Archive for the ‘Math’ Category
I just did this vid on Primes in Python, which is my top ranking popst here…
One of the things about math is that the more problems we look at the more we find a finite set of mathematical objects that can be generated in more than one way, observed in more than one context. These patterns recur in varying and apparently unconnected places.
Here are just a few of the “great ideas” and their specialised manifestations. Every area of maths and science displays them. Patterns that appear in separate domains, systems, phenomena and problems. I say apparently unconnected because, if anything, writing this article has made me realise how what the mystics say is so true: all is one and interconnected.
This list is of course vastly incomplete. After a while of coming up with more and more patterns you just say “right, that’s enough to make the point!” In fact I believe the one true exhaustive list of this kind is infinite. I have no idea for a proof or disproof of that ! Suggestions please.
When they removed Einstein’s brain (don’t worry it was after his death) they found the region that usually takes the role of spatial reasoning was enlarged, actually it had crowded out part of the language region.
If you want to be like Einstein I suggest you get into visualising geometry and topology of all sorts. The easiest is to visualise a perfectly flat plane, with straight and curved journeys, triangles, squares and other shapes, but once you’ve done that you can move on up to subtler and more complex manifolds, like the sphere and then the torus, which is the shape of a ring doughnut. It’s got a hole.
Let’s allow the proportions of our torus to be about the same as the doughnut. Imagine you were an ant confined to crawl on the surface of this torus. In how many directions could you set out (following a straight line), such that you would eventually return to where you started ? Read the rest of this entry »
Sprouts is a game based on graph theory that I first discovered through a Martin Gardner article.
Start by placing some dots on a piece of paper. each player then takes turns to draw a line connecting 2 dots and placing a new dot on the middle of the line. each dot can have only 3 lines coming from it. and no lines may cross.
the person who can’t move first is the loser.
here is a simple sample game:
What is integration ?
Well in two variables, integrating is something you do to a function over a given range to generate a new function which will give us the area under the curve of the function..
lets think about areas under lines: its easy to find the area under a simple graph like y=5 between 1 and 8
To be a Mathematician…
some ideas I have found useful to revive flagging spirits and keep the great project going.
Cultivate the right attitude for doing maths
Precision, thoroughness and tenacity are obvious skills you will need but in this little post i hope to show there are lots of others too, many of which are applicable to many other areas of life. A love and respect for knowledge in general is also good and resist temptation to think you have the only path to truth. Poets and social scientists are doing good work too, as well as carpenters and nurses. In maths we purify and formalise knowledge, but it is not the only possibility.
Have you ever wondered how to find out the volume of an egg ? The volume of a cube is easy enough… a^3 where a is the side length, but calculations involving curves rather than straight lines seem to be a bit harder.
The branch of maths that deals with finding stuff about curves out is called calculus, and we’ll start to look at it here.
you may know that the equation of a straight line can be given as:
where c is the y-intercept and m is the gradient. The gradient is defined as the rise over the run… the change in y over the change in x, so for a line like