okay so for our first module i'm going to discuss nothing basically are the nature of mathematics or similarly so first i would like you to look around and look for patterns or designs there are plenty right so marami from the pattern of your windows to your tiles yuma spiderwebs not in the hat patterns and all those patterns are can be described by mathematics okay so according to this one recognizing patterns feels natural like our brain is hardwired to recognize them familiar so let us proceed with patterns and numbers in nature and the world okay so first but [Music] patterns are regular repeated or recurring forms of design so here we have an example so we have a smiley now along and then we have a next example so consider this one so based on the pattern i know you'll make annoyi [Music] usually square so triangle so since we only have two choices so we have two stars is [Music] malamancy letter b okay how about this one uh here we have two or at least three patterns so anova pattern standouts are not in detail so notice that uh so parang rotation box nothing so for each step you box nothing i negro rotate now 90 degrees counter clockwise so for the first one we're going to try on it online then channel 90 degrees okay [Music] image in this pattern would look like this ah previous one okay see let's proceed all right so here we have examples of numbers with patterns so in the first one meji madali uh to make things short uh your pattern d to i more like squared so i one squared or one times one okay another seven ethyl number nine two times two three times three sixteen i 16i four times four or four squared 25 i five squared and then one among you is just one of the six squared which is six by six or 36 so your next terms are see it is nothing i 36 okay okay so a few other patterns and i observe nothing i young punch you change now face no nothing moon so as you can see here uh in the first image so you pattern nothing and google from a half moon to this one and then we have a full moon crescent uh and then next we have the crescent okay so this one is a repeating pattern i know a [Music] a point closest to the sun ago aquarium i think a summer okay and then at that point uh for this i in the aquarium i think winter okay and then i go online pattern nothing everywhere spring summer winter uh will it so it is one of the patterns then observed or [Music] okay and then diffusion now diffusion processes processes governed by mathematics okay okay another good example of matam uh application of mathematics the megitan at insta nature's eye packing problem sodito uh so see you define mona natin packing problems involved finding the optimum method of filling up a space such as a cubic or a spherical container space okay so [Music] maximizing storage while uh reducing the amount of wax that the bees use okay so maximum storage better minimum amount of wax okay so optimize channel okay and then and the next pattern i make it in among the flowers i usually young flowers nothing i antosometime up flowers with three petals and then five petals so sabineela and pinaka common down belong petals i you okay and then a beautiful pattern can be seen in the sunflower so as you can see maruta manga spiral okay nana grow rotate from counterclockwise so as you can see [Music] [Music] [Music] the next one is the snails [Music] and then it follows an equiangular spiral okay from the root word equal in galsanos not equal so as distance from the center increases the angles form by the radii to the point in the tangent to the point remain constant what do i mean by this okay so if we connect a point ascend from the center and then i connect not inches syllabus and then we will form an angle angular spiral uh sometimes is referred to as a logarithmic spiral okay now we proceed with uh next topic which is symmetry so i think now encountering so symmetry is indicated that you can draw a line an imaginary line across an object and the resulting parts are mirror images of each other so we have an example here so atom first image i asymmetric straight lines and then you left at side i mirror images so with the second example okay so we call objects that are not symmetric asymmetric okay again this symmetrical diagonal asymmetric okay okay so i'm type nah symmetry dot i thought about bilateral symmetry into two so a meaning into two mirror images okay next uh okay so here we have a bit ruby and man so paginat uh this one is an example of a bilateral symmetry okay so it's an example okay so oh we have other types of symmetry so you can in a bilateral symmetry uh here we have a rotational symmetry [Music] [Music] uh starfish okay so rotational symmetry is the property a shape has when it looks the same after some rotation by a partial term so anger so degrees [Music] so here we have the formula 360 divided by n where the n is the order of rotation sir panopuny [Music] one two three four and five so meaning uh number of and nothing i equal sapphire the tournament and nothing i uh equal three has an angle of rotation it is 60 divided by 3 which is 120 degrees okay and then the tournament 360 divided by 5 is 72 equal to 72 degrees angle of rotation okay [Music] okay next we have and definitions uh patterns and makita nothings are numbers okay so a sequence is an ordered list of numbers called terms that may have repeated values the arrangement of these terms is set by a definite rule okay so sequence sha meaning in order order sequence [Music] for example this one so we have one and the next term is ten and then one hundred then one thousand so what happens uh you can be right pero since [Music] so what we're actually doing is multiply the first number by 10 and then your social note by 10 by 10 by 10 right so by doing this 1000 times 10 we get the next term to be 10 000. how about this one we have 5 9 14 20 okay so uh another pattern that we can notice is at all so two negative five and one at in the last time and three five nagging nine plus 20 okay so you know this new 99 additional pattern in time subtraction multiplication uh it's up to you to figure things out okay so we have another example so i think you can try this at home so try 16 32 64 128 i think my job is to mentor multiply okay and then your second term complicated three plus five eight five uh times eight up five plus eight is thirteen so our next term is thirteen actually merentine tags patterns continuing this one five pairs and then the next one is it okay so john donnan [Music] fibonacci sequence okay see again so the fibonacci sequence is a sequence named after a leonard of pisa which uh who has a nickname fibonacci okay so tata [Music] okay so geometrically on fibonacci sequence [Music] spiral surpassing spiral fibonacci sequence nothing starts out one by one a square and then one by one two by two term and then we add a three by three square with like another one so i think one by one i square one by one then two by two three by three four by four and then as a five by five and a square it by eight 13 by 13 and then 21 by 21. [Music] golden spiral okay okay so fibonacci sequence has uh interesting properties fibonacci number for example one plus one divided by one one two divided by one two three divided by two one point five five divided by three one point six six seven etcetera t guilt is a one point one six okay so ethernet last part nothing discussion uh uh mathematics parasitic model or mathematics for our world okay so not impeding your math so one obvious part of application of mathematics is [Music] [Music] [Music] nila next one is mathematics for predictions uh one very special application of the math of mathematics for prediction predictions okay and then next one issue mathematics for control and also you know the observations of nature as well as their interactions and relationship could be more elegantly described by means of mathematics so actually everything around us can be described by mathematics okay so in population population cases mathematics and then last but not the least is that the fact that mathematics is indispensable what do we mean by indispensable [Music] foreign engineers [Music] and all of these things use mathematics okay so uh what i'm trying to say is mathematics is an important part of our life in everything we do okay so i hope you uh learned how to appreciate mathematics uh in this lecture so you modulate and i upload kundalini group and then at the end of it you will find an assessment madeline young module assessment and then young and more on patterns okay so thank you for listening