Mathematical patterns in nature
- 1. MATHS HOLIDAY HOMEWORK TOPICS- MATHEMATICAL PATTERNS IN NATURE
- 2. NAME- ANSHUMAN SINGH CLASS- 9‘C’ ROLL NUMBER- 5 ADMISSION NUMBER- 1068
- 3. ACKNOWLEDGEMENT: • What is a Pattern in Nature? • Mathematical Patterns in Nature • Different mathematics pattern • 5 stunning ways we see mathematical patterns in nature
- 4. WHAT IS A PATTERN IN NATURE? The world is full of naturalvisualpatterns,fromspots ona leopard to spirals of a fiddlehead fern. Some patterns are as small as the moleculararrangement ofcrystals and as big as the massive spiralpatternof the Milky Way Galaxy. Patterns canbe found everywhereinnature. While one might think of patterns as uniformand regular, some patterns appear more randomyet consistent. The definition of a patternin nature is a consistent form, design, or expressionthat is not random. There are multiple causes ofpatterns in nature. Some patterns are governedby mathematics. These are called the “GoldenRatio”, this is a rule that describes a specific pattern in nature. This mathematicalformula is seenin spiral patterns suchas a snail’s shell or the whorls of a lily
- 5. SOME OF THE CAUSES OF PATTERNS IN NATURE ARE: • Reaction-diffusioneffect:chemicalinteractions ofpigment-formingmolecules in organisms create the spots, stripes, and other visible patterns;this is also called the turingmodel. • Law of conservationofmass:predictable patternsofchemical interactions are governed by this law of nature whichstates that matter is conservedbut changeable in a reaction. • Law of naturalselection:patternsinthe appearance and behavior ofa species can change over time due to the interactionofinheritable traits and the organism’s environment. • Animal behavior:patterns observedin animal behavior, suchas the productionof hexagons in honeycombs, are oftenthe result of genetics and the environment. • Laws of physics:the interactionofmatter and energy create predictable patternssuchas weather patterns due to the interactionofsolar energy, mass,and gravity. Planetary motionis a predictable patterngoverned by inertia, mass, and gravity.Also, weathering patterns cancreate unusualrockformations suchas the giant’s causeway
- 6. MATHEMATICAL PATTERNS IN NATURE Mathematics is seen in many beautiful patterns in nature, such as in symmetry and spirals. Both are aesthetically appealing and proportional. Symmetry can be radial, where the lines of symmetry intersect a central point such as a daisy or a starfish. Bilateral symmetry describesobjects or patterns that are equal on both sides of a dividingsector, as seen in butterflies, mammals, and insects.
- 7. MATHEMATICAL PATTERNS IN NATURE Spirals are more mathematically complexand varied. A spiralpatternwould be described as a circular patternbeginning at a center point and circling around the center point as the pattern moves outward. Examples of spirals would be a chameleon’s tail, analoe plant, or a nautilus shell. There are various types ofspirals;while they look very similar, mathematically, theyare only approximately close. Alogarithmicspiral, as shownbelow, increases the distance ofeach spiral logarithmically. Ina Golden Spiral, the increasingrectangles demonstratePhi, or the GoldenRatio of 1.618, based on the length versus the width of eachrectangle. Eachlooks very similar, but mathematically they are slightly different.
- 8. DIFFERENT MATHEMATICS PATTERN Waves representthe periodic distributionof some natural medium like water, air, sound, electromagnetic field or solid materials, etc., visually. The waves are coming in a pattern called waves pattern. Sometimes the waves come in a regular pattern. Sometimes, it comes in an irregular pattern. This type of pattern can see in patterns in nature. 1 Wave in water 2 Wave in Air 3 Wave in Sound
- 9. FIVE STUNNING WAYS WE SEE MATHS IN THE WORLD Have you ever stopped to lookaround and notice all the amazingshapes and patterns we see in the world around us?Mathematics forms the building blocks of the naturalworld and canbe seenin stunning ways. Here are a few of my favorite examples of math in nature, but there are many other examples as well. 1The Fibonacci Sequence 2 Fractals in nature 3 Hexagons in nature 4 ConcentricCircles in Nature 5 Maths in outer space
- 10. 1THE FIBONACCI SEQUENCE Named for the famous mathematician, Leonardo Fibonacci, this number sequenceis a simple, yet profound pattern. Based onFibonacci’s ‘rabbit problem,’this sequencebegins withthe numbers 1 and 1, and theneach subsequent number is found by addingthe two previous numbers.Therefore,after 1 and 1, the next number is 2 (1+1). The next number is 3 (1+2) and then 5 (2+3) and so on What’s remarkable is that the numbers in the sequenceare oftenseenin nature. Afew examples include the number of spirals in a pine cone, pineapple or seeds in a sunflower, or the number of petals on a flower. The numbers in this sequence also forma unique shape known as a Fibonacci spiral, which again, we see in nature inthe form of shells and the shape of hurricanes.
- 11. 2FRACTALS IN NATURE Fractals are another intriguing mathematical shape that we seen in nature. A fractal is a self-similar, repeating shape, meaning the same basic shape is seen again and again in the shape itself. In other words, if you were to zoom way in or zoom way out, the same shape is seen throughout. Fractals make up many aspects of our world, included the leaves of ferns, tree branches, the branching of neurons in our brain, and coastlines.
- 12. 3HEXAGONS IN NATURE Another of nature’s geometricwonders is the hexagon. A regular hexagonhas 6 sides of equal length, and this shape is seenagainand again in the world around us. The most commonexample of nature usinghexagons is in a bee hive. Bees build their hive using a tessellationofhexagons. But did you know that every snowflake is also in the shape of a hexagon? We also see hexagons in the bubbles that make up a raft bubble. Althoughwe usually think of bubbles as round, whenmany bubbles get pushed togetheron the surface of water, they take the shape of hexagons.
- 13. Another commonshape in nature is a set of concentric circles. Concentricmeans the circles all share the same center, but have different radii. This means the circles are all different sizes, one inside the other. A common example is in the ripples of a pond when somethinghits the surface ofthe water. But we also see concentriccircles in the layers ofan onion and the rings of trees that formas it grows and ages. If you live near woods, you might go looking for a fallen tree to count the rings, or look for an orb spider web, which is built with nearly perfect concentriccircles. 4CONCENTRIC CIRCLES IN NATURE
- 14. 5MATHS IN OUTER SPACE Moving away fromplanet earth, we canalso see many of these same mathematicalfeatures inouter space. For instance, the shape of ourgalaxy is a Fibonacci spiral. The planets orbit the sun on paths that are concentric. We also see concentriccircles in the rings of Saturn. But we also see a unique symmetryinouter space that is unique (as far as scientists cantell) and that is the symmetry betweenthe earth, moonand sunthat makes a solar eclipse possible. Every two years, the moonpasses betweenthe sunand the earthin sucha way that it appears to completely cover the sun. But how is this possible whenthe moonis so much smaller thanthe sun?Every two years, the moonpasses betweenthe sunand the earthin sucha way that it appears to completely cover the sun. But how is this possible whenthe moonis so much smaller than the sun?