query: Rational points on circles centered at the origin
positive_passages.docid: 20034
positive_passages.text: Does $a^2+b^2=1$ have infinitely many solutions for $a,b\in\mathbb{Q}$?
negative_passages.docid: 36937
negative_passages.text: How to find a starting point for root finding in complex plane?
negative_passages.docid: 158933
negative_passages.text: Rational solutions of $y^2 = x^3 - x$
negative_passages.docid: 157171
negative_passages.text: Gauss circle problem : a simple asymptotic estimation.
negative_passages.docid: 141835
negative_passages.text: Rigorous Proof: Circle cannot be embedded into the the real line!
negative_passages.docid: 83596
negative_passages.text: A simple proof that a polygon circumscribing a circle overestimates its perimeter
negative_passages.docid: 85650
negative_passages.text: Number or regions formed when $n$ points on a circle are joined
negative_passages.docid: 140851
negative_passages.text: Precalculus unit circle with imaginary axis.
negative_passages.docid: 59564
negative_passages.text: Centre of the circle
negative_passages.docid: 94051
negative_passages.text: How to show that all points are inside of unit circle?
negative_passages.docid: 12070
negative_passages.text: Probability that n points on a circle are in one semicircle
negative_passages.docid: 72707
negative_passages.text: Property of Medians and Cirumcircle
negative_passages.docid: 92751
negative_passages.text: What algorithm can I use to determine points within a semi-circle?
negative_passages.docid: 84374
negative_passages.text: Rational function with absolute value $1$ on unit circle
negative_passages.docid: 39416
negative_passages.text: The space obtained by identifying the antipodal points of a circle
negative_passages.docid: 82184
negative_passages.text: Foci of a general conic equation
negative_passages.docid: 95728
negative_passages.text: The union of growing circles is not homeomorphic to wedge sum of circles