标题： 重叠圆网格用圆规和直尺绘制于公元前14世纪的埃及文物上 显示英文标题

标题： Overlapping Circles Grid Drawn with Compass and Straightedge on an Egyptian Artifact of 14th Century BC

摘要： 研究古代文明的数学和几何学是一项似乎非常困难甚至不可能完成的任务，如果从过去遗留下来的文献很少或者根本没有的话。 然而，除了可以从书面文件中获得直接信息外，我们还可以通过对文物上发现的装饰图案的分析来间接了解一些数学和几何知识。 在这里，我们将展示古埃及人能够使用圆规和直尺进行几何构造，这比大约公元前450年左右生活的希腊人俄诺皮德斯还要早。 事实上，在第十八王朝（公元前1400年至公元前1350年）为三位国王服务过的建筑师卡哈的坟墓中发现的一块覆盖着重叠圆圈网格图案的木板表明，在俄诺皮德斯时代约九百年前的古埃及已经使用了一些简单的圆规和直尺几何构造方法。 显示英文摘要

摘要： The study of the mathematics and geometry of ancient civilizations is a task which seems to be very difficult or even impossible to fulfil, if few written documents, or none at all, had survived from the past. However, besides the direct information that we can have from written documents, we can gain some indirect evidence on mathematics and geometry also from the analysis of the decorations we find on artifacts. Here, for instance, we will show that ancient Egyptians were able of making geometric constructions using compass and straightedge, quite before the Greek Oenopides of Chois, who lived around 450 BC, had declared some of their basic principles. In fact, a wood panel covered by an overlapping circles grid pattern, found in the tomb of Kha, an architect who served three kings of 18th Dynasty (1400-1350 BC), evidences that some simple constructions with compass and straightedge were used in ancient Egypt about nine centuries before Oenopides' time.