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Geometry in Nature

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Page 1: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

Geometry in Nature

Page 2: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

Geometry is a Greek word meaning earth measure.

Page 3: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

Symmetry-a rotation or slide of a figure

that leaves it unchanged although its position may be

altered

Shapes-Many geometric shapes

are found in nature

-

Repeating patterns- some are the same size (congruent) and some are simply repeating

patterns

Parallel Lines – same distance apart

Proportion- a relationship between quantities such that is one varies the other varies in a manner

dependant on the first

LOOK FOR:

Page 4: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

The bees make their hives into regular hexagons

Page 5: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

Honeycomb

Page 6: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

The following slides are some

more examples of geometry in

nature

Page 7: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered
Page 8: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered
http://mypointexactly.wordpress.com/2007/10/07/comparative-studies/dusty-miller/
Page 9: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

These flowersillustrates perfect symmetryfound in many ofnatures plants.

Page 10: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

Passionfruit Flower

Page 11: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered
Page 12: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

Symmetry in Leaves

Page 13: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered
Page 14: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

A salsify seed head displays Mother Nature's magnificent grasp of geometry.

Page 15: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered
Page 16: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered
Page 17: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

Mt. Pisgah - March 2006

Page 18: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered
Page 19: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

PINECONE

Page 20: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

See the symmetry in each slice of fruit.

Page 21: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

Fossil SanddollarThis beautiful fossil

sanddollar from Madagascar has incredible detail.  The original shell consisted of small, thin, interlocking calcareous plates that have completely turned to stone.  This fossil shows the 5 point "flower" symmetry common to the animal in the echinodermato phylum.  This sanddollar is slightly less than 3" in diameter and protrudes 1" at its center high point.

Page 22: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

snowflake

Page 23: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

Ghost of a melting snowflake

Page 24: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

Pyramids

Twenty years were spent in erecting the pyramid itself: of this, which is square, each face is eight plethra, and the height is the same; it is composed of polished stones, and jointed with the greatest exactness; none of the stones are less than thirty feet." -Heroditus, Chap. II, para. 124.

A plethra is a measurement used in Ancient times, equal to 100 Greek feet

Page 25: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

See the symmetry in the wings of the butterflies.

Page 26: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

Starfish

Page 27: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

The holes in radiolarian and diatom shells respectively exist for differing reasons. Both types of skeleton are formed from silicon compounds. In diatoms, the holes collectively take on the role of a sieve, a two-way filtration mechanism across which water and nutrient molecules permeate the cell.

Page 28: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

Just think about a spider's web. That is a complicated geometric design. And it is created, usually, in a perfect manner. Even though I majored in Drawing and Painting in college, and even though I am a Graphic Artist at work, I could not draw a design that perfectly, freehand. Yet a spider, using only his body, continually creates geometrically complex advanced shapes that few, if any, human adults could perfectly duplicate, without the aid of machines, or tools such as a pencil and ruler...and even with a pencil and ruler, it would be very complicated, and possibly even impossible, for most people to exactly duplicate.

(by Jeff Jenkins)

Page 29: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

What geometric aspects do you see in each spider web?

Page 30: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered
Page 31: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered
Page 32: Geometry is a Greek word meaning earth measure. Symmetry-a rotation or slide of a figure that leaves it unchanged although its position may be altered

You can find geometry in many more things in nature. Look around and see what you can find. You will be amazed!


Symmetry and Aesthetics in Contemporary Physicsweb.physics.ucsb.edu/~jatila/sym-lectures/Class_02_2016.pdf · symmetry translational symmetry reflection symmetry screw symmetry =

Symmetry Section 3.1. Symmetry Two Types of Symmetry:

SYMMETRY ELEMENTS AND SYMMETRY OPERATIONS

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Implementation of distortion symmetry for the nudged ... · pathway, leave it unchanged or result in an equivalent pathway configuration: Rr ... conventional symmetry operation or

Symmetry operations are movements or actions that leave the molecule apparently unchanged. Symmetry elements are the points, lines, or planes in space

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Symmetry Tomáš Suk. Symmetry Symmetry in art - harmonious or aesthetically pleasing proportionality and balance Symmetry in physics - quantum symmetry,

SEC Course unchanged

Main Idea/Vocabulary line symmetry line of symmetry rotational symmetry angle of rotation Identify line symmetry and rotational symmetry

users.uoa.grusers.uoa.gr/~cdokou/TheoryCriticismTexts/Aristotle Poetics.docx  · Web viewAn altered word is one in which part of the ordinary form is left unchanged, and part is

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Symmetry operations are movements or actions that leave the molecule apparently unchanged

Symmetry OPEN CCESSA symmetry

Area Unchanged

IxNetwork Report - Arista · 2014. 4. 18. · Unchanged- 1 512 Unchanged-1 - 1024 Unchanged-1 1280 Unchanged-1 - 1518 Unchanged-1 - 9216 Unchanged-Agg Throughput Max Throughput (

Review Notes on Point Groups and Symmetry from ... · The symmetry of a given molecule depends which type and how many operations leave it unchanged. Before we go over the symmetry

Kingdom Animalia · 2019. 11. 28. · Body Symmetry Asymmetry –no symmetry, sponge Radial symmetry- repeats around an axis, jellyfish and starfish Bilateral Symmetry - symmetry

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INDEX Symmetry Picture1 Symmetry in the field of mathematics Picture2 Reflection symmetry Symmetry in history, religion, and culture picture3 Symmetry

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BMD Support Ship (T-BMD)2n.mit.edu/sites/default/files/documents/BMD-10.pdf · 1.3.2 Design Margins The ship margins are not altered for unchanged parts of the T-AKE baseline ship

Point Groups - Cairo University point group: Molecules that have no symmetry elements at all except the trivial one where they are rotated through 360º and remain unchanged, belong

[Unchanged] Growth Matters

Vocabulary symmetry line symmetry line of symmetry rotational symmetry center of symmetry order of symmetry magnitude of symmetry

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