I am applying to study Mathematics next year as are my peers who attended this lecture. The lecture has taught me so much: not only about where the golden ratio comes from, but also its interesting supposedly biblical connotations and biological real life examples. I felt inspired after attending this lecture and am grateful to Brampton College for arranging it. Finally, you work out the distance ratio each quarter- turn which turns out to be Φ. As the numbers expand, the distance from centre in golden spiral after turns is approximately square root of FnFn+1. This implies that the population of male and female generation in a bee colony follows a Fibonacci sequence: 1, 1, 2, 3, 5, 8 …Īs an A2 Further Maths student, what I found the most interesting in this public lecture is the part on golden and logarithmic spirals as we have learnt from polar coordinates that the general polar form for a spiral is r= a Θ. Female bees on the other hand, hatch from fertilised eggs and they have both parents. Male bees hatch from unfertilised egg, i.e. closer to the ‘standard ratio’, approximately 1.618.īut we can see the golden ratio in nature! The bees follow an interesting sex-determination system called haplodiploïde : not all bees have to have two parents. As the numbers in the ratio gets bigger, the ratio itself becomes converges, i.e. After rearranging, one of the solutions to the quadratic formed by equating ratios of the intersecting diagonals, is also equal to (1+sqrt(5))/2 the golden irrational number Φ.
With some prior knowledge of this topic, I immediately grasped Sarah’s derivation: In a regular pentagon, the diagonal x is composed by one long line and one short line with length x-1 and 1 respectively. Is this just a coincidence with the number? Certainly not! The golden ratio simply dropped in our lap halfway through our solution. Fortunately, just two weeks ago before Sarah Hart’s lecture I was guided to derive the formula for nth Fibonacci term by my Further Maths teacher, Imran Imam.
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