This is our second collection of stage 5 epsilons. An epsilon problem is quick to read and understand. They might not be so easy to solve!
Epsilons will be good for filling spare mathematical moments. Why not carry a few around with you? (Our first collection of epsilons are here).
A small circle fits between two touching circles so that all three
circles touch each other and have a common tangent? What is the
exact radius of the smallest circle?
Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2
Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of
If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?
Four rods are hinged at their ends to form a quadrilateral with
fixed side lengths. Show that the quadrilateral has a maximum area
when it is cyclic.
If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.