Can you find a way to prove the trig identities using a diagram?
The length AM can be calculated using trigonometry in two different
ways. Create this pair of equivalent calculations for different peg
boards, notice a general result, and account for it.
Find out how the quaternion function G(v) = qvq^-1 gives a simple
algebraic method for working with rotations in 3-space.
Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?
If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0
what can you say about the triangle?
Can you explain what is happening and account for the values being
See how 4 dimensional quaternions involve vectors in 3-space and
how the quaternion function F(v) = nvn gives a simple algebraic
method of working with reflections in planes in 3-space.
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. . . .
Beautiful mathematics. Two 18 year old students gave eight
different proofs of one result then generalised it from the 3 by 1
case to the n by 1 case and proved the general result.
Draw graphs of the sine and modulus functions and explain the
Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.
A short introduction to complex numbers written primarily for students aged 14 to 19.
Join some regular octahedra, face touching face and one vertex of
each meeting at a point. How many octahedra can you fit around this
This polar equation is a quadratic. Plot the graph given by each
factor to draw the flower.