Euler ′ s summation formula is an extremely important formula. This paper first introduces Euler ′ s summation formula, after that it gives some application in asymptotic estimate.

Finally, the generalized Euler eigenvalue and the generalized Gauss Bonnet Theorem and the generalized Euler ′ s formula are given to polyhedra.

最后给出多面体的广义欧拉特征值、广义Gauss-Bonnet定理及广义欧拉公式.这些理论和方法，共同构成实体模型边界表示的拓扑与几何一致性检验的有效工具。

Mick's always throwing his weight about and telling people what to do.

米克老是飞扬跋扈地告诉人们干什么事情.

Before his direct gaze her eyes fell again in real confusion.

在他咄咄逼人的目光下,她的眼光带着真正的困惑又一次垂下来.

Could you qualify his behavior as offensive?

你能把他的行为说成是咄咄逼人 吗 ?

He has a pleasing face.

他和颜悦色.

He always talks with his pupils with kind and pleasant countenance.

他跟同学们讲话总是和颜悦色的.

The teacher is all sweetness and light with the students.

老师对学生总是和颜悦色.

She shows the same kind manner towards great and small alike.

她对待大小人物一样和颜悦色.

The measuring apparatus made trades fair so that disputes became less.

量器统一,童叟无欺,纠纷就少,民间一团和气.

Right is right, wrong is wrong, one must not keepon the right side of everyone.

对是对, 错是错, 不能一团和气.

The porter stood by the bed. He had a nice face and was very kind.

门房站在床边,他脸长得好,一团和气.

And let the winds the heavens dance between you.

让天堂的风在你们之间翩翩起舞.

You wore a red jacket, walking in the snow, like butterfly dance.

你穿了一件红色的外套, 走在雪地里, 就像一只蝴蝶翩翩起舞.

There have a few beautiful butterflies dancing in the flowers in it!

那儿还有几只漂亮的蝴蝶在花丛中翩翩起舞呢!

Cultural diplomacy died down after the cold war ended.

于是人们涌上街道,翩翩起舞.

Do you really wanna know how I was dancing on the floor?

你真的想知道我是如何翩翩起舞的 吗 ?

She hovered over it like a butterfly.

她就象蝴蝶那样,在话题上翩翩起舞.

B : Stop rubbing it in, OK?

别落井下石了, 好 吗 ?

If a man once fall all will tread upon him.

落井下石.

But you are evidently in sore trouble and distress, so I will not desert you.

但你正处在危难中, 我不能落井下石.