Art And Mathematics:Escher And Tessellations On first thought, mathematics and art seem to be totally opposite fields of study with absolutely no connections. However, after careful consideration, the great degree of relation between these two subjects is amazing. Mathematics is the central ingredient in many artworks. Through the exploration of many artists and their works, common mathematical themes can be discovered. For instance, the art of tessellations, or tilings, relies on geometry
how long the shape is (Length) W is how wide the shape is (Width) The area formula was mainly put into practice to calculate the area of the middle sections of the prism and the area of the regular polygon bases, whereas the perimeter formula was put into practice to calculate the perimeter of the regular polygon bases. The investigation was divided into 3 main parts. The first two parts primarily considered solving the topic question and developing the shortcut formula, whereas the third part considered
and is used lots in places (most things use rectangles for design- basic cube .etc). To start with what type of rectangle gives the best result. A regular square or an irregular oblong? I start by having 4 individual squares. [IMAGE] [IMAGE] [IMAGE] [IMAGE] [IMAGE][IMAGE] Goes to [IMAGE] [IMAGE] Regular square irregular oblong Now look at how many sides are exposed on each shape- å sides of each cube internal1 å sides of each cube internal2 [IMAGE][IMAGE]Ratio
The perimeter must be 1000m, and the shapes can be regular or irregular. First of all I will experiment with different rectangles, the different triangles, then pentagons. Then I will experiment with more regular shapes (or whatever type of shape has the largest area) to see the effect on area changing the number of sides has. I predict that the largest shape will be a regular circle, and the more sides a shape has and the more regular it is, the larger its area. (Taking a circle as having
show what I have found. Length (m) Width (m) Area (m) 400 100 40 000 300 200 60 000 250 250 62 500 150 350 52 500 I will now further my investigation by looking at shapes of a different nature: [IMAGE] Regular Pentagon ---------------- The regular pentagon has 5 sides, and as we get 1000m of fencing, this means each side will be 200m (1000¸5=200).
The Fencing Problem There is a need to make a fence that is 1000m long. The area inside the fence has to have the maximum area. I am investigating which shape would give this. Triangles: Scalene [IMAGE] The diagram above is not to scale. Instead of having the perimeter to 1000m, only in this diagram, I have made the perimeters of the shape to 10, only to make this part of the investigation easier to understand. We know that the base of all the shapes is 2. The lengths for the equilateral
perimeter (or circumference) of 1000m. She wishes to fence of the plot of land with the polygon with the biggest area. To find this I will find whether irregular shapes are larger than regular ones or visa versa. To do this I will find the area of irregular triangles and a regular triangle, irregular quadrilaterals and a regular square, this will prove whether irregular polygons are larger that regular polygons. Area of an isosceles irregular triangle: ========================================
------------------------------------------------------ [IMAGE] A regular triangle for this task will have the following area: 1/2 b x h 1000m / 3 - 333.33 333.33 / 2 = 166.66 333.33² - 166.66² = 83331.11 Square root of 83331.11 = 288.67 288.67 x 166.66 = 48112.52² [IMAGE]A regular square for this task will have the following area: Each side = 250m 250m x 250m = 62500m² [IMAGE] A regular circle with a circumference of 1000m would give an area of: Pi x 2
The Fencing Problem Introduction I am going to investigate different a range of different sized shapes made out of exactly 1000 meters of fencing. I am investigating these to see which one has the biggest area so a Farmer can fence her plot of land. The farmer isnÂ’t concerned about the shape of the plot, but it must have a perimeter of 1000 meters, however she wishes to fence off the plot of land in the shape with the maximum area. Rectangles I am going to look at different size
triangles; using trigonometrical functions (sine, tangent and cosine) to calculate either angles or sides of triangles constructed. Sometimes there are no known exact formulae for working out the area of certain shapes such as octagon and more complex polygons. In such cases, given shapes are split into shapes that have known formulae for areas and the worked out the areas are added together. Areas of the following shapes were investigated: square, rectangle, kite, parallelogram, equilateral triangle
to identify tier one, tier two and tier three words according to Beck, McKeown, & Kucan (2002). On page 42 of the geometry book, the first page of section 1.6: Classify Polygons, the book highlights the key vocabulary for this section on the side: polygon, side, vertex, convex, concave, n-gon, equilateral, equiangular, and regular. The first five of these terms are defined on this page. Other words that can be identified as tier level words are plane figure, segments, vertices, consecutive, interior
spatial analysis was discussed namely queries, transformations, measures and spatial interpolation. Under transformation buffering, point-in-polygon, polygon overlay are some operations that were discussed. Under measure the distance and length measurements were discussed as well as slope and aspects. Finally under the subject of spatial interpolation Theissen polygons, inverse-distance weighting and kriging were elaborated on. To conclude, spatial data analysis and just data analysis in general is an
drawing. These parallel lines formed planes. The parallel planes formed walls and rooms of our house. Two polygons are congruent if they are the same size and shape, and if their corresponding angles and sides are equal. Examples of congruent polygons in our home are the opposite walls of each room. We made them congruent so the rooms would form squares or rectangles. Another example of congruent polygons is the roof. We made each side of each roof the same so it would fit together and look nice. I’m not
Cisneros uses rhetorical devices in her story “Eleven” to not only explain the story but also to show Rachel’s feelings throughout the story. As Rachel talks about her past on her eleventh birthday, the various rhetorical devices serve to allow her to express her feelings to the reader, more so than if she had just used literal language in its place. Without the figurative language, the story would be much more simplistic, as it would be unable to convey the main focus of the story, that of Rachel’s
Gissel Perez Mary Adelyn Kauffman IDH1001 15 October 2015 How does the Flatland view of irregularities in configuration relate to the question of whether nature or nurture has a greater influence on character development? How are irregulars treated in Flatland society? Nature versus nurture has been an ongoing argument about whether nature (a persons’ genes), or nurture (environmental factors) has a greater influence on human development. However, many people would agree “It no longer makes any
Archimedes used the Pythagorean Theorem to find the perimeter of two regular polygons. He used at first a Hexagon, but then thought is not a circle just a polygon with so many sides that you can’t count (He might not have actually said that). So he went on doubling the sides of these polygons (on the left), until he reached a 96-gon as we demonstrated in our model, knowing the more sides the more accurate the number. These polygons were inscribed and circumscribed
have no concept of depth, only length and width. The world appears to be vertical because the rain simply falls from north to south. The houses are made in the shape of a pentagon. Fog is fairly common in this world. In Flatland, the men are all polygons, and the women are lines. The fewer equal sides a person contains, the
Carl Friedrich Gauss is revered as a very important man in the world of mathematicians. The discoveries he completed while he was alive contributed to many areas of mathematics like geometry, statistics, number theory, statistics, and more. Gauss was an extremely brilliant mathematician and that is precisely why he is remembered all through today. Although Gauss left many contributions in each of the aforementioned fields, two of his discoveries in the fields of mathematics and astronomy seem to
Introduction: Pi is an incredibly essential number in our world, without it there would be a lack of innumerable things that have come to be necessary in our daily lives. We would not have the knowledge we have now about the celestial paths in our solar system and beyond. For common people, pi is the circumference of a circle divided by its diameter but there is so much more to this number. It is an irrational and transcendental number who has mathematicians’ interest peaked. It is not possible to
Archimedes was one of the last ancient Greek mathematicians, following in the footsteps of Plato, Socrates, and Euclid. Historians call him "the wise one," "the master" and "the great geometer". Although he was also a scientist and inventor, it was his work in mathematics that has ranked him as one of the three most important mathematicians in history, along with Sir Isaac Newton and Carl Friedrich Gauss. Further, he was one of the first scientists to perform experiments to prove his theories. Archimedes’