Abstract
A cube is a hexahedron of six identical squares. Duplication of a cube; or the Delian Problem, means starting with a cube of edge e, having a volume if v<sup>3</sup> then proceeding to replace it by another cube of edge k, having volume, 2e<sup>3</sup>. To construct the replacement cube requires the construction of k = e <sup>3</sup>√2. Not until the 19<sup>th</sup>Century was it proved that there was no possible geometric construction for k= e<sup>3</sup>√ 2. The solution to this problem is to bypass the impossible and deal with the possible by starting with a range of cubes of exactly known edges, e<sup>n</sup>, and their corresponding exactly known volumes, V<sup>n</sup>, and then establishing graphically the relationship between e<sup>n</sup> and V<sup>n</sup>, to produce a practical tool. Using this practical tool in conjunction with the well established problem solving technique of working backwards, any exact value of e and its corresponding value of volume V are determined by compass extent. A determination is made of the volume of the replacement cube- the duplication- by repeating in adjoining sequence, this compass extent twice on the volume axis. Identification of the corresponding value of edge e, on the graph gives the value of k, the edge of the replacement cube. With compass extent of value, k, the cube that duplicates the original is constructed.
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