Using Properties of Triangle Circumcenter for Location Estimation
"Mathematics Can Be Applied in Daily Life"
A University of Tokyo student in Tokyo, Japan, who lost one side of his Bluetooth earphones outdoors, momentarily recalled the 'circumcenter formula of a triangle' and managed to find them, drawing attention to the story.
Japanese online media 'Livedoor News' reported on the 29th (local time) the story of A, a first-year student at the University of Tokyo. A is a student deeply immersed in mathematics, solving math problems as a hobby. Recently, while strolling around the campus with Bluetooth earphones in his ears, he lost one side of the earphones.
In a large campus, losing Bluetooth earphones practically means there is no way to find them. While considering giving up and ordering another pair, a lightning-fast idea flashed through A's mind. He explained the situation at the time, saying, "I calmly switched Bluetooth ON and started retracing the path I had walked."
The formula A applied to find the Bluetooth earphones was the 'property of the circumcenter of a triangle.' He found the center point, called the 'circumcenter,' where the perpendicular bisectors of the three sides of a triangle intersect. Since the distance between the circumcenter and each vertex of the triangle is equal, using the property of the circumcenter allows one to estimate the approximate distance to the earphones.
First, A identified three points where the Bluetooth signal was lost. Connecting these three points in his mind formed a triangle, and by calculating the circumcenter of that triangle, he moved toward the vicinity of the circumcenter. Eventually, after only about 10 minutes of searching, he was able to retrieve the Bluetooth earphones that had fallen on the ground. He emphasized, "It is faster to mark points and estimate than to look for (the earphones) with the eyes."
The distance from the circumcenter O of a triangle to each vertex is the same. [Image source: Online community capture]
A said, "People usually think math is not helpful in daily life, but there are many cases where simple calculations or formulas can be usefully applied, like in this case," adding, "Perhaps we study math to recall such applications."
Local netizens who heard the story reacted with comments such as "Top university students are different," "I would have wandered forever crying while looking for my earphones," and "Why not just buy earphones with location tracking?"
Meanwhile, the University of Tokyo is considered one of Japan's top higher education institutions. It has always been included among the highest-ranked universities in Asia in international university rankings. In last year's global top 200 universities ranking by the world-renowned university evaluation organization Times Higher Education (THE), the University of Tokyo ranked 29th overall and was third among Asian universities after Peking University and the National University of Singapore.
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