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Prashant tiwari ppt 2

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What is the connection between Mathematics in different subject?

Connection of mathematics in many subject like – science,, chemistry , physics(it is also math.) ,English, Sst,and etc.

Mathematics is life of people. . . .

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At school, you do math 

during math class.But you do math throughout the day in other subjects too.

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IN Social Studies You read graphs that compare information.   Which state has the highest 

  population?                                       How many people live in

NY?                                                             

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IN SCIENCE

After planting seeds,  you measure the plants  each week to see how   they have grown.

 How tall was the plant after   Week I?

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CONNECTION OF MATHS WITH SCI (chemistry)

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The Bridges of Koenigsberg can also be a good introduction to applications of mathematics, in this case graph theory (and group theory) in chemistry: Pólya – enumeration of isomers (molecules which differ only in the way the atoms are connected); a benzene molecule consists of 12 atoms: 6 C atoms arranged as vertices of a hexagon, whose edges are the bonds between the C atoms; the remaining atoms are either H or Cl atoms, each of which is connected to precisely one of the carbon atoms. If the vertices of the carbon ring are numbered 1,...,6, then a benzine molecule may be viewed as a function from the set {1,...,6} to the set {H, Cl}.

Clearly benzene isomers are invariant under rotations of the carbon ring, and reflections of the carbon ring through the axis connecting two oppposite vertices, or two opposite edges, i.e., they are invariant under the group of symmetries of the hexagon. This group is the dihedral group Di(6). Therefore two functions from {1,..,6} to {H, Cl} correspond to the same isomer if and only if they are Di(6)-equivalent. Polya enumeration theorem gives there are 13 benzene isomers.

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2(1+2+...+n)=n(n+1) 1+3+5+...+(2n-1)=n2

Pythagorean number theory

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What is a football? A polyhedron made up of regular pentagons and hexagons (made of leather, sewn together and then blouwn up tu a ball shape). It is one of the Archimedean solids – the solids whose sides are all regular polygons. There are 18 Archimedean solids, 5 of which are the Platonic or regular ones (all sides are equal polygons). There are 12 pentagons and 20 hexagons on the

football so the number of faces is F=32. If we count the vertices, we’ll obtain the number V=60. And there are E=90 edges. If we check the number V-E+F we obtainV-E+F=60-90+32=2.This doesn’t seem interesting until connected to the Euler polyhedron formula which states taht V-E+F=2 for all convex polyhedrons. This implies that if we know two of the data V,E,F the third can be calculated from the formula i.e. is uniquely determined!

Polyhedra – Plato and Aristotle - Molecules

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In 1985. the football, or officially: truncated icosahedron, came to a new fame – and application: the chemists H.W.Kroto and R.E.Smalley discovered a new way how pure carbon appeared. It was the molecule C60 with 60 carbon atoms, each connected to 3 others. It is the third known appearance of carbon (the first two beeing graphite and diamond). This molecule belongs to the class of fullerenes which have molecules shaped like polyhedrons bounded by regular pentagons and hexagons. They are named after the architect Buckminster Fuller who is famous for his domes of thesame shape. The C60 is the only possible fullerene which has no adjoining pentagons (this has even a chemical implication: it is the reason of the stability of the molecule!)

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ideas for discussions or simply for enlivening the class

•Albert Einstein (1879-1955)Imagination is more important than knowledge.•René Descartes (1596-1650)Each problem that I solved became a rule which served afterwards to solve other problems.•Georg Cantor (1845-1918)In mathematics the art of proposing a question must be held of higher value than solving it. •Augustus De Morgan (1806-1871)The imaginary expression (-a) and the negative expression -b, have this resemblance, that either of them occurring as the solution of a problem indicates some inconsistency or absurdity. As far as real meaning is concerned, both are imaginary, since 0 - a is as inconceivable as (-a).

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There is a huge ammount of topics from history which can completely or partially be adopted for classroom presentation.The main groups of adaptable materials areanecdotes quotesbiographies historical books and papersoverviews of development historical problemsThe main advantages are (depending on the topic and presentation)imparting a sense of continuity of mathematicssupplying historical insights and connections of mathematics with real life (“math is not something out of the world”)plain fun

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Mathematics are connected with the other subjects. We all know that betterly our life are full of mathematics in everywhere but how? •We do any work like study , buy,bought we go anywhere suppose I want some thing buy where use of maths are coming. In science we see that earlier time in chemistry , bio, physics it all are the maths. I would like to tell about maths history ‘’ science is the queen of mathematics how? In this way in earlier time science is Maths but according to changing of time theory are come in science so science aredifferent from maths.. So atlast maths are in every subject.

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