{"id":1461,"date":"2017-02-21T13:38:45","date_gmt":"2017-02-21T17:38:45","guid":{"rendered":"http:\/\/willistonblogs.com\/math\/?p=1461"},"modified":"2017-02-28T17:08:38","modified_gmt":"2017-02-28T21:08:38","slug":"steiner-point-construction","status":"publish","type":"post","link":"https:\/\/willistonblogs.com\/math\/steiner-point-construction\/","title":{"rendered":"Steiner Point Construction"},"content":{"rendered":"

This just in from Mrs. Hill<\/a>:<\/p>\n

Topics in Discrete Mathematics students got to review some lessons from geometry when they learned how to construct the Steiner Point of a triangle. The Steiner Point in a triangle is the point from which three branches lead out to the triangle\u2019s vertices at perfect 120\u00b0 angles. (See diagram below.) This Steiner Point has important modern day applications for creating the shortest (and therefore cheapest) possible fiber optic network between any three locations. If a triangle\u2019s angle measures are all less than 120\u00b0, then the Steiner Point can be found inside the triangle using a geometric construction first developed by Italian mathematician Evangelista Torricelli in the early 1600\u2019s. Torricelli (most famous for his work in physics but also an accomplished mathematician) was a prot\u00e9g\u00e9 of Galileo, and in 1641 succeeded Galileo as the court mathematician to Grand Duke Ferdinand II of Tuscany.<\/p>\n

\"Figure
Figure 2<\/figcaption><\/figure>\n

Torricelli\u2019s method for finding the Steiner Point in a triangle requires only the use of the traditional geometric construction tools \u2013 straightedge and compass. Using properties of equilateral triangles and inscribed angles from elementary Euclidean Geometry, the basics of the construction are shown below in Figure 1 (a,b,c). The students in Topics further learned how the Steiner Point was used in 1989 to connect Hawaii, Japan, and Guam via the Third Trans-Pacific Cable (TPC-3). Also below, Figure 2 shows a stamp issued by the Japanese Postal Service to commemorate the completion of TCP-3. As one can see from the picture, the three undersea cables meet at 120\u00b0 angles under the western Pacific Ocean.<\/p><\/blockquote>\n

\"Figures
Figures 1a, 1b, and 1c<\/figcaption><\/figure>\n

Student constructions:<\/strong><\/p>\n