I have always loved the naming of quadrilaterals, right from when I first heard about it in high school. I’m not entirely sure why, but some of it has to do with the nested nature of the definitions – I like that a square is a kind of rectangle and a rectangle is a kind […]

Every so often, someone brings up the thing with tau (τ) versus pi (π) as the fundamental circle constant. In general I find the discussion wearisome because it usually focuses on telling people they are stupid or wrong for choosing to use one constant or the other. There are more productive uses of your time, […]

Converses

In maths, or at least university maths, there are a lot of statements that go like this: “If …., then …” or “Every …, has ….” or “Every …, is …”. For example, “Every rectangle has opposite sides parallel”, “If two numbers are even, then their sum is even”, “Every subspace contains the zero vector”, […]

Posted in Being a good teacher, Thoughts about maths thinking
Tagged books, maths language

1 Comment

1 Comment

This is the last (for now) in a series of posts about Where the Complex Points Are. To catch you up, I discovered a way of visualising where the complex points are in relation to the points of the real plane. All the complex points (p+ri,q+si) are in a plane attached to the real plane […]

Posted in Isn't maths cool?, Thoughts about maths thinking
Tagged complex numbers, finite geometry, iplanes

5 Comments

5 Comments

This is the fourth in a series on Where the Complex Points Are.

Where the complex points are: introduction to the iplane concept

Where the complex points are: on a line

Where the complex points are: on a parabola

Where the complex points are: the graph of a function (YOU ARE HERE)

Where the complex points are: where the idea […]

Posted in Isn't maths cool?, Thoughts about maths thinking
Tagged complex numbers, iplanes

3 Comments

3 Comments

This is the third in what has turned out to be a series on Where the Complex Points Are.

Where the complex points are: introduction to the iplane concept

Where the complex points are: on a line

Where the complex points are: on a parabola (YOU ARE HERE)

Where the complex points are: the graph of a function

Where the […]

Posted in Isn't maths cool?, Thoughts about maths thinking
Tagged complex numbers, iplanes, maths

2 Comments

2 Comments

This is the second in what has turned out to be a series on Where the Complex Points Are.

Where the complex points are: introduction to the iplane concept

Where the complex points are: on a line (YOU ARE HERE)

Where the complex points are: on a parabola

Where the complex points are: the graph of a function

Where the […]

Posted in Isn't maths cool?, Thoughts about maths thinking
Tagged complex numbers, iplanes, maths

3 Comments

3 Comments

When you first learn complex numbers, you find out that they give you ways to solve equations that were previously unsolvable. The classic example is the equation equation x^2 + 1 = 0, which if you’re only using real numbers has no solutions, but with complex numbers has the solutions x=i and x=-i.

As someone who […]

Posted in Isn't maths cool?, Thoughts about maths thinking
Tagged complex numbers, iplanes, maths

8 Comments

8 Comments