Spieker circle
geometric object
In geometry, the incircle of the medial triangle of a triangle is the Spieker circle, named after 19th-century German geometer Theodor Spieker. Its center, the Spieker center, in addition to being the incenter of the medial triangle, is the center of mass of the uniform-density boundary of triangle. The Spieker center is also the point where all three cleavers of the triangle (perimeter bisectors with an endpoint at a side's midpoint) intersect each other.
History
The Spieker circle and Spieker center are named after Theodor Spieker, a mathematician and professor from Potsdam, Germany. In 1862, he published Lehrbuch der ebenen geometrie mit übungsaufgaben für höhere lehranstalten, dealing with planar geometry. Due to this publication, influential in the lives of many famous scientists and mathematicians including Albert Einstein, Spieker became the mathematician for whom the Spieker circle and center were named.
Construction
To find the Spieker circle of a triangle, the medial triangle must first be constructed from the midpoints of each side of the original triangle. The circle is then constructed in such a way that each side of the medial triangle is tangent to the circle within the medial triangle, creating the incircle. This circle center is named the Spieker center.
Nagel points and lines
Spieker circles also have relations to Nagel points.
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This entry incorporates text from “Spieker circle” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.