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    Chapter I. Nature of Mathematics: Mathematics in Our World

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    Brian Andrei Casabay
    This document discusses patterns and symmetries found in nature. It begins by defining patterns as regular repetitions in nature, design, or ideas. Symmetry is defined as a geometrical regularity of an object that remains invariant under certain operations. The main symmetry operations discussed are reflection, rotation, translation, and glide reflection. Examples of symmetries found in nature include the hexagonal patterns of honeycombs, leaf arrangements in plants, stripes on tigers and spots on hyenas which provide camouflage. Students are assigned to take photos representing examples of the four symmetry operations found in nature.

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    Chapter I. Nature of Mathematics: Mathematics in Our World

    Uploaded by

    Brian Andrei Casabay
    181 views15 pages
    This document discusses patterns and symmetries found in nature. It begins by defining patterns as regular repetitions in nature, design, or ideas. Symmetry is defined as a geometrical regularity of an object that remains invariant under certain operations. The main symmetry operations discussed are reflection, rotation, translation, and glide reflection. Examples of symmetries found in nature include the hexagonal patterns of honeycombs, leaf arrangements in plants, stripes on tigers and spots on hyenas which provide camouflage. Students are assigned to take photos representing examples of the four symmetry operations found in nature.

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    Math-01-Lecture-1.1

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    This document discusses patterns and symmetries found in nature. It begins by defining patterns as regular repetitions in nature, design, or ideas. Symmetry is defined as a geometrical regularity of an object that remains invariant under certain operations. The main symmetry operations discussed are reflection, rotation, translation, and glide reflection. Examples of symmetries found in nature include the hexagonal patterns of honeycombs, leaf arrangements in plants, stripes on tigers and spots on hyenas which provide camouflage. Students are assigned to take photos representing examples of the four symmetry operations found in nature.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    181 views15 pages

    Chapter I. Nature of Mathematics: Mathematics in Our World

    Uploaded by

    Brian Andrei Casabay
    This document discusses patterns and symmetries found in nature. It begins by defining patterns as regular repetitions in nature, design, or ideas. Symmetry is defined as a geometrical regularity of an object that remains invariant under certain operations. The main symmetry operations discussed are reflection, rotation, translation, and glide reflection. Examples of symmetries found in nature include the hexagonal patterns of honeycombs, leaf arrangements in plants, stripes on tigers and spots on hyenas which provide camouflage. Students are assigned to take photos representing examples of the four symmetry operations found in nature.

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    Chapter I.

    Nature of Mathematics

    Mathematics in Our World

    DIVINA GRACIA V. CRISTAL


    Department of Mathematics
    Math 01 – Mathematics in the Modern World College of Arts and Sciences
    Mathematics in Our World

    Math 01 – Mathematics in the Modern World


    PATTERNS AND NUMBERS IN
    NATURE AND THE WORLD

    Definition
    A pattern is a regularity in the world, in human-made design, or in abstract
    ideas. As such, the elements of a pattern repeat in a predictable manner.

    Math 01 – Mathematics in the Modern World


    SYMMETRY

    Definition
    Symmetry is a geometrical or other regularity that is possessed by an object
    and is characterized by the operations that leave the object invariant.

    Math 01 – Mathematics in the Modern World


    SYMMETRY OPERATIONS:
    REFLECTION

    Definition
    Reflection is a symmetry consisting of a mirror line or axis on the plane and
    maps points from one side of the line to the other side at the same distance
    from the axis. Reflection is also called line symmetry or mirror symmetry.

    Math 01 – Mathematics in the Modern World


    BILATERAL SYMMETRY

    Definition
    Bilateral symmetry is the simplest form of reflection involving only one mirror
    axis. A type of symmetrical arrangement of the parts of an organism along a
    central axis, so that the organism can be divided into two equal halves.

    Math 01 – Mathematics in the Modern World


    SYMMETRY OPERATIONS:
    ROTATION
    Definition
    Rotation is a symmetry fixing one point (the center or rotocenter) and rotates everything by
    the same amount (angle) around that point.

    Note: The number of times an


    image appear in its original form
    is called the order of rotation.

    Math 01 – Mathematics in the Modern World


    SYMMETRY OPERATIONS:
    ROTATION

    Order 3 Order 4 Order 5

    Math 01 – Mathematics in the Modern World


    SYMMETRY OPERATIONS:
    TRANSLATION

    Definition
    Translation is a symmetry operation which moves everything by a certain
    distance in a particular direction.

    Math 01 – Mathematics in the Modern World


    SYMMETRY OPERATIONS:
    TRANSLATION

    Definition
    Translation is a symmetry operation which moves everything by a certain
    distance in a particular direction.

    Math 01 – Mathematics in the Modern World


    SYMMETRY OPERATIONS:
    GLIDE REFLECTION

    Definition
    Glide reflection is a combination of a reflection with a translation along the
    direction of the mirror line.

    Math 01 – Mathematics in the Modern World


    SYMMETRIES IN NATURE

    Honeycomb
    A honeycomb is a mass of
    hexagonal prismatic wax cells
    built by honeybees in their
    nests to contain their larvae
    and stores of honey and
    pollen. The structural design
    encloses regions of maximum
    area but with minimum
    perimeter, suggesting that
    honeybees are economists and
    mathematicians.

    Recommended video:
    Why do bees build hexagonal honeycombs? by BBC
    Math 01 – Mathematics in the Modern World Link: https://www.bbc.co.uk/programmes/p03zn0bp
    SYMMETRIES IN NATURE

    Phyllotaxis/Phyllotaxy
    Leaf arrangements known as phyllotaxis
    or phyllotaxy come in many forms. Leaves
    of plants may have the same arrangement
    on opposite sides where pairs of leaves are
    attached at a node. The arrangement of
    leaves may also alternate along the stem.

    Recommended reading:
    https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/phyllotaxis
    Math 01 – Mathematics in the Modern World
    SYMMETRIES IN NATURE

    Tiger’s Stripes
    The stripes on the tiger’s skin
    are patterns that are actually
    part of the animal’s skin so it
    appears below the fur as well. Hyena’s Spots
    Tiger stripes have probably The base color on the fur of spotted hyenas
    developed because the pattern are irregular pattern of roundish spots. The
    helps hide them and protect spots may be reddish, deep brown or almost
    them in their natural blackish and like the tiger, the spots of the
    environment. hyena serves to hide them from prey.

    Recommended reading:
    How animals got their spots and stripes – according to maths
    Link: http://theconversation.com/how-animals-got-their-spots-and-stripes-according-to-maths-85053
    Math 01 – Mathematics in the Modern World
    ASSIGNMENT

    “Photography patterns in nature and the world.”

    Take a good picture of nature, an object, an architecture or scenery around


    you that represents the four symmetry operations discussed. Indicate in the
    picture taken the observed symmetry operation. One photo for each of the
    4 operations.

    Math 01 – Mathematics in the Modern World

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