Wired
•83% Informative
In 1917 , the Japanese mathematician Sichi Kakeya asked how small an area a needle can sweep out while pointing in all possible directions.
In the infinite limit, you can obtain a set that mathematically has no area but can still accommodate a needle pointing in any direction.
A new proof strikes down a major obstacle that has stood for decades .
A Kakeya set must always have the same dimension as the space it inhabits, says Charles Fefferman of Princeton University .
The Minkowski dimension is related to but not quite the same as an ordinary dimension.
It measures the rate at which the number of balls you need to cover your set grows as the diameter of each ball gets smaller.
If you want a fattened version of Besicovitch ’s set to have an area of 1/10 of a square inch , each needle needs to have a thickness of around 0.000045 inch .
In 1995 , Thomas Wolff proved that the Minkowski dimension of a Kakeya set in 3D space has to be at least 2.5 .
In 1999 , Nets Katz , Izabella aba, and Terence Tao proved that this is true.
Katz and Tao later hoped to apply some of the ideas from that work to attack the 3D conjecture in a different way.
VR Score
84
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