Page 2 of 3 FirstFirst 123 LastLast
Results 21 to 40 of 47

Thread: Math game (fun quizzes) ^^

  1. #21
    Kyriakos's Avatar Praeses
    Join Date
    Nov 2012
    Location
    Thessalonike, The Byzantine Empire
    Posts
    9,815

    Default Re: Math game (fun quizzes) ^^

    nhytgbvfeco2 never wants to reply, unless he is given a cookie But I am interested (question in post 20).

    Anyway, here is a new problem:

    You are fighting in the Trojan war, as one of the Greeks. High above you, Aphrodite -who famously sided with the Trojans, due to the apple - appears. Diomedes is planning to strike her, but he is on the opposite side to you (=Aphrodite is between you, high up). Your angle of elevation (the angle in which you raise your head to see Aphrodite) is 20 degrees. Diomedes' angle is 25 degrees. You do know that the distance between you and Diomedes is 500 meters, so the question is: how high above you is Aphrodite?
    Last edited by Kyriakos; January 17, 2023 at 06:55 AM.
    Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
    "While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
    Anaxagoras of Klazomenae, 5th century BC










  2. #22
    nhytgbvfeco2's Avatar Praefectus
    Join Date
    Jul 2010
    Location
    Israel
    Posts
    6,398

    Default Re: Math game (fun quizzes) ^^

    Quote Originally Posted by Kyriakos View Post
    nhytgbvfeco2 never wants to reply, unless he is given a cookie But I am interested (question in post 20).
    Oh, real classy calling a Jew greedy
    I wouldn't consider my knowledge of mathematics wholly insufficient to answer the question in your previous post. I think if the first cut is too close to one of the edges then the next cut has to be in the middle of what's left for it to be a viable triangle, but I'd have no idea on how to calculate the odds on any of that.


    Anyway, here is a new problem:

    You are fighting in the Trojan war, as one of the Greeks.
    That's quite the transition
    High above you, Aphrodite -who famously sided with the Trojans, due to the apple - appears. Diomedes is planning to strike her, but he is on the opposite side to you (=Aphrodite is between you, high up). Your angle of elevation (the angle in which you raise your head to see Aphrodite) is 20 degrees. Diomedes' angle is 25 degrees. You do know that the distance between you and Diomedes is 500 meters, so the question is: how high above you is Aphrodite?
    Just to clarify, is she in the middle between us, or just somewhere between us?

  3. #23
    Kyriakos's Avatar Praeses
    Join Date
    Nov 2012
    Location
    Thessalonike, The Byzantine Empire
    Posts
    9,815

    Default Re: Math game (fun quizzes) ^^

    Depends on what you mean: she is in the same line, just higher. She is NOT at the same distance from you and Diomedes (otherwise you'd both be looking at the same angle). I guess I should have made the fight take place in a deep schism in the mountain (furthermore, due to the relative distance, you can take the two people pretty much as being at the same height as the ground - they aren't tens of meters tall ^^)
    Last edited by Kyriakos; January 17, 2023 at 08:00 AM.
    Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
    "While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
    Anaxagoras of Klazomenae, 5th century BC










  4. #24
    nhytgbvfeco2's Avatar Praefectus
    Join Date
    Jul 2010
    Location
    Israel
    Posts
    6,398

    Default Re: Math game (fun quizzes) ^^

    Here is my professional solution:

  5. #25
    Kyriakos's Avatar Praeses
    Join Date
    Nov 2012
    Location
    Thessalonike, The Byzantine Empire
    Posts
    9,815

    Default Re: Math game (fun quizzes) ^^

    I don't have more cookies,currently :/
    Correct. Other methods could be used, but tangent is the briefest - eg law of sines is another method.

    Do you plan to at least look for a puzzle this time?
    (btw, your pixel drawing looks nasty :o )
    Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
    "While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
    Anaxagoras of Klazomenae, 5th century BC










  6. #26
    nhytgbvfeco2's Avatar Praefectus
    Join Date
    Jul 2010
    Location
    Israel
    Posts
    6,398

    Default Re: Math game (fun quizzes) ^^

    Quote Originally Posted by Kyriakos View Post
    I don't have more cookies,currently :/
    Correct. Other methods could be used, but tangent is the briefest - eg law of sines is another method.

    Do you plan to at least look for a puzzle this time?
    Hey, I provided one last time. It might not have been very good, but I did!
    (btw, your pixel drawing looks nasty :o )
    Now that's rude and uncalled for

    Alright then:
    2_1_6_6 = 48
    Fill in with: + - : *
    Make the equasion work.

  7. #27

    Default Re: Math game (fun quizzes) ^^

    Quote Originally Posted by nhytgbvfeco2 View Post
    Now that's rude and uncalled for
    Given what an absolute beauty it is, Kyriakos is way out of line.

  8. #28
    nhytgbvfeco2's Avatar Praefectus
    Join Date
    Jul 2010
    Location
    Israel
    Posts
    6,398

    Default Re: Math game (fun quizzes) ^^

    Quote Originally Posted by Septentrionalis View Post
    Given what an absolute beauty it is, Kyriakos is way out of line.
    Thank you. It feels good to be appreciated.

  9. #29
    Kyriakos's Avatar Praeses
    Join Date
    Nov 2012
    Location
    Thessalonike, The Byzantine Empire
    Posts
    9,815

    Default Re: Math game (fun quizzes) ^^

    Quote Originally Posted by nhytgbvfeco2 View Post
    Thank you. It feels good to be appreciated.
    I am starting to think you work in a matrix factory or something
    I got the solution, but not with any generalized method, so pls share that (I suppose one with... matrices? ^^)
    Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
    "While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
    Anaxagoras of Klazomenae, 5th century BC










  10. #30
    nhytgbvfeco2's Avatar Praefectus
    Join Date
    Jul 2010
    Location
    Israel
    Posts
    6,398

    Default Re: Math game (fun quizzes) ^^

    You.. jusrt want me to share the answer without answering it yourself? Nah man, post an answer xD
    No matrices or anything complicated involved. Though be aware, it doesn't follow PEMBAS, just goes by order of left to right.

  11. #31
    Kyriakos's Avatar Praeses
    Join Date
    Nov 2012
    Location
    Thessalonike, The Byzantine Empire
    Posts
    9,815

    Default Re: Math game (fun quizzes) ^^

    Eh, I mean intuitively one can find that it is [2(1)+6]6. But I am sure there are generalized methods (this wouldn't work easily if you had... 100 numbers ).
    I did spend 5 min trying to work out a general method on my own, using the fact this has 4(4)4 combinations, but although I couldn't, I am sure such do exist, and matrices appear linked very directly (a second matrix would be the directions).
    But unlike you, I haven't studied them at all ^^

    I also suspect it might be possible to work it out using nested functions and a floating C value, but again couldn't do it in a few min and gave up.
    Last edited by Kyriakos; January 17, 2023 at 12:21 PM.
    Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
    "While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
    Anaxagoras of Klazomenae, 5th century BC










  12. #32
    nhytgbvfeco2's Avatar Praefectus
    Join Date
    Jul 2010
    Location
    Israel
    Posts
    6,398

    Default Re: Math game (fun quizzes) ^^

    That is correct
    I don't know if there's any fancy shmansy way to solve it, i think it's just clear you need to multiply by at least one of the sixes, then you just figure out how to get an 8,

  13. #33
    Kyriakos's Avatar Praeses
    Join Date
    Nov 2012
    Location
    Thessalonike, The Byzantine Empire
    Posts
    9,815

    Default Re: Math game (fun quizzes) ^^

    "Fancy shmansy" is the very reason math exists ^^ Otherwise you'd be stuck with the Babylonians and non-theorem-based math.
    Or at least that used to be the prevalent view - that proof-based math originated with ancient Greece in the west. The opposing view is (afaik) still not well-documented, so might as well be false
    Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
    "While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
    Anaxagoras of Klazomenae, 5th century BC










  14. #34
    Kyriakos's Avatar Praeses
    Join Date
    Nov 2012
    Location
    Thessalonike, The Byzantine Empire
    Posts
    9,815

    Default Re: Math game (fun quizzes) ^^

    Anyway...
    Here is a different riddle (though based again on geometry and simple procedures there; just requires a bit of imagination if you have never seen it...)
    Construct a line which would be equal to the square root of another line You only have ruler and compass at your disposal.

    (obviously you can draw any line you want, as that to find the square root of, so that first step is merely to draw any line; BUT your way of finding the square root should be workable for any line length anyone can pick)
    Last edited by Kyriakos; January 18, 2023 at 02:55 PM.
    Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
    "While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
    Anaxagoras of Klazomenae, 5th century BC










  15. #35
    nhytgbvfeco2's Avatar Praefectus
    Join Date
    Jul 2010
    Location
    Israel
    Posts
    6,398

    Default Re: Math game (fun quizzes) ^^


  16. #36
    Kyriakos's Avatar Praeses
    Join Date
    Nov 2012
    Location
    Thessalonike, The Byzantine Empire
    Posts
    9,815

    Default Re: Math game (fun quizzes) ^^

    Come on, man, that's a crap single case solution
    Obviously I mean to present a method which works for any line length ^^

    It's actually a very neat bit of geometry. And (in the end), that if (something)=sqr1, then x=sqroriginal line, is used
    Last edited by Kyriakos; January 18, 2023 at 02:56 PM.
    Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
    "While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
    Anaxagoras of Klazomenae, 5th century BC










  17. #37
    Kyriakos's Avatar Praeses
    Join Date
    Nov 2012
    Location
    Thessalonike, The Byzantine Empire
    Posts
    9,815

    Default Re: Math game (fun quizzes) ^^

    Anyway, let me give you a hint, using the case nhyt did



    So, the general solution should have to do with the above, but altered in a way. Can you find how? ^^
    Last edited by Kyriakos; January 18, 2023 at 03:09 PM.
    Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
    "While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
    Anaxagoras of Klazomenae, 5th century BC










  18. #38
    nhytgbvfeco2's Avatar Praefectus
    Join Date
    Jul 2010
    Location
    Israel
    Posts
    6,398

    Default Re: Math game (fun quizzes) ^^

    Well, I did figure it probably has something to do with radius's and circles and whatnot, as I know the circle's.. circumferance? has to do with R^2. Well, also because what on earth else would you need the compass for.
    But anyway I've already given a good solution

  19. #39
    Kyriakos's Avatar Praeses
    Join Date
    Nov 2012
    Location
    Thessalonike, The Byzantine Empire
    Posts
    9,815

    Default Re: Math game (fun quizzes) ^^

    No you haven't and you should feel ashamed of yourself for that post
    Anyway, I will give it a day or two and then post the answer if no one gets it by then.
    Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
    "While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
    Anaxagoras of Klazomenae, 5th century BC










  20. #40
    Kyriakos's Avatar Praeses
    Join Date
    Nov 2012
    Location
    Thessalonike, The Byzantine Empire
    Posts
    9,815

    Default Re: Math game (fun quizzes) ^^

    Two days later, as promised, here is the solution:



    The first part(above) is in Greek - but so was the Ptolemaic Empire's translation of the Old Testament, nhy -, but it is just the Thales1 (above angle is 90 degrees) followed by applying the pyth theorem to show that in those conditions (similar triangles) you end up with the height being sqr BD(sqrDC).
    Of course this doesn't just mean you can replace (eg BD) with 1, and then measure the height, because DB=1 has to satisfy the equation (this is the second part of the construction) BC=f(DC)=DC+1 => your BC has to be measured by 1 or vice-versa.

    You can also take this to be a proof for the (obvious) fact that there is only one square root of each number, for there is only one x for every f(x)=x+C.

    Open floor
    Last edited by Kyriakos; January 21, 2023 at 03:09 AM.
    Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
    "While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
    Anaxagoras of Klazomenae, 5th century BC










Page 2 of 3 FirstFirst 123 LastLast

Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •