of a comedian’s repertoire is a keen sense of character and be able to make laughs from impersonation.
- Mr. Highpants - The towns leading vendor of candy and all things sugared, Mr. Highpants’ store is also a party venue, such as in ‘Fairy Yakkity’. Highpants is quite fastidious in appearance and is proud of his store which has won the civic ‘Best Business Award’ since his family created the award. A town ‘Mr. Fix it’, Highpants volunteers and/or runs many other smaller businesses - such as the volunteer fire brigade, Neighbourhood watch and he also moonlights as the town's dentist. While popular, he’s the towns gossip - if you want to spread a rumour in Onion Falls, go see Mr. Highpants. He's good friends with Keo's Dad and always a helping hand with advice for Yakkity and Keo.
- Granny Yak - Granny Yak is … funnily enough … Yakkity’s Granny. She takes care of Yakkity and in many ways is his mother, father and big brother all rolled into one. While she is a good sounding board in a parental way, she also has some of Yakkity’s impulsive genes, so is quite often the first in line for the rollercoaster when the carnival comes to town.
- Keo - Keo is Yakkity’s best pal and biggest fan. He lives next door to Yakkity with his father, henceforth known only as ‘Keo’s Dad’ who Keo has to look after quite a bit. Although they have their problems as any budding teenager and his Father could have, Keo loves his Dad although as we see in ‘Pineapple Upside Down Dead Cake’ wishes he could be a little less bossy and see his view at times.
- Lemony - Lemony is the third member in Yakkity’s gang of sorts. She’s in the same classes as Yakkity and Keo and has been friends with the two since primary school. While down-to-earth and resourceful, she has quite a fantastical imagination as we see in ‘Pineapple Upside Dead Cake’. Lemony prefers aliens to dating magazines, octopuses to puppies and is tune with anything fantastical - like Fairy Wanda and her disco.
- Keo's Dad - Keo's Dad is a pineapple but quite an opinionated one. He’s full of advice and very willing to get involved in everyone’s business. While he can’t walk, if he wants to go somewhere in town, Keo (or his best pal Mr. Highpants) can carry him - or he can take a taxi or get a ride with Granny. He speaks in a classic TV Dad brogue although his advice isn't always the best source of information – as too often he speaks about things he has never experienced.
- Prof. Crazyhair - Eccentric inventor/scientist with a day-job as the science teacher at Onion Falls High, Crazyhair is also a boarder at Yakkity’s house. He rents out the basement at Yakkity's house - which he doubles as a small private laboratory with a bunk bed on the side. Yakkity and Keo are eternally curious about the smells and noises emitted from his room. The Professor is usually focused on his experiments to the exclusion of everyone else but can be a handy housemate to have if you have a scientific based problem. Just plan to stay a while as the Prof isn’t one for quick analogies. As we see in ‘Yak TV’, Crazyhair favourite movies usually entail a tale of a misunderstood scientist.
- Penelope - Due to stringent cutbacks by the Board of Education, Prof. Crazyhair is without a lab assistant. He quickly builds "Penelope" as an assistant. Prof. Crazyhair being who he is, totally disregards adding a personallity/social skills. Penelope is super-intelligent, but has zero confidence and absolutely no social skills. Sort of like a shy Mr. Spock who’s always saying the wrong things at the wrong times. She does, however, goes to Yakkity and is a friend of sorts to him.
- Rondo - High school senior, captain of the Onion Falls High football team and town hero, Rondo is Lemony’s older brother and one of Yakkity’s main antagonists. Although their spirits are unified on the football field, Rondo and Yakkity both share a desire to be in the spotlight – Rondo as football hero, Yakkity as comedic genius and inevitably get in each others’ way.
- Trilo - Trilo is a ‘trilobite’. A former circus performer who now runs his own Entertainment Agency, offering the likes of Yakkity, Fairy Wanda and Chuck Damage for children's parties, store openings and as in ‘And That’s The Weather’ weatherman appointments too. Hardly a perceptive businessperson, Trilo is hopeless with money, easily talked into crazy Yakkity plans (such as his ‘Yakstravaganza’ and ‘End of the Line’) and always looking for a new market or gimmick. Business isn’t great in either Onion Falls or it’s next town Griswold Junction, but Trilo manages to just stay afloat, except in ’10 % Solution’ where Yakkity has to help him out.
- Wanda - Wanda is the school's young hip librarian - recently moved to Onion Falls from the city for a bit of a 'sea change', as she puts it. Behind the shy smile and stylish glasses, she has a few secrets. On the weekend she turns into a stunning fairy, the children, particularly the girls lover her. At school, she certainly makes the trip to the library that much more interesting. She's seen as slightly eccentric but is very popular - she also DJs older kids parties so is pretty hip all round.
- Chuck Damage - Former wrestling champion, now turned children's entertainer, Chuck re-enacts his championship days with the magic of hand puppets. Despite his gruff looks, Chuck is very animated and fun to watch when he's performing. His shows are hugely popular particularly among the boys. A local celebrity with enigmatic fame to boot – no one has ever seen his face. Chuck is one of Yakkity's heroes and a would-be mentor if he had the chance, so it is devastating to Yakkity when he is responsible for injuring Chuck in ‘Regarding Chuck’. Chuck lives in a small house on the edge of a quarry and drives an old tow-truck.
Episode Synopsis
Episode 1A - Yakstravaganza
Synopsis: To convince Mr. Trilo to back his variety show (the "Yakstravaganza"), Yakkity needs to convince a star to be in the show. When Yakkity discovers Keo's Dad's show business past and convinces him to be in the Yakstravaganza, he thinks his problem is solved – but a round of new problems are only beginning. Keo's Dad behaves like a real ‘prima donna’, to Keo's enormous embarrassment, and ends up driving a wedge between Yakkity and Keo because he devotes more time and attention to Yakkity. Eventually, Keo's Dad's massive ego causes him to push Yakkity out of the show altogether and keep all the stage time for himself. But Yakkity never loses faith in Keo's Dad and comes to the rescue when Keo's Dad is in danger of being humiliated in front of the whole town.
Category:Nicktoons
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