Here’s Mathematician KP Hart’s Math Question and Answer for Friday, October 9th!
Can you make a circle that is completely free from angles?
Can you use nanotechnology to create a circle that has, at nano-level, no angles/corners? The (perfect) circle, defined in the Cartesian coordinates as the set of (x,y) pairs that fit the equation x2 + y2 = r2 can “exist” as a mathematical abstraction. Reference Can a perfect circle exist in the real world?
We cannot expect to make a `real’ circle: Euclid wanted his lines and circles to be breadthless lengths and whatever we make the result will always have non-zero breadth.
We can try to make an annular region in the plane or a torus in space but ultimately the inherent discreteness of matter will defeat us. Even is we manipulate sufficiently many atoms into a ring shape then we get no more than a (very fine) string of beads. The centers of these atoms form a regular polygon and the `beads’ are according to the common models of atoms quite empty: between the consecutive nuclei there is still a lot of white on the `paper’.
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Read all of KP Harts math questions here!
About Dutch Mathematician KP Hart: In the beginning of this year the Dutch government opened a website, The Dutch Science Agenda, where everyone could post questions that they thought were of scientific interest. This was an attempt to involve the whole country in determining what the Dutch science agenda should be in the coming years.
I looked through the questions and searched for terms like `mathematics’, `infinity’ … to see what mathematical questions there were and I noticed various questions that already have answers (and have had for a long time). On a whim I decided to post answers to those questions, in Dutch. For your edification I will translate these posts into English.
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