Maths puzzle time!

greg66_tri_v2.0

Everybody loves a maths puzzle, right? Yes, I know they do. The ones that say that they don't a just barefaced liars.

So here's a little puzzle.

I wish to construct a square based pyramid from acrylic sheet. The sides of my square base are each of length a. The faces of the pyramid are to stand at 45 degrees to the base.

Q1 What length should I cut the edges of the pyramid faces?

My acrylic sheet is a few mm thick. I must mitre the bottom edge of each face at 45 degrees for a flush fit between the faces and the pyramid base.

Q2 To what angle should I mitre the edges of the faces that abut one another for a flush fit?

(For the determined) I want to make more pyramids with faces at different angles to the base. If the angle of a face to the base is theta,

Q3 What length should I cut the edges of the pyramid face in terms of a and theta, and

Q4 To what angle in terms of a and theta should I mitre the edges of the faces that abut one another for a flush fit?

daviesee

A. Google.

arran77

You really think you're going to get a sensible answer on here, it's like when people ask for medical advice on here

rolf_f

Just download a file and have it 3d printed. All this cutting and mitre-ing is so last century.

greg66_tri_v2.0

I dunno. The youth of today...

<dodders off aimlessly, muttering about the Kaiser...>

tgotb

3. a*sqrt(0.25+0.5cos(theta))
1. a*sqrt(0.25+sqrt(2))

Edit: This is a guess, but is 4 just theta?

daviesee

Greg66 Tri v2.0 wrote:

I dunno. The youth of today...

<dodders off aimlessly, muttering about the Kaiser...>

Youth? :oops: :P
Nicest thing anyone has said about me......


.. in decades.

greg66_tri_v2.0

TGOTB wrote:

3. a*sqrt(0.25+0.5cos(theta))
1. a*sqrt(0.25+sqrt(2))

Bzzt! Try again.

TGOTB wrote:

Edit: This is a guess, but is 4 just theta?

No. Not least because if you made a box rather than a pyramid, theta would be 90 degrees but the mitre would be 45 degrees.

tgotb

Doh!
0.5a*sqrt(1+1/(cos(theta)^2))

Edit: And 0.5sqrt(3) (obviously, given the above)

greg66_tri_v2.0

Is that Q3? And Q1?

If so, correct (though there's an "a" missing from the answer to Q1).

tgotb

Sorry, that was 3 again; I'm actually pretty confident it's correct (though I guess it could possibly be simplified). Gives the right answer for theta=0 and 90 degrees.

Still struggling with the angles.

tgotb

Greg66 Tri v2.0 wrote:

(though there's an "a" missing from the answer to Q1).

My maths teachers always used to tell me off for getting all the hard bits right and then making a silly mistake at the end.

Mikey23

You need to 1) get yourself to A&E, 2) notify the police, 3) get an estimate from your LBS..

Sorry, wrong thread!

greg66_tri_v2.0

Do I look like your maths teacher?

tgotb

I had an engineering tutor who was quite a good triantelope, but I doubt you look like her.

I can't remember all the clever bits for simplifying trignometrical expressions, but 4 is something along the lines of:
sin^-1(1/sqrt(2-0.5cos^2(theta)))

Works for theta=0 and 90; if it's wrong I can't be bothered to find the mistake, but it's something along those lines...

Gives ~49.1 degrees for the first answer, which feels about right.

greg66_tri_v2.0

TGOTB wrote:

I had an engineering tutor who was quite a good triantelope, but I doubt you look like her.

I can't remember all the clever bits for simplifying trignometrical expressions, but 4 is something along the lines of:
sin^-1(1/sqrt(2-0.5cos^2(theta)))

Works for theta=0 and 90; if it's wrong I can't be bothered to find the mistake, but it's something along those lines...

Gives ~49.1 degrees for the first answer, which feels about right.

That's pretty close but not quite there, and crucially doesn't give the correct answer when theta = 45 degrees.

ETA: Sarah Springman?

stu-bim

1 = square root of (.5a squared + .5a squared) gives height of pyramid

2 = 22.5%

3 = theta - 90 = b, sin (b

4 = (90 - theta) / 2

tgotb

G66 - correct!

greg66_tri_v2.0

stu-bim wrote:

1 = square root of (.5a squared + .5a squared) gives height of pyramid

2 = 22.5%

3 = theta - 90 = b, sin (b

4 = (90 - theta) / 2

Bzzzt! Try again!

For 1, the question is the length of the sloping edges, not the height of the pyramid. And for 2 it is the mitre along those edges.

tgotb

sin^-1(sqrt((cos^2(theta)+1)/2))

For 45 degrees, gives sin^-1(sqrt(3/4)) which of course is 60 degrees; should have seen that one coming...

greg66_tri_v2.0

Bingo!

I may have to break out the 50p problem at this rate...

rjsterry

May I refer you to the stacked bricks problem I mentioned in your previous thread.

BTW, am I detecting a wish for a change of career?

itboffin

Your recent "i'm bored with my life" threads have given me an idea, perhaps I should post some of my frankly almost impossible work problems that need a formula found.

greg66_tri_v2.0

itboffin wrote:

Your recent "i'm bored with my life" threads have given me an idea, perhaps I should post some of my frankly almost impossible work problems that need a formula found.

Eg: Windows has frozen + my internet connection is borked = Turn it off and on again.

Something like that, perhaps?

greg66_tri_v2.0

rjsterry wrote:

May I refer you to the stacked bricks problem I mentioned in your previous thread.

BTW, am I detecting a wish for a change of career?

Took a somewhat linear approach to that, and assumed that the overhang of each new domino placed on the stack had to be the same amount as the previous overhang - ie a stack with a fixed straight line tilt. The question then is whether you can ever place a domino on the stack that sits wholly outside the footprint of the domino at the base, and if not, why not. Managed in the end to work out a generalised proof as to why you can't.

The harmonic series and the curved line tilt is a bit beyond what I can dreg up from my days of doing sums. Used to be able to do that stuff, but it's all too rusty now. Depressing.

I've often thought that I'd quite like to be a maths teacher at GCSE and A level, but the big obstacle is the need to keep myself in the lifestyle to which I have become addicted...

itboffin

Greg66 Tri v2.0 wrote:

itboffin wrote:

Your recent "i'm bored with my life" threads have given me an idea, perhaps I should post some of my frankly almost impossible work problems that need a formula found.

Eg: Windows has frozen + my internet connection is borked = Turn it off and on again.

Something like that, perhaps?

The Internet is down ....what would you do?

tgotb

itboffin wrote:

The Internet is down ....what would you do?

Call the helpdesk. Duh!

OK, two from me. First the easy one:

1. The king of a particular country announces that each family is only allowed to have one male child, and that once they have had that child, they may have no more children. If their first child is a girl they can have another child, and carry on doing so until they have a boy. The probability of any specific child being born a boy is 50%, and no selective abortions or infanticide take place; everyone follow the rules. For the purpose of this exercise, assume that every family keeps having children until either they have a boy or have had 8 girls. What effect does this have on the proportion of males in the population?

2. I need to kick a rugby ball from the touchline, to score a conversion. Unusually, I am blessed with the ability to kick the ball any distance, but the direction is not amazingly accurate. In other words, if I kicked the ball from beyond the far end of the pitch it would still cross the tryline above the level of the crossbar, but might not go between the posts. Assume the width of the pitch is a, and the distance between the posts is w, and I am allowed to chose any point on the touchline; from what point along the touch line should I kick the ball in order to get the best chance of scoring?

greg66_tri_v2.0

1. Proportion of makes stays at 50%

2. Struggling to see why the answer isn't dead centre, but that's not backed with any sums.

dhope

Greg66 Tri v2.0 wrote:

1. Proportion of makes stays at 50%

2. Struggling to see why the answer isn't dead centre, but that's not backed with any sums.

http://projecteuler.net/problems

Should see you through a quiet few days/weeks/lifetimes

greg66_tri_v2.0

dhope wrote:

Greg66 Tri v2.0 wrote:

1. Proportion of makes stays at 50%

2. Struggling to see why the answer isn't dead centre, but that's not backed with any sums.

http://projecteuler.net/problems

Should see you through a quiet few days/weeks/lifetimes

Oh, bollocks.

You bastard.

dhope

Greg66 Tri v2.0 wrote:

dhope wrote:

Greg66 Tri v2.0 wrote:

1. Proportion of makes stays at 50%

2. Struggling to see why the answer isn't dead centre, but that's not backed with any sums.

http://projecteuler.net/problems

Should see you through a quiet few days/weeks/lifetimes

Oh, ****.

You bastard.

Uh huh.
Once you've signed up then let us know the username so we can check you're not slacking. I'll race you to 50 solved...