Recent content by tomwilliam2

Homework Statement My son's textbook says In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point. He asked me why two lines couldn't be drawn on top of each other...to which I replied that they would have the same algebraic...

Thanks, that's crystal clear. My son is learning math in the Portuguese system, where they do things a lot more formally than they did where I learned it (the UK). Still, it's good to know this reasoning so I can explain why the correct answer is correct.

My thinking exactly, but it does seem that a few of the knowledgeable posters in the thread you indicated agree with my son's textbook. It would appear that the way I was taught (i.e. that f(x) = ax + b is linear) is really a simplification, and they should have called it an affine function. It...

Homework Statement My son (aged 13) received his math test back, and got the following problem wrong: Which of the following functions is linear? A: f(x) = -3x + 5 B: g(x) = x^2 C: h(x) = 6x - (1/2) D: p(x) = 4x/5 The attempt at a solution He answered B, which is clearly wrong, but it wasn't...

Thanks both.

I'm trying to do some practice Putnam questions, and I'm stuck on the following: For ##a,b,c \geq 0##, prove that ##(a+b)(b+c)(c+a) \geq 8abc## (https://www.math.nyu.edu/~bellova/putnam/putnam09_6.pdf) I started off by expanding the brackets and doing some algebraic rearranging, but I don't...

Intuitively I would say 3 points chosen arbitrarily can always be made to fit into a correctly chosen hemisphere, but the fourth point...I can’t see an intuitive jump to explain the 1/8 probability. The video below is very clear. It must be that my method doesn’t bring any added value.

Thanks, that is a really elegant explanation.

Yes, although I've just realized I wrote it down wrong. I figured that the first point can be anywhere, so it has a probability of 1. The second would have a probability of 1/2 of falling within the hemisphere we've defined, as would the third and fourth, so that line should have read ##1...

This is a well-known problem I think: take four arbitrary points on a sphere as the vertices of a tetrahedron. What is the probability that the centre of the sphere will be located within the tetrahedron? A friend gave me this puzzle to solve, and I came up with the answer P = 1/8. This is the...

Thanks for the responses: Yes, indeed there are 32 cards not 40...I was trying to simplify for myself, but I guess it shouldn't be any different. Actually, we've been playing with him only getting one turn (one pick) per round, and having to complete both shopping lists to win, so I'm guessing...

I have a probability question which has cropped up while playing a game called "Shopping List" with my sons. The game is played like this: you pick a fixed shopping list of 10 items, and three other players do the same. You have all of the items on cards, face down on the floor in-between the...

I'm currently doing an MSc in Space Science and Technology. I've done engineering, celestial dynamics, astronomy and planetary science at postgrad level. I need to choose a thesis topic, and I'm a little short of ideas. I'm interested in theoretical physics and cosmology, but need inspiration...

Thanks. I think you're probably right. The part about being immersed in water threw me too, when going through the test with him. I knew that the water exerts a buoyant force which counteracts the diver's weight, but I wasn't sure whether his "weight" was considered to be the balance of vertical...