Use Geometry example essay topic

Math and many of its aspects are a major part of everyday life. We spend the majority of our school years studying and learning the concepts of it. Many times, the question of why do we need to know these things has been asked. The following report will explain the history and purpose of geometry in our lives. Geometry means measure of the earth. In ancient Egypt, the Nile would flood its banks each year, flooding the land and destroying the farm areas.

When the waters receded and the people had to redefine the boundaries. This work was called geometry and was seen as a re-establishment of the principle of law and order on earth. (Lawlor, 6) Geometry is the mathematics of the properties, measurement, and relationship of the points, lines, angles, surfaces, and solids (Foner and Garraty). An ancient Greek mathematician, named Euclidean, was the founder of the study of geometry. Euclids Elements is the basis for modern school textbooks in geometry. On the other hand, there is non-Euclidean geometry.

This refers to the types of geometry which deny Euclids postulate about parallel lines. Once Albert Einstein put forth the theory of Relativity other approaches to geometry, besides Euclids was needed. (Kett and Trefil) Pythagoras emphasized the study of musical harmony and geometry. His theorem was that the square of the length of the hypotenuse is equal to the sum of the other two sides. (Kett and Trefil) Johannes Kepler, formulator of the laws of planetary motion is quoted as saying, Geometry has two great treasures: one of them is the theorem of Pythagoras, the other the division of a line into mean and extreme ratios, that is the Golden Mean. (Lawlor, 53) There are great philosophical, natural and artistic things which have surrounded this dimension ever since humanity first began to reflect upon the geometric forms of the world.

Its presence can be found in the sacred art of Egypt, India, China Islam and other traditional civilizations. It dominates Greek architecture and is hidden in the monuments of the Gothic Middle Ages. It then reappears widely in the Renaissance. The Golden Mean is found wherever there is an intensification of function or a particular beauty and harmony of form.

The Golden divisions contained in a pentagon are shown to determine the proportions of the ancient mask of Hermes. (Lawlor, 55) Exponents are shown in the equation spirals based on the roots of 2, 3 and 5. The Golden Mean spiral is found in nature in the beautiful conch shell or Nautilus pompilius which Shiva in the Hindu religion holds in one of his hands as an instrument to initiate creation. Through Pythagorean eyes, however, this form embodies the dynamics of the rhythmic generation of the cosmos, and through its harmonic principal, represents universal love. The spiral is found to be overlapping on the foetus of man and animals, and is present in the growth patterns of many plants. For example, the distribution of seeds in a sunflower is governed by the Golden Mean spiral.

The sunflower has 55 clockwise spirals overlaid into either 34 or 89 counterclockwise spirals. (Lawlor, 56 & 57) The name Fibonacci often appears to describe natural occurrences. The Fibonacci Series governs the laws involved with the multiple reflections of light through mirrors, as well as the rhythmic laws of gains and losses in the radiation of energy. It portrays the breeding patterns of rabbits, and the ratio of males to females in honey beehives. A botanist would be interested by the Fibonacci Series because of the distribution of leaves around a central stem. All the members of fractions lie between 1/2 and 1/3, creating a situation where leaves are separated from one another by at least one third of the stems circumference, therefore insuring a maximum of light and air for the leaf which is below.

The Golden Section can be found in all flowers having five petals or multiples of five, the daisy will always have a number of petals from the Fibonacci Series. The rose family is one of those based on five, as are all the flowers of the edible fruit-bearing plants. Walnuts, for example grow in clusters of five and six are truly rare. (Hargittai, 112) The plants displaying a sixfold structure such as the tulip, lily and the poppy, are poisonous or only medicinal for man. (Lawlor, 58 & 59) One major part of geometry is symmetry.

It has been found that things which are symmetrical, are more appealing to the eye. Bank logos often have rotational symmetry. It was suggested that the logos are rotational so that there is a continuous exchange of money. The Mitsubishi has a rotational and mirror symmetry. The hubcaps on cars are often very symmetrical. The cupolas of many state capitals and other important buildings have reflectional and rotational symmetry together.

For example, the Capital Dome in Washington D.C., St. Issac Cathedral, and the Cupola of Hungarian Parliament in Hungary. Other famous buildings include the leaning tower in Pisa, Italy, and the towers of the Vasili i Blazhenii. Returning to the buildings, they sometimes have to be viewed from above. The Eiffel Tower and the Washington Monument both have a square shape.

When viewed from above the Pentagon in Washington D.C. is in the shape of the pentagon, and the Lincoln Memorial has a rectangular shape. The Coliseum in Rome and the bull fighting arena in Spain have circular shapes. Some of the most beautiful examples of reflection and rotation can be shown in snowflakes. Each snowflake has a hexagonal structure, that is, the arrangement of the water molecules in the crystals. Crystals and minerals have a beautiful, symmetric outward shape when viewed by the naked eye. Like the snowflake, the internal structure is what forms the rest of the gem.

(Hargittai, 70) Then, finally, some geometry is just used for decoration. Advertisements use eye-catching shapes to draw attention to its product. Laces and designer clothing are sewn in a symmetrical pattern for the cloths durability. We sometimes use geometry without even knowing it, but several times we depend on taking measurements that will be used in the future as a reference.

1. Foner, Eric and Garraty- The American Heritage Dictionary, 1996.2. Hargittai, Istvan and Magdolna- Symmetry, Shelter Publications, Inc., 1994.3. Kett, Joseph and Trefil, James- Dictionary of Cultural Literacy, 1996.4. Lawlor, Robert- Sacred Geometry, Thames and Hudson Ldt, 1982.