Two Fibonacci Problems

Fibonacci is today one of the world's most famous mathematicians, but it was in 1202 that he produced 'Liber abaci' (or 'Book of Squares') which was paramount in introducing the Hindu-Arabic numerals we use today. Robin Wilson, Gresham Professor of Geometry, looks at two short problems which appear in this book, as a taster to the types of problems he was concerned with.

This is the fifth part of 'A Millennium of Mathematical Puzzles'.
The full lecture is available (in 24 parts) here on YouTube, or it can be downloaded (like all of our lectures) in its complete form from the Gresham College website, in video, audio or text formats:
http://www.gresham.ac.uk

Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website.

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Education

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• Math
• Maths
• Mathematics
• Wilson
• Geometry
• Algebra
• Fraction
• Problem
• Puzzle
• Lecture

[xAmpersand]

First one is easy; second one is a little harder, but i got it by finding the average of 4, 5, and 6; which is 5, then divide by three; which is 1 and 2/3.

[messakg123]

(1/4+1/3)l=21

(3/12+4/12)l=21

7l/12=21

l=12x21/7

=12x3

=36

[Libervurto]

I did the tree one a weird way but maybe this helps.

1/4 + 1/3 is under ground so I need to subtract the sum from 1 to find the portion above ground.

To add them together we need a common denominator: 12, so 3/12 + 4/12 = 7/12.

So 5/12 is above ground.

We know 21 palmi is underground (which is 3*7) so I did 5*3 = 15 palmi above ground. Above ground + below ground = 36 palmi.

I didn't catch on that 7/12 means a 12p tree would have 7p underground so 21/7=3, 3*12=36, 21/36=7/12, Answer is 36.

[cembry90]

Good exercise ;)

1/4 + 1/3 = 3/12 + 4/12 = 7/12

7/12 = 21 palmi [below ground]

21/7 = 3 palmi [1/12 total size]

12*3 = 36 palmi [total size]

[eltotoX]

Sweet problems! I couldn't do the first one but the second one came easy.