Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

下面是手画的和拍的一些图片,出自标题中的那两本书,在图书馆草草浏览了半个小时,就把一眼能看出来的摘到这里了,再复杂一些的感觉违背了无字证明的初衷了,就没有摘录:

勾股定理:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

希波克拉底定理:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

无限步三等分一个角:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

五角星顶角和为180 度:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

完全平方:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

余弦定理:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

半角公式:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

反正切函数的和:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

均值定理:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

一个正数及其倒数的和至少为2:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

整数求和:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

内含正方形的正方形:连接正方形各顶点与对边中点,则小正方形的面积 = 1/5 大正方形的面积

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

直角三角形内接圆半径的两种表示方法:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

这里ab/(a+b+c) = (a+b-c)/2,可以得出勾股定理(又一种证明方式)a^2+b^2 = c^2。

几何级数:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

斐波那契数列的平方求和:

Proofs without Words:Exercises in Visual Thinking(v.1 and v.2)

体悟到数学的绝妙之美了吗:-?

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