The first part of an investigation into how to represent numbers
using geometric transformations that ultimately leads us to
discover numbers not on the number line.
Introduces the idea of a twizzle to represent number and asks how
one can use this representation to add and subtract geometrically.
How can you use twizzles to multiply and divide?
Track the roots of quadratic equations as you move the corresponding graphs and discover the transitions from real to complex roots.
Make a conjecture about the curved track taken by the complex roots of a quadratic equation and use complex conjugates to prove your conjecture.
See eight different methods of solving this problem and a
generalisation from 3 by 1 to n by 1.
Go to last month's problems to see more solutions.
This article introduces complex numbers, brings together into one
bigger 'picture' some closely related elementary ideas like vectors
and the exponential and trigonometric functions and their
derivatives and proves that e^(i pi)= -1.
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on the
intersections between two diagonally adjacent squares.