论文标题
可视化几何序列
Visualize Geometric Series
论文作者
论文摘要
我们回顾了Mabry's，Edgar's和The Viewpoints 2000小组的证明，而没有单词几何系列公式。马布里（Mabry）和埃德加（Edgar）证明了 $ \ frac {1} {4} + \ left（\ frac {1} {4} {4} \ right）^2 + \ left（\ frac {1} {1} {4} {4} \ oright） } \ Quad \ frac {4} {9} + \ left（\ frac {4} {9} {9} \ right）^2 + \ left（\ frac {4} {4} {9} {9} \ right）^3 + \ cdots \ cdots \ cdots \ cdots \ cdots \ = \ = \ \ \ \ \ \ \ \ \ \ \ frac {4} {4} {4} {5} {5} {5}，$我们表明，他们的证据满足了使它们与众不同的某些要求。然后，我们说明了他们和观点2000小组的证明之间的共同思想。
We review Mabry's, Edgar's, and the Viewpoints 2000 Group's proofs without words for the geometric series formula. Mabry and Edgar proved without words that $$\frac{1}{4} + \left(\frac{1}{4}\right)^2 + \left(\frac{1}{4}\right)^3 + \cdots\ =\ \frac{3}{4}\quad\mbox{ and }\quad\frac{4}{9} + \left(\frac{4}{9}\right)^2 + \left(\frac{4}{9}\right)^3 + \cdots\ =\ \frac{4}{5},$$ respectively. We show that their proofs satisfy certain requirements that make them unique. We then illustrate a common idea between their and the Viewpoints 2000 Group's proofs.
