The next issue of chalkdust isn’t coming until September. Even our crossnumber won’t take quite long enough to entertain you until then. So what are you to do with all this free time? At chalkdust HQ, we have come up with a solution to this problem. Without further ado, let me welcome you to the chalkdust blog.
This blog will include anything and everything mathematical, from articles and opinion to puzzles and games. New posts will be published each Thursday. We can plot a graph showing this information:
By extending this graph, we can show that by the year 7000 we will have posted over a quarter of a million blog posts.
Alternatively, we can plot the graph of blog posts per week.
This graph shows that if $b(t)$ is the number of blog posts per week at a given time $t$ then,
$$\lim_{t\rightarrow\infty}b(t)=-e^{i\pi}.$$
In calculating this limit, we have made the assumption that the world, and indeed the universe, will never end.
There is other information about the blog that we can plot, for example:
Completion of the final graph is left as an exercise to the reader:
Until the next blog post, here is a puzzle for you to think about:
Rectangles
This rectangle has been split into smaller rectangles so that none of the lines touch more than one side of the rectangle (ie. none of the lines completely cross the rectangle).
The rectangle which has been coloured red does not touch any of the sides of the large rectangle.
Prove that for any rectangle split in this way there always will be a rectangle inside which does not touch the sides.
If you have solved this puzzle, why not post an explanation in the comments below? If you have not proved it yet, be warned that comments may contain spoilers.
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