welcome support to nagunang lesson patterns and numbers in nature and the word patterns indicate a sense of structure and organization that it seems only humans are capable of producing this intricate creative and amazing information it is from this perspective that some people see an intelligent design in the way that nature forms the first pattern that we're going to discuss is about symmetry symmetry indicates that you can draw an imaginary line across an object and the resulting parts are mirror images of each other examples the butterfly leonardo da vinci's vertovian man and the starfish it sesamahalimbavanito in nature ironbutterfly the butterfly is symmetric about the axis indicated by the line note that the left and the right portion are exactly the same so this type of symmetry is called bilateral symmetry next is the leonardo da vinci pertuvian man it shows the proportion and symmetry of the human body there are other types of symmetry depending on the number of sides or faces that are symmetrical isang halimbawa jana and starfish the alan stark fish a metal five full symmetry note that if you rotate the starfish you can still achieve the same appearance as the original position so igniting dawn is rotational symmetry the smallest measure of an angle that a figure can be rotated while still preserving the original position is called the angle of rotation a more common way of describing rotational symmetry is by order of rotation in order of rotation a figure has a rotational symmetry of order n times the n full rotational symmetry if one over n of a complete turn leaves the figure and chains to compute for the angle of rotation we can use this formula 360 degree over n so somehow i the snowflake this pattern the pattern of the snowflake repeats six times indicating that there is a six fold symmetry so using the formula 360 degree over n the angle of rotation is 60 degree although many combination and complex shape of snowflakes may which leads some people to think that no two are alike the el marami snowflakes are indeed perfectly symmetric because of humidity and temperature another marble of nature design is the structure and shape of the honeycomb wipers use hexagon in making honeycomb and not any other polygons to conclude why hexagonal formation are more optimal in making use of the available space maritime tina tawagna packing problem so nobody unpacking problem it involved finding the optimal method of filling up a given space such as a cubic or a spherical container that the hexagonal formation are more optimal in making use of the available space so proof suppose you have circle of rages one centimeter each of which will then have an area of pi square centimeter we are then going to fill a plane with this circle using square parking and hexagonal so square pakistan to compute the percentage and square area by a circle so mulassa figurine formula area of the circles divided by area of the square times 100 percent square centimeters so it did divide like nothing times 100 and that is equivalent to 78.54 percent so it um percentage non-square backing next nothing is for hexagonal packing we can think of its hexagon as composed of six equilateral triangle with side equal to two centimeters so this formula the side squared times square root of three over four so again so many times one centimeter so subtitles and two centimeters squared times square root of three over four and two squared two centimeters squared is four squared centimeter so mata is therefore the area of each triangle in the hexagonal packing is square root of 3 square centimeter to compute the percentage and hexagon the area of a hexagon is six square root of three square centimeter bucket that square root is three squared centimeters so times six things nothing can again six square root of three square centimeter and young area and hexagon so young air in a hexagon and is six square root of three square centimeter leon del martin tatloon circle ankasha celeb dang hexagon it gives a total of so using the formula area of the circles divided by the area of the hexagon times one hundred percent substitute like nothing times one hundred percent the percentage of hexagonal parking is ninety point sixty nine percent now comparing the two percentage we can clearly see that using the hexagon will copper a larger area when using square therefore we can conclude that hexagonal formation are more optimal in making use of the available space now you know hexagonal and behind peace thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button put updated ko for more video tutorial this is your guide in learning your mod lesson your walmart channel