Wow (read only if you're interested in maths)

Cornersteady
Cornersteady Club Member Posts: 14,425 ✭✭✭
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edited July 2018 in General Chat #1

Warning stop now if you don't like maths

Even now I am at times amazed by a new to me maths theorem that I haven't seen before.

Draw any three different size circle that do not over lap. Draw tangents joining each circle. The intersection points of the three pairs of tangents all meet in a straight line. WOW

Comments

  • Tinwheeler
    Tinwheeler Forum Participant Posts: 23,135 ✭✭✭
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    edited July 2018 #2

    Wow, indeed. My eyes have gone funny 🤨

     

  • huskydog
    huskydog Club Member Posts: 5,460 ✭✭✭✭✭
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    edited July 2018 #3

    I thought it was modern art , I'd hang that on my wall surprised

  • Tinwheeler
    Tinwheeler Forum Participant Posts: 23,135 ✭✭✭
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    edited July 2018 #4

    Please, Sir, can we colour it in? laughing

     

    Sorry, Corners, no offence intended. smile

  • huskydog
    huskydog Club Member Posts: 5,460 ✭✭✭✭✭
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    edited July 2018 #5

    Yes, but don't go over the lines wink

  • EasyT
    EasyT Forum Participant Posts: 16,194
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    edited July 2018 #6

    I like that!

    (OH wasn't impressed though)

  • brue
    brue Forum Participant Posts: 21,176 ✭✭✭✭✭
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    edited July 2018 #7

    Very clever Corners, even with vertical circles. Does the theorem have a name? laughing

  • Unknown
    Unknown Forum Participant
    edited July 2018 #8
    The user and all related content has been Deleted User
  • Rocky 2 buckets
    Rocky 2 buckets Forum Participant Posts: 7,101
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    edited July 2018 #9

    Without numbers as a guide I’m stumped😢, I can neither fill the gaps with the relevant colours nor join the lines. . . .Bummer☹️

  • Cornersteady
    Cornersteady Club Member Posts: 14,425 ✭✭✭
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    edited July 2018 #10

    actually you don't realise how happy that question makes teachers, and especially when on supply.

    It is absolutely amazing the calming effect of colouring in has on the most 'challenging' of classes, even in year 11. Get out the crayons (posh kids will have their own gel pens) and everyone is happy and quiet. Really! I suppose it takes them back to primary school?

  • Cornersteady
    Cornersteady Club Member Posts: 14,425 ✭✭✭
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    edited July 2018 #11

    thanks for all the replies, I got this last night in the form of a question last night, what's the probability of drawing three circles and.....

    It's one of those questions that you immediately think that can't be true, but then can it? Guess who sadly drew out some examples? embarassed

    Found out last night that you can use the same idea with 3D spheres (football, tennis, and table tennis balls) and tangent cones, a very easy to follow proof is here.

     

    so... a caravan (club site naturally) has an infinite number of pitches and they are all taken, after 12 an outfit turns up, what happens?

     

  • Wherenext
    Wherenext Club Member Posts: 10,586 ✭✭✭
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    edited July 2018 #12

    It is absolutely amazing the calming effect of colouring in has on the most 'challenging' of classes, even in year 11. Get out the crayons (posh kids will have their own gel pens) and everyone is happy and quiet. Really! I suppose it takes them back to primary school?

    Or the last wall they sprayed with Graffiti.surprised

  • Wherenext
    Wherenext Club Member Posts: 10,586 ✭✭✭
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    edited July 2018 #13

    This theorem cropped up in a drawing instruction book that Mrs WN was reading some time ago. She likes drawing. Just shows that Maths and the Arts live together quite happily. Angles and perspective anyone?

  • moulesy
    moulesy Forum Participant Posts: 9,402 ✭✭✭✭✭
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    edited July 2018 #14

    "so... a caravan (club site naturally) has an infinite number of pitches and they are all taken, after 12 an outfit turns up, what happens?"

    Can I be the first pedantic one to ask if it's possible that all pitches are taken if there's an infinite number of them, Corners? wink

  • Tinwheeler
    Tinwheeler Forum Participant Posts: 23,135 ✭✭✭
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    edited July 2018 #15

    so... a caravan (club site naturally) has an infinite number of pitches and they are all taken, after 12 an outfit turns up, what happens?”

    An argument with the warden followed by a moan on CT?😛

    Or, another pitch appears?

  • Cornersteady
    Cornersteady Club Member Posts: 14,425 ✭✭✭
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    edited July 2018 #16

    post edit

    I should add, in case you're doing supply work soon, that the class themselves have to ask to do it? If you gave out the crayons and tell them to colour in you'll get the we're not babies/at primary school now you know type of cries.

  • Cornersteady
    Cornersteady Club Member Posts: 14,425 ✭✭✭
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    edited July 2018 #17

    great question, see what fun you can have with infinity? Hours and hours of it

  • Cornersteady
    Cornersteady Club Member Posts: 14,425 ✭✭✭
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    edited July 2018 #18

    smile

  • Cornersteady
    Cornersteady Club Member Posts: 14,425 ✭✭✭
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    edited July 2018 #19

    and again last one (this was my favourite till the circles)

    the infinite sequence 

    1 -1 +1 -1 +1 -1 + 1 -1 .....

    has sum 0, 1, or even (mind bendingly) a half?

  • mickysf
    mickysf Forum Participant Posts: 6,474 ✭✭✭
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    edited July 2018 #20

    I wonder if some interesting theorem is out there if taken into the 3rd of possibly 4th dimension.wink

    I remember 'messing about' with Möbius loops in maths lessons introducting double or triple twists etc.and cutting along length having attempting to predict outcomes. Those always fascinated me and I never managed to understand the results which baffled me.

  • brue
    brue Forum Participant Posts: 21,176 ✭✭✭✭✭
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    edited July 2018 #21

    The mention of the word "infinity" in a maths class years ago put me off totally, I just thought that's it then, we might as well all go home there's no end, we're not going to solve this. wink

  • Wherenext
    Wherenext Club Member Posts: 10,586 ✭✭✭
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    edited July 2018 #22

    Lots of interesting questions on here. Now it's infinity.

    Where will it end?smile

  • Rocky 2 buckets
    Rocky 2 buckets Forum Participant Posts: 7,101
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    edited July 2018 #23

    Buzz knows👍🏻-

  • Cornersteady
    Cornersteady Club Member Posts: 14,425 ✭✭✭
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    edited July 2018 #24

    yes still do that mobius loop if the class is capable of using scissors with too much harm or haircuttingsmile

    (A mobius bottle is easily made, get a strip of paper make a loop but before you stick the ends together twist one end by half a turn. You now have a shape with only one edge and one side, try cutting it in half along the strip and if that doesn't make you chuckle try why did the chicken cross the Mobius strip)

     

  • Kennine
    Kennine Forum Participant Posts: 3,472
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    edited July 2018 #25

    so... a caravan (club site naturally) has an infinite number of pitches and they are all taken, after 12 an outfit turns up, what happens?.

    ------------------------------------------------------------

     

     

    The guy at reception tells that outfit to "go away" or words to that effect laughinglaughinglaughing

    OR --

    He insists that those leaving site do the right thing and leave before 12.00 laughinglaughinglaughing

    wink

     

  • redface
    redface Forum Participant Posts: 1,701
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    edited July 2018 #26

    Corners found tangents, circles and straight lines?

    Something does not add up there!laughing

  • Cornersteady
    Cornersteady Club Member Posts: 14,425 ✭✭✭
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    edited July 2018 #27

    LOL

  • SteveL
    SteveL Club Member Posts: 12,299 ✭✭✭
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    edited July 2018 #28

    I lost the will to live with math, when our pure maths teacher apparently proved a circle had its centre outside of itself.🤔

  • Tinwheeler
    Tinwheeler Forum Participant Posts: 23,135 ✭✭✭
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    edited July 2018 #29

    The Compleat Angler?😀