1995 British Mathematics Olympiad problem

Comments · 482

• MI

  @michaelkotthaus7120 · 2 years ago · pinned

  Thank you for this great episode. This problem is really awesome! And I tell you why. Being also interested in music theory and tuning systems, I found a strong relation to this domain.<br>Translated into the language of music, this equation asks: How can I divide an octave (which is the frequency ratio of 2 to 1) into three simple intervals where the nominator is one more than the denominator. In just intonation, such intervals are: octave = 2/1, fifth = 3/2, fourth = 4/3, major third = 5/4, minor third = 6/5, major second = 9/8 or 10/9, minor second = 16/15 or 17/16.<br>For example, the solution a=4, b=5 and c=3 leads to the factors 5/4, 6/5 and 4/3, which are a major third, a minor third and a fourth. If I start at C3, the following notes are E3, G3 and C4. This is a major chord. Great.<br>Another example, the solution a=2, b=4 and c=15 maps to the intervals of a fifth, a major third and a minor second. Starting at C3 the following notes are G3, B3 and C4.<br>For me, there is a heavenly connection between mathematics and music.

  372

• QU

  @quack8550 · 2 years ago

  &quot;I don&apos;t want to write it&quot;, proceed to write out more than previously needed.

  567

• JL

  @jlmassir · 2 years ago

  I like very much the way you teach. You experiment with possibilities, instead of being smarty and immediately &nbsp;presenting the solution. In this way, the student feels like participating in the solution instead of passively watching it. You&apos;re a great tracher.

  235

• 0X

  @0x_min · 2 years ago

  (1+1/3)(1+1/4)(1+1/5) is just beautiful

  199

• PA

  @patomatma · 2 years ago

  The most charismatic teacher that I have ever seen.

  40

• MA

  @MaximusU76 · 2 years ago

  One of the finest math explanation I&apos;ve ever seen on Youtube. Excelent job. Man you are a real Teacher.

  30

• SY

  @syamantagogoi · 2 years ago

  Awesome reasoning towards getting these solutions.Very much captivating... please continue discussion of such problems.

  65

• LO

  @Lost_In_Space_123 · 2 years ago

  Great analysis and solution. I have to admit that I viewed this video three time to thoroughly understand your solution. Thank you!!

  53

• NI

  @nishan375 · 2 years ago

  Your presentation and demeanor is just co calming and engaging. Love from Sri Lanka.

  33

• BO

  @borisjaulmes5773 · 2 years ago

  Never stop learning. I&apos;m 34, out of school since a while, and I loved this video.<br>Thank you ❤

  38

• AR

  @AryanAgarwal-v7y · 1 year ago

  These questions truly invoke the though process and helps to gain from what is taught in the classroom!! Amazing work by sir!! Thanks a lot. A math question a day keeps boredom away:yougotthis:

  2

• DA

  @darrenstensland5301 · 8 months ago

  I would not have EVER figured that out. &nbsp;I love this. &nbsp;I just watched like two hours of your videos. &nbsp;THANK YOU, keep it up!