谈数学中的外在美和内在美
数学美是一种客观存在，主要体现在数学的方法和理论上。对称美是数学美的核心之一，利用对称性能使问题的解答简洁。对称多项式是对称美的具体表现形式之一。数学中广泛存在着对称，对称上升为一种问题解答的数学思想方法，在数学问题解答中利用和创造对称性，体验数学美,能产生数学学习和研究的动力。数学美是一种客观存在,是自然美在数学中的反映。本文主要讨论数学的内在美和外在美。
数学的外在美主要有简洁美和谐美和奇异美。首先是简洁美数学的简洁美首先体现为数学符号的简洁数学符号从自然数到分数、从整数到小数、从正数到负数、从有理数到无理数、从实数到虚数无不体现了数学的简洁。试想没有这些简单的符号人类会遇到何等的麻烦。更不用说方程的符号、函数的符号、微积分的符号、微分方程、积分方程的符号这些符号所反映极其抽象的关系给人类带来了无尽的方便。和谐之美是数学美的一大特点。数学的这种和谐美表现在它的对立统一之中。数学的奇异与变异也是数学美的源泉。
数学的内在美主要表现在数学的精神上主要有理性精神求实精神和创造精神。理性精神是人们对外部客观世界与自身的一种理智的、根本的看法或基本态度它对人类自身存在和文化发展具有特别重要的意义。数学研究对象和研究方法所蕴含的理性精神对于人类发展和认识世界、改造世界具有特殊的重要意义。从人类的各个发展阶段看无不印证着数学中充满理性精神是其它任何一门学科都无法比拟和所能代替的。求实精神表现为尊重事实、尊重科学、尊重规律、实事求是讲究逻辑、不迷信、不盲从。
通过数学教学内容美学因素的发现,阐述了数学美在培养人的学习兴趣、审美能力、思维能力和人格品质等方面起着重要的作用,充分利用数学美,可以为培养全面发展人才做出更大的贡献。熟悉美是一种理性美是一种冷而严肃的美。
第二篇：内在美、
我们常说一句话：爱美之心人皆有之。We often say a word: love beautiful heart the person all has.
内在美是指人的内心世界的美，是人的思想、品德、情操、性格等内在素质的具体体现，所以内在美也叫心灵美。Inner beauty is refers to person's inner world beauty, is the human mind and morals, sentiment, character and other internal quality concrete manifestation, so inner beauty also called noble soul.
外在美易于被人发现，也易于被人遗忘，所引起的美感是变动的、不确定的，易逝的，因而也是不深刻的；心灵美则能给人以长时间的、强烈的、深刻的感受Beauty is easy to be found, and easy to be forgotten, caused by change, the aesthetic feeling of uncertainty, fleeting, and therefore is not deep; Beauty is mind can give a person with long, intense, deep feelings 现代人既要具有美的内在精神，又要重视美的外在表现，努力达到内在美与外在美的统一，才是我们所要追求的人的美。
Modern both the inner spirit with, and attention should be paid to the external performance, try hard to attain the inner and outer beauty unity, is we have to the pursuit of the people of the United States.
内在美更重要。但在实际的现实生活中人们往往还是重视外表美更深一些。Inner beauty is more important. But in actual real life people often or stress physical beauty deeper.
无论是男生还是女生都应该内外兼修，形相美属于外表，内在美则指人的德性。单有外表的形相美，而没有内在的德性，这还是有缺陷，不算完全的美。所以人生除了有外表的形相美之外，必须充实内在的德性美；内外俱美，才可以称为庄严的人生；而庄严的人生，才是快乐、幸福、完美的人生。
Both boy or girl should be inside and outside and repair, visual beauty belongs to appearance, inner beauty is to people's virtue. Single have the vision of beautiful appearance, and no inner character, this still have defects, is not completely beautiful. So life in addition to the vision of beautiful appearance outside, must enrich inner virtue beauty; Both inside and outside beauty, can be called life solemn; And solemn life, is happiness, happiness, perfect life.
事例：有一个病蚌生珠的事例。野生珍珠的培养蚌，越是外表看起来很丑陋的蚌，里面生出的珍珠越是圆润、光滑。因此，外表看起来不光鲜不漂亮的东西，内在不见得不美，反之也许更好! There is a disease of pearl oyster born case. The
cultivation of wild pearl oyster, the more appearance looks very ugly clam, it gives birth to the more fruity, smooth the pearl. Therefore, appearance looks not bright not
beautiful things, inner not is not beautiful, and perhaps better!
倘若我们光从表面判断一个人，往往会被其表面现象蒙蔽，得出的结果与人本身更是大相径庭。
赵奢乃一代虎将，骁勇善战。但若按“有其父必有其子”而思，则绝对出人意料。谁曾料到其子赵括尽会纸上谈兵而不知实战，终落得兵败身死为后人笑的下场。同样，伯乐之子按图索骥而最终得到一只青蛙的笑谈，无不证明了这一观点的不可信。
由此可见，外观与环境决不是影响人事的因素，只有了解内在，才能让我们认清本质。If we light from the surface judge of a man, often can be its surface phenomenon is veiled, of result and people itself is very different.
ZhaoSha Iliad is a generation, and bravery. But if the press "like father, like son" and think, the absolute unexpected.
Who has expect its zhao as an armchair strategist and doesn't know u will be practical, eventually end up dead body defeat for later generations of laugh off. Also, the son of bole and finally got a press diagram suo ji frog's a proverb, all this has proved a point of not credible.
This shows, appearance and the environment is not influence factors of personnel, only understand internal, can let us understand the essence.
1、奥巴马、马丁〃路德〃金冲破种族获成功；
2、拿破仑、晏子、朱元璋、左思、庞统、郭橐驼、马云、俞敏洪等都是其貌不扬，却能通过提升内在取得成功；
3、霍金、史铁生、司马迁、海伦〃凯勒等身体残疾，却靠内在获得人们的称颂；
1, barack Obama, Martin Luther King breaks through the race success;
2, napoleon, YanZi, zhu yuanzhang, recites thinks, pang tong accidental GuoTuoTuo, jack ma, Mr Yu, is ugly, but it can through ascension inner success;
3, hawking, making, sima qian, Helen Keller and physical disabilities, but by inside of getting people praise;