![]() The blue line continues to curl across these shapes. The vertical rectangle is further divided into a square labelled 8, and a horizontal rectangle that is divided again. It is overlaid with a curved blue line from the top right to the bottom left. The square labelled 21 is overlaid with another quarter circle, from the top left, to the bottom right corner. This is divided into a square, labelled 21, and another, smaller, horizontal rectangle. To the right of the square is a vertical rectangle. The blue line over it curves from the bottom left to the top right corner, in a quarter circle. The largest, on the left, is a square labelled with the number 34. The largest rectangle is divided into many smaller shapes. Shown is a black and white illustration of a rectangle divided into smaller squares and rectangles, overlaid with a blue spiral line. Two quantities have the Golden Ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities: ![]() The Golden Ratio can also be found using two quantities, like the lengths of two line segments. The Golden Ratio is also known as the Golden Section, the Golden Mean and the Divine Proportion. It also has other unusual mathematical properties. It can also be represented by the symbol Φ, the 21st letter of the Greek alphabet. The Golden RatioĪs the Fibonacci numbers get bigger, the ratio between each pair of numbers gets closer to 1.618033988749895. When students look at the relationship between one term and the next, they are doing a type of thinking called recursive thinking. ![]() A horizontal oval with a vertical line through the centre. This is labelled with the symbol for Phi. These ratios are written in the centre of each bar.Ī dotted line stretches across the graph, at the level of 1.618033988749895. The last bar, labelled 21/13 is bright blue, and reaches up to 1.615. The bar labelled 13/8 is turquoise and reaches to 1.625. The bar labelled 8/5 is orange and reaches up to 1.6. The bar labelled 5/3 is dark purple and reaches up to 1.667. The bar labelled 3/2 is bright purple and reaches up to 1.5. The bar labelled 2/1 is gold and reaches up to 2.0. Shown is a colour bar graph with 0 - 2.0 on the y axis, and 1/1, 2/1, 3/2, 5/3, 8/5, 13/8, 21/13 on the x axis.įrom left to right: the bar labelled 1/1 is pale purple and reaches up to 1.0. This sequence of numbers may not seem like much. The Fibonacci sequence can also be expressed using this equation: F n = F (n-1) + F (n-2) The individual numbers within this sequence are called Fibonacci numbers. His solution to this problem led to a series of numbers. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair from which the second month on becomes productive? In the same book, Fibonacci introduced his famous rabbit problem:Ī certain man put a pair of rabbits in a place surrounded by a wall. This is the same number system we still use today. He introduced the Arabic numeral system to the Western world in his book Liber Abaci. He was not called Fibonacci during his lifetime.įibonacci was one of the most important mathematicians in the middle ages middle ages. He was even better known as Fibonacci, which means “son of Bonacci” in Italian. Leonardo Bonacci became known as Leonardo of Pisa because he was from Pisa. This was identified by mathematician Leonardo Bonacci around the year 1202. So where does this “golden” number come from? The ratio is based on a sequence of numbers known as Fibonacci numbers, or the Fibonacci sequence. According to mathematicians as far back as the ancient Greeks and Egyptians, this element is a ratio of 1:1.618. There is a common element in many of the things humans describe as beautiful. It turns out the Greeks were right about beauty and math. It is perched on a glossy red flower with a large yellow stamen. The lower edges of the wings have a thick stripe of black, with rows of white dots.īetween its wings, the butterfly has a slim black torso and long antennae. The butterfly's wings are dark blue at the top, near its head, brightening to deep blue in the centre, near its torso, then bright blue. The pattern on the left and right wings are mirrors of each other. Shown is a colour photograph of an insect with two wings patterned in shades of blue. Open Professional Learning × Close Professional Learning Open Educational Resources × Close Educational Resources
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