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    was just in bed and saw a shape like it and thought about it.

    so, what is the minimum you would have to remove for the central cross to be able to rotate freely (about a central pivot) within the square?

    it's not very hard (could be on a core1 paper) but i thought it was quite cool

    say that the length of a side of the square is 10 and the width of the cross sections is 2.

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    Unless I'm very much mistaken, the minimum area needing to be removed is

    \displaystyle 8 \times \left(5 - \sqrt{6} - \frac{25}{2} \arcsin \left(\frac{1}{5}\right)\right)
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    definitely NOT on c1
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    (Original post by Hartemop)
    definitely NOT on c1
    why not? it's easy.
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    (Original post by Hartemop)
    definitely NOT on c1
    It's pretty easy.
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    (Original post by Chewwy)
    why not? it's easy.
    Oh I thought OP meant on the latest C1 paper :confused:
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    Ahhhhh how did I end up in a maths thread... I am exiting quickly
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    (Original post by cool guy reli)
    I think its safe to assume that the shape was, or never will be, that of another human being beside you in bed?
    I'm pretty sure Totally Tom will be able to afford to buy a thai bride when older.
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    I like the fact that potential mathematics questions present themselves to tom as he lies in bed. It is reassuring to know I am not alone. In my case, being awake is entirely optional. Unfortunately, if I don't write down what I was thinking as soon as I wake up, the question slips away and I am left with a tantalising feeling that I was onto something good but can't quite remember what.
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    (Original post by Mr M)
    I like the fact that potential mathematics questions present themselves to tom as he lies in bed. It is reassuring to know I am not alone. In my case, being awake is entirely optional. Unfortunately, if I don't write down what I was thinking as soon as I wake up, the question slips away and I am left with a tantalising feeling that I was onto something good but can't quite remember what.
    For what it's worth, I was woken up by having accidentally proven an identity involving sums of multinomial coefficients recently. So I wrote it down and went back to sleep. (And for the first time ever, it wasn't complete nonsense when I woke up in the morning.)
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    (Original post by generalebriety)
    For what it's worth, I was woken up by having accidentally proven an identity involving sums of multinomial coefficients recently. So I wrote it down and went back to sleep. (And for the first time ever, it wasn't complete nonsense when I woke up in the morning.)
    Back in the days when I was an extremely minor pop star, I used to compose songs (of variable quality) while I was asleep. Brains seem to have a lot more freedom to figure things out while your body is motionless.
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    I got the minimum as  40-8\sqrt6-50\mathrm{arcsin}(\frac{1}{5}) Which is the same as Elongars
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    (Original post by Simplicity)
    I'm pretty sure Totally Tom will be able to afford to buy a thai bride when older.
    gonna have to price me one of these babies up some day.

    + i confess to have not actually worked it out, it's more of what to do than anything else.
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    give up, how do you do it? :P
 
 
 
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