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Not only does maths underlie every process and pattern that occurs in the world around us, but having a good understanding of it will help enormously in everyday life. Being quick at mental arithmetic will save you pounds in the supermarket, and a knowledge of statistics will help you see through the baloney in television adverts or newspaper articles, and to understand the torrent of information you'll hear about your local football team. MATHS IN NATURE : MATHS IN NATURE HEXAGON IN NATURE : HEXAGON IN NATURE A honeycomb is an array of hexagonal (six-sided) cells, made of wax produced by worker bees. Hexagons fit together to fill all the available space, giving a strong structure with no gaps. Squares would also fill the space, but would not give a rigid structure. Triangles would fill the space and be rigid, but it would be difficult to get honey out of their corners. FRACTIONS OF TOMATO : FRACTIONS OF TOMATO Slide 7: You can cut all sorts of fruit and vegetables into fractions: cut a tomato in half, an apple into quarters or a banana into eighths, although you would have to be very accurate. An orange might have 20 segments, and each would be a 20th of the whole orange ROTATIONAL SYMMETRY IN GLOBE : ROTATIONAL SYMMETRY IN GLOBE Slide 9: A globe is a good example of rotational symmetry in a three-dimensional object. The globe keeps its shape as it is turned on its stand around an imaginary line between the north and south poles. The globe shown here dates from the late 15th or early 16th century and is one of the earliest three-dimensional representations of the surface of the Earth. It can be found in the Historical Academy in Madrid. UNDERSTANDING PERCENTAGE : UNDERSTANDING PERCENTAGE Slide 11: Using money is a good way of understanding percentages. As there are 100 pence in £1, one hundredth of £1 is therefore 1 pence, meaning that 1 per cent of £1 is 1 pence. From this we can calculate that 50 per cent of £1 is 50 pence. This photograph shows three British currency notes: a £5 note, a £10 note and a £20 note. If 50 pence is 50 per cent of £1, then £5 is 50 per cent of £10, and so £10 is 50 per cent of £20. DECIMAL CALCULATOR : DECIMAL CALCULATOR Slide 13: A pocket calculator is one way in which decimals are used in everyday life. The value of each digit shown is determined by its place in the entire row of numbers on the screen. In this photograph, the 7 is worth 700 (seven hundreds), the 8 is worth 80 (eight tens) and the 6 is worth 6 (six ones). SYMMETRY IN TOWER : SYMMETRY IN TOWER MATHS HELPING OUR LIVES : MATHS HELPING OUR LIVES Slide 16: An article in the Sunday Times in June 2004 revealed the fact that you can't even assume that buying larger bags of exactly the same pasta would work out cheaper. It said that in many of the supermarkets buying in bulk, for example picking up a six-pack of beer rather than six single cans, was in fact more expensive. The newspaper found that the difference can be as much as 30%. The supermarket chains may be exploiting the assumption people have that buying in bulk is cheaper, but if you work it out quickly in your head you'll never be caught out. SPOTTING DODGY STATISTICS : SPOTTING DODGY STATISTICS Slide 18: How many adverts have you heard that make some claim such as "8 out of 10 women prefer our shampoo to their old one"? Did those enthusiasts think it was greatly better, or not really much of a difference? What about the other 20%? They might have absolutely hated it because it made all their hair fall out! And what question were they answering: that they really believe it made their hair any cleaner than a different shampoo, or that they preferred the smell, or shape of the bottle? MATHS IN ENGINEERING : MATHS IN ENGINEERING If it is rainy and cold outside, you will be happy to stay at home a while longer and have a nice hot cup of tea. But someone has built the house you are in, made sure it keeps the cold out and the warmth in, and provided you with running water for the tea. This someone is most likely an engineer. Engineers are responsible for just about everything we take for granted in the world around us, from tall buildings, tunnels and football stadiums, to access to clean drinking water. They also design and build vehicles, aircraft, boats and ships. What's more, engineers help to develop things which are important for the future, such as generating energy from the sun, wind or waves. Maths is involved in everything an engineer does, whether it is working out how much concrete is needed to build a bridge, or determining the amount of solar energy necessary to power a car. GEOMETRY IN CIVIL : GEOMETRY IN CIVIL This a pictures with some basic geometric structures. This is a modern reconstruction of the English Wigwam. As you can there the door way is a rectangle, and the wooden panels on the side of the house are made up of planes and lines. Except for really planes can go on forever. The panels are also shaped in the shape of squares. The house itself is half a cylinder. LINES&PLANES : LINES&PLANES Here is another modern reconstruction if of a English Wigwam. This house is much similar to the one before. It used a rectangle as a doorway, which is marked with the right angles. The house was made with sticks which was straight lines at one point. With the sticks in place they form squares when they intercepts. This English Wigwam is also half a cylinder. PARALLELOGRAMS : PARALLELOGRAMS This is a modern day skyscraper at MIT. The openings and windows are all made up of parallelograms. Much of them are rectangles and squares. This is a parallelogram kind of building. CUBES AND CONES : CUBES AND CONES This is the Hancock Tower, in Chicago. With this image, we can show you more 3D shapes. As you can see the tower is formed by a large cube. The windows are parallelogram. The other structure is made up of a cone. There is a point at the top where all the sides meet, and There is a base for it also which makes it a cone. SPHERE AND CUBE : SPHERE AND CUBE This is another building at MIT. this building is made up of cubes, squares and a sphere. The cube is the main building and the squares are the windows. The doorways are rectangle, like always. On this building There is a structure on the room that is made up of a sphere. PYRAMIDS : PYRAMIDS This is the Pyramids, in Indianapolis. The pyramids are made up of pyramids, of course, and squares. There are also many 3D geometric shapes in these pyramids. The building itself is made up of a pyramid, the windows a made up of tinted squares, and the borders of the outside walls and windows are made up of 3D geometric shapes. RECTANGLES AND CIRCLES : RECTANGLES AND CIRCLES This is a Chevrolet SSR Roadster Pickup. This car is built with geometry. The wheels and lights are circles, the doors are rectangular prisms, the main area for a person to drive and sit in it a half a sphere with the sides chopped off which makes it 1/4 of a sphere. If a person would look very closely the person would see a lot more shapes in the car. Too many to list. GEOMETRY IN CAD : GEOMETRY IN CAD Geometry is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences Computer-aided design, computer-aided geometric design. Representing shapes in computers, and using these descriptions to create images, to instruct people or machines to build the shapes, etc. (e.g. the hood of a car, the overlay of parts in a building construction, even parts of computer animation). Slide 28: Computer graphics is based on geometry - how images are transformed when viewed in various ways. Robotics. Robotic vision, planning how to grasp a shape with a robot arm, or how to move a large shape without collission. STRUCTURAL ENGINEERING : STRUCTURAL ENGINEERING Structural engineering. What shapes are rigid or flexible, how they respond to forces and stresses. Statics (resolution of forces) is essentially geometry. This goes over into all levels of design, form, and function of many things. MATHS IN MEDICINE : MATHS IN MEDICINE Medical imaging - how to reconstruct the shape of a tumor from CAT scans, and other medical measurements. Lots of new geometry and other math was (and still is being) developed for this. Protein modeling. Much of the function of a protein is determined by its shape and how the pieces move. Mad Cow Disease is caused by the introduction of a 'shape' into the brain (a shape carried by a protein). Many drugs are designed to change the shape or motions of a protein - something that we are just now working to model, even approximately, in computers, using geometry and related areas (combinatorics, topology). MATHS IN BIOLOGY : MATHS IN BIOLOGY Physics, chemistry, biology, Symmetry is a central concept of many studies in science - and also the central concept of modern studies of geometry. Students struggle in university science if they are not able to detect symmetries of an object (molecule in stereo chemistry, systems of laws in physics, ... ). the study of transformations and related symmetries has been, since 1870s the defining characteristic of geometric studies MATHS IN MUSIC : MATHS IN MUSIC Music theorists often use mathematics to understand musical structure and communicate new ways of hearing music. This has led to musical applications of set theory, abstract algebra, and number theory. Music scholars have also used mathematics to understand musical scales, and some composers have incorporated the Golden ratio and Fibonacci numbers into their work. INTONATION : INTONATION If we take the ratios constituting a scale in just intonation, there will be a largest prime number to be found among their prime factorizations. This is called the prime limit of the scale. A scale which uses only the primes 2, 3 and 5 is called a 5-limit scale; in such a scale, all tones are regular number harmonics of a single fundamental frequency. Below is a typical example of a 5-limit justly tuned scale, one of the scales Johannes Kepler presents in his Harmonice Mundi or Harmonics of the World of 1619, in connection with planetary motion. The same scale was given in transposed form by Alexander Malcolm in 1721 and theorist Jose Wuerschmidt in the last century and is used in an inverted form in the music of northern India. American composer Terry Riley also made use of the inverted form of it in his "Harp of New Albion". Despite this impressive pedigree, it is only one out of large number of somewhat similar scales. MATHS IN FORENSIC : MATHS IN FORENSIC MATHS IS APLLIED TO CLARIFY THE BLURRED IMAGE TO CLEAR IMAGE. THIS IS DONE BY USING DIFFERENTIAL AND INTEGRAL CALCULUS. TO FIND RACE : TO FIND RACE In forensic department the race and sex of humans can be found by using subpubic angles between the bones of pelvis. You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.