https://www.khanacademy.org/college-careers-more/bjc/x4c51c62a:2022-challenge/x4c51c62a:2022-challenge-popular-vote-regional-champions/v/josefina-chile-math-s-america-region-champion-semifinalist-2022-breakthrough-junior-challenge 2023-04-06T04:51:06.745361174Z Fibonacci Numbers FIBONACCI NUMBERS Learn more at https://breakthroughjuniorchallenge.org. The Breakthrough Junior Challenge is an annual competition for students, ages 13-18, to share their passion for math and science with the world! Each student submits a video that explains a challenging and important concept or theory in mathematics, life sciences, or physics. The winner receives a $250,000 college scholarship. The winning student's teacher and school also benefit: $50,000 for the teacher and a state-of-the-art $100,000 science lab for the school. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Fibonacci Numbers FIBONACCI NUMBERS Learn more at https://breakthroughjuniorchallenge.org. The Breakthrough Junior Challenge is an annual competition for students, ages 13-18, to share their passion for math and science with the world! Each student submits a video that explains a challenging and important concept or theory in mathematics, life sciences, or physics. The winner receives a $250,000 college scholarship. The winning student's teacher and school also benefit: $50,000 for the teacher and a state-of-the-art $100,000 science lab for the school. https://cdn.kastatic.org/ka-youtube-converted/GzM_zfDHajM.mp4/GzM_zfDHajM.mp4 90 Understanding and exploring the fibonacci sequence https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:sequences-and-series-ncert-new/x0419e5b3b578592a:series/v/worked-example-fibonacci-sequence 2025-03-01T15:52:37.13987578Z Worked example - Fibonacci sequence Given the recursion formula for Fibonacci sequence, how do we generate the list of first few numbers. We first try playing with the recursion formula but then quickly realise the pattern. Every term is equal to the sum of the previous two. The question asks us to find the ratio of consecutive terms which means we briefly get to say hello to the golden ratio! Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Worked example - Fibonacci sequence Given the recursion formula for Fibonacci sequence, how do we generate the list of first few numbers. We first try playing with the recursion formula but then quickly realise the pattern. Every term is equal to the sum of the previous two. The question asks us to find the ratio of consecutive terms which means we briefly get to say hello to the golden ratio! https://cdn.kastatic.org/ka-youtube-converted/KaF0rEG8ySM.mp4/KaF0rEG8ySM.mp4 346 Understanding and exploring the fibonacci sequence