Tutorial 3

Nombor RekreasiUrutan Fibonacci dan Golden ratioPetak ajaibPenyelesaian MasalahWah Mong WehJabatan MatematikIPG KSAH

Nombor Fibonacci Dalam Matematik, Urutan Fibonacci adalah seperti berikut:

1,1,2,3,5,8,13,21,34,55,89,.

Fibonacci numberThe first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two :1 + 1 = 21 + 2 = 32 + 3 = 53 + 5 = 8.

Fibonacci numberIn mathematics terms, the sequence F of Fibonacci numbers is defined by the recurrence relation

Fn-2 + Fn -1= Fn

Strategies for Problem SolvingTry simpler problemsGuess a patternTest the patternExplain ( if possible)Use the pattern

Mathematical Notesrabbits problem

Bees family tree

Golden RectanglesA Golden Rectangle in which the ratio of the length to the width is the Golden Ratio.

In other words, if one side of a Golden Rectangle is 2 unit long, the other side will be 2 * (1.62) = 3.24 unit

Golden RectanglesThis number (1.618..) is called the golden ratio.A rectangle that satisfies this proportion for finding the golden ratio is called a golden rectangle.

Golden Rectangles.

Construction of Golden Rectangle

Fibonacci SequenceIn the Fibonacci Sequence, suppose we consider the ratios of the successive terms, as you go farther and farther to the right, the ratio of the term will get closer and closer to the Golden Ratio

Fibonacci Sequence

LETS TRY

Magic Square/ Petak Ajaib

A magic square is an arrangement of the number from 1 to n^2 ( n-square) in an n x n matrix, with each number occurring exactly once, and the sum of the entries of any row, any column or any main diagonal is the same.

Examples of Magic Squares One of the most famous magic squares is that of Albrecht Drer. It was created in 1514 and is shown below 15141496712510118163213

Drers Square As you can see from the square, the total of each row, column, diagonal and small square is 34. You can also see that the year it was made (1514) appears in the squareHere is the year

Some More Magic SquaresThe total for each row, column etc. is 15816357492The total for each row, column here is 50

206717915141213111016818195

Magic SquareThe value of the sums can be shown to be

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