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Fibonacci Sequence and the Golden Ratio, Slides of Mathematics

The connection between the fibonacci sequence and the golden ratio, an irrational number with the approximate value of 1.61803. The fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1. The document also discusses leonardo fibonacci, the italian mathematician who introduced the sequence to europe. Additionally, it explains how the golden ratio appears in art and architecture.

Typology: Slides

2023/2024

Available from 02/20/2024

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THE ANGELITE PRAYER
Almighty God, we glorify You for giving us
the Angelite Charism. We thank You for the gift of
your Son, Jesus Christ, who is the Way, Truth, and
Life. We bless you for the continuous guidance of
the Holy Spirit.
Grant us, we pray, courage and strength
that we may give perpetual praise to You in
whatever we do. We ask this through Christ, our
Lord. Amen.
Oh, Holy Guardian Angels, guide us and
protect us! Laus Deo semper!
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THE ANGELITE PRAYER

Almighty God, we glorify You for giving us

the Angelite Charism. We thank You for the gift of

your Son, Jesus Christ, who is the Way, Truth, and

Life. We bless you for the continuous guidance of

the Holy Spirit.

Grant us, we pray, courage and strength

that we may give perpetual praise to You in

whatever we do. We ask this through Christ, our

Lord. Amen.

Oh, Holy Guardian Angels, guide us and

protect us! Laus Deo semper!

FIBONACCI SEQUENCE

  • A.k.a. Leonardo Pisano, Leonardo of Pisa
  • Italian Mathematician
  • Fibonacci ( Son of Bonacci ) LEONARDO FIBONACCI 1170 - 1240

Fibonacci Sequence ๐… ๐’ Term ๐… ๐ŸŽ 0 ๐… ๐Ÿ 1 ๐… ๐Ÿ 1 ๐… ๐Ÿ‘ 2 ๐… ๐Ÿ’ 3 ๐… ๐Ÿ“ 5 ๐… ๐Ÿ” 8 ๐… ๐’ = ๐… ๐’โˆ’๐Ÿ + ๐… ๐’โˆ’๐Ÿ

FIBONACCI SPIRAL

1

GOLDEN RATIO

GOLDEN RATIO

  • A.k.a. as Golden Mean or Divine Proportion
  • Represented by Greek letter phi ๐‹ or ๐œฑ
  • An irrational number, equal to
  • โ‰ˆ 1.

Vitruvian Man

โ€œGolden ratio is also at the heart of many proportion in our body.โ€

GOLDEN RECTANGLE 2

Parthenon

The Annunciation The Last Supper

Mona Lisa

๐’ Term Ratio ๐…๐ŸŽ^0 ๐… ๐Ÿ 1 undefined ๐… ๐Ÿ

๐Ÿ‘

๐Ÿ’

๐…๐Ÿ“^5 1.

๐Ÿ”

๐Ÿ•

๐Ÿ–

๐Ÿ—

๐’ Term Ratio ๐…๐Ÿ๐ŸŽ^55 ๐… ๐Ÿ๐Ÿ

๐Ÿ๐Ÿ

๐Ÿ๐Ÿ‘

๐Ÿ๐Ÿ’

๐…๐Ÿ๐Ÿ“^610

๐Ÿ๐Ÿ”

๐Ÿ๐Ÿ•

๐Ÿ๐Ÿ–

๐Ÿ๐Ÿ—

๐’ Term Ratio ๐…๐ŸŽ^0 ๐… ๐Ÿ 1 undefined ๐… ๐Ÿ

๐Ÿ‘

๐Ÿ’

๐…๐Ÿ“^5 1.

๐Ÿ”

๐Ÿ•

๐Ÿ–

๐Ÿ—

๐’ Term Ratio ๐…๐Ÿ๐ŸŽ^55 1. ๐… ๐Ÿ๐Ÿ

๐Ÿ๐Ÿ

๐Ÿ๐Ÿ‘

๐Ÿ๐Ÿ’

๐…๐Ÿ๐Ÿ“^610 1.

๐Ÿ๐Ÿ”

๐Ÿ๐Ÿ•

๐Ÿ๐Ÿ–

๐Ÿ๐Ÿ—