Patterns Symmetry in Math_ SUNY Cortland_072010
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Seeing is believing. Can students transfer their knowledge of math and see it in the world of nature. Co-presenters Lee Kaltman and Tracy Wixsom
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This document discusses patterns and symmetry in nature and mathematics. It begins by defining what patterns are and provides examples of patterns commonly found in nature, such as the stripes on tigers and spots on hyenas. It then discusses different types of patterns like fractals, spirals, and chaos. The document also defines symmetry and provides examples of different types of symmetries like reflection symmetry, rotational symmetry, and translational symmetry. It describes an activity where students look for and document examples of symmetry in their surroundings.
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This PowerPoint presentation discusses symmetry in nature, architecture, and geometry. It provides examples of line symmetry in animals like butterflies, shells, crabs, and starfish. Symmetry is also seen in human faces and bodies, as well as architectural structures like the Taj Mahal. Different 2D shapes have varying numbers of lines of symmetry: equilateral triangles have 3, squares have 4, regular pentagons have 5, and so on.
Line symmetry
This PowerPoint presentation introduces the concept of line symmetry through examples found in nature, architecture, art, and everyday objects. It explains that line symmetry exists when one half of a shape is the mirror image of the other half. Examples discussed include butterflies, human faces and bodies, shells on the beach, underwater creatures like crabs and starfish, animal shapes, reflections in water, and architectural structures like the Taj Mahal. The presentation also examines line symmetry in 2D shapes like triangles, squares, pentagons, hexagons, and octagons.
Symmetry
This document discusses different types of symmetry, including line symmetry and rotational symmetry. It provides examples of line symmetry in letters of the alphabet and examples of rotational symmetry in shapes like triangles, squares, and pentagons. It also discusses symmetry in architecture, flags, and natural phenomena. Symmetry is a fundamental organizing principle in nature and art that involves preserving certain properties when an object is transformed in some way.
Unit 3 symmetry
The document discusses symmetry in nature, architecture, and art. It defines symmetry as a spatial relationship where one half of a shape is the mirror image of the other half. There are different types of symmetrical lines including horizontal, vertical, and diagonal. Symmetry can be classified as axial or radial depending on whether equal elements are equidistant from a central axis or point.
Line symmetry
This PowerPoint presentation discusses line symmetry in nature, animals, humans, architecture, and 2D shapes. Some key examples provided include butterflies, shells, starfish, human faces, Leonardo da Vinci's drawing of human proportions, the Taj Mahal, and regular polygons like triangles, squares, and hexagons. The presentation shows how line symmetry exists all around us and is considered aesthetically pleasing, appearing commonly in both natural and man-made structures.
Symmetry,rotation, reflection,translation
The document discusses different types of symmetry including lines of symmetry, reflection, rotation, and translation. It provides examples of these symmetries using shapes like hearts, flags, polygons and math symbols. Regular polygons are noted to have multiple lines of symmetry and there is a pattern to how many lines different regular polygons will have.
H0.2b Line Symmetry2
This document discusses different types of symmetry found in nature, architecture, and shapes. It provides examples of line symmetry in shells, crabs, starfish, masks, the human face, reflections in water, and the Taj Mahal. It also examines the number of lines of symmetry in different polygons, finding that an equilateral triangle has 3 lines of symmetry, a square has 4, a regular pentagon has 5, a regular hexagon has 6, and a regular octagon has 8.
WELL PRESENTED & DETAILED PROJECT FILE ON SYMMETRY
This document discusses the concept of symmetry in geometry. It defines symmetry as identical parts of a figure after folding or flipping. There are three main types of symmetry discussed: linear symmetry where a line divides a figure into identical parts, rotational symmetry where a shape is rotated around a central point, and reflection symmetry where a shape is divided by a mirror line into matching halves. The document aims to introduce the key ideas of symmetry and stimulate discussion around different symmetry types.
CHAP1.pdf
Mathematics is evident everywhere in nature and is an integral part of our lives. It is the science of patterns, quantities and relationships. The document discusses several examples of patterns in nature like geometric shapes, symmetry, the Fibonacci sequence and golden ratio that are all deeply rooted in mathematics. It also elaborates on the importance and applications of mathematics in fields like science, technology, medicine and more, establishing it as an indispensable and universal language.
Maths in nature (complete)
Radial, bilateral, translational, and wallpaper symmetries are prevalent in nature. Examples include starfish with dihedral symmetry, trees with translational strip patterns, hexagonal structures like honeycombs and the Giant's Causeway that tessellate plane patterns, and the approximate bilateral symmetry found in human faces. Symmetry represents a balance and order that is reflected in both man-made and natural designs.
POWER POINT IN PATTERN IN NATURE.pdf
Mathematics can be seen throughout nature in stunning patterns and symmetry. The document discusses several common patterns found in nature such as spirals, fractals, stripes, waves, and meanders. Many natural phenomena exhibit mathematical qualities like symmetry, repetition of shapes, and self-similarity across scales. Nature provides abundant examples of patterns that can be described using mathematical concepts.
Mathematics in nature
Mathematics is present throughout nature. Many natural phenomena exhibit geometric shapes, symmetry, Fibonacci spirals, the golden ratio, and fractal patterns. For example, beehives form hexagonal cells, volcanoes form conical shapes, sunflower seeds arrange in Fibonacci spirals, and coastlines display self-similar fractal patterns across scales. Nature demonstrates that mathematics is a language used to describe the physical world.
Maths Project: Symmetry
This document presents a maths project on symmetry by Riya Ben of class 7. It defines symmetry as identical matching of two or more parts of a figure after folding or flipping. A line of symmetry, also called an axis of symmetry, is an imaginary line that divides a shape into two identical pieces. There are different types of symmetry including linear symmetry where a line divides a figure into identical parts, rotational symmetry where a shape is rotated around a central point, and reflection symmetry where a shape matches its mirror image when reflected across a dividing line.
Mathematics in nature
The document discusses how mathematics is present in nature. It provides examples of symmetry, shapes, parallel lines, and the Fibonacci spiral that can be observed in the natural world. Radial and bilateral symmetry are seen in structures like flowers and the human body. Common shapes found in nature include spheres, hexagons used by bees to build hives efficiently, and cones formed by volcanoes. Parallel lines can be seen in dune formations, and the Fibonacci spiral appears in nautilus shells. The document aims to show how nature demonstrates mathematical concepts and patterns.
Fractals and symmetry by group 3
Symmetry is the correspondence of form and configuration on opposite sides of a dividing line or plane. It is present in many areas including geometry, mathematics, science, and nature. Fractals are self-similar patterns that repeat at different scales and often have non-integer fractal dimensions. Benoît Mandelbrot coined the term fractal and studied fractals like the Mandelbrot set, which demonstrate iterative processes that lead to increasingly complex patterns appearing as one zooms in. Fractals are used in computer graphics, geography, art and other applications to model real-world irregular forms and processes.
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WELL PRESENTED & DETAILED PROJECT FILE ON SYMMETRY
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Patterns Symmetry in Math_ SUNY Cortland_072010
- 1. Symmetry, Patterns, andSymmetry, Patterns, and Geometric Shapes in theGeometric Shapes in the Adirondack MountainsAdirondack Mountains By Lee Kaltman andBy Lee Kaltman and Tracy WixsonTracy Wixson
- 2. What is a pattern? A Pattern constitutes a set of numbers or objects in which all the members are related with each other by a specific rule. Pattern is also known as sequence. There can be finite or infinite number of members in a pattern.
- 3. What is Symmetry? Symmetry is when one shape becomesSymmetry is when one shape becomes exactly like another if you flip, slide orexactly like another if you flip, slide or turn it.turn it. Another type of symmetry is reflectionAnother type of symmetry is reflection symmetry or line symmetry. One half issymmetry or line symmetry. One half is the reflection of the other half.The "Linethe reflection of the other half.The "Line of Symmetry" is the imaginary lineof Symmetry" is the imaginary line where you could fold the image andwhere you could fold the image and have both halves match exactly.have both halves match exactly.
- 4. Why the Adirondacks? History Big Camps Architecture and art of William West Durant Nature Forever Wild
- 5. Now we are going to do an activity See if you can identify any of these things in the following pictures: Do you see any patterns? Do you see symmetry? Do you see any geometric shapes?
- 6. What do you see in this picture?
- 7. What do you see in this picture?
- 8. What do you see in this picture?
- 9. What do you see in this picture?
- 10. What do you see in this picture?
- 11. What do you see in this picture?
- 12. What do you see in this picture?
- 13. What do you see in this picture?
- 14. What do you see in this picture?
- 15. What do you see in this picture?
- 16. What do you see in this picture?
- 17. What do you see in this picture?
Editor's Notes
- Symmetry, Patterns, and Geometric Shapes in Nature