3 out of 3
Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.
1 out of 3
Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.
3 out of 3
Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?
2 out of 3
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
2 out of 3
In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?
3 out of 3
It starts quite simple but great opportunities for number discoveries and patterns!
3 out of 3
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
2 out of 3
Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?
