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Poly Fibs
A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.
Fibonacci Factors
For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?
Fixing It
A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?
Age 16 to 18 Challenge Level:
A triangle $ABC$ is inscribed in a circle with $AB$ as diameter. Find the maximum value of $AC + CB$.
Now generalise your result to the case where $AB$ is fixed but not a diameter of the circle.
Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius $r$ that has the maximum perimeter and the maximum area.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.