If you opt to take the optional Writing essay section, you will add an extra 40 minutes to the end of your test. The key concepts tested on each section of the ACT are as follows: If you opt to take the optional Essay section, you will add an extra 50 minutes to your test-day experience.

Indeed, the many interconnections between mathematics and art provide a wealth of material from which organizers of Math Awareness Month events can select. The list of sources on the Math Awareness web site is a great place to start. In this brief essay, I'll highlight a few of the possible ways to fill in the blanks above.

I hope that this will stimulate you to explore many others. Mathematics produces art At the most practical level, mathematical tools have always been used in an essential way in the creation of art.

Since ancient times, the lowly compass and straightedge, augmented by other simple draftsmen's and craftsmen's tools, have been used to create beautiful designs realized in the architecture and decoration of palaces, cathedrals, and mosques.

Berkeley application essay question intricate Moorish tessellations in tile, brick, and stucco that adorn their buildings and the equally intricate tracery of Gothic windows and interiors are a testament to the imaginative use of ancient geometric knowledge.

The symbiosis of art and mathematics during these times as linear perspective and projective geometry were developing is one of the most striking examples of art and mathematics evolving almost simultaneously in new directions.

In the hands of an artist, computers can produce art, powered by unseen complex internal mathematical processes that provide their magical abilities.

Mathematical transformations provide the means by which an image or form in one surface or space is represented in another. Art is illusion, and transformations are important in creating illusion.

Isometries, similarities, and affine transformations can transform images exactly or with purposeful distortion, projections can represent three and higher -dimensional forms on two-dimensional picture surfaces, even curved ones.

Special transformations can distort or unscramble a distorted image, producing anamorphic art. All these transformations can be mathematically described, and the use of guiding grids to assist in performing these transformations has been replaced today largely by computer software.

Compasses, rulers, grids, mechanical devices, keyboard and mouse are physical tools for the creation of art, but without the power of mathematical relationships and processes these tools would have little creative power. Mathematics generates art Pattern is a fundamental concept in both mathematics and art.

Mathematical patterns can generate artistic patterns. Often a coloring algorithm can produce "automatic art" that may be as surprising or aesthetically pleasing as that produced by a human hand. Colored versions of the Mandelbrot set and Julia sets are striking examples of this: The intricacy of these images, their symmetries, and the endless in theory continuance of the designs on ever-smaller scales, makes them spellbinding.

For example, begin with an array of numbers such as a large data set, a sequence, a modular operation table, or Pascal's triangle and color the numbers in the array according to some rule. Often surprising patterns -- even art -- emerges. Recursive algorithms applied to geometric figures can generate attractive self-similar patterns.

Begin with a curve, a closed figure, or a simple spatial form, apply an algorithm to alter that figure by adding to or subtracting from specified parts of that figure, then repeat the algorithm recursively.

Many nonperiodic tilings such as the Penrose tilings can also be generated automatically, beginning with a small patch of tiles and then applying a recursive "inflation" algorithm. Transformations and symmetry are also fundamental concepts in both mathematics and art.

Mathematicians actually define symmetry of objects functions, matrices, designs or forms on surfaces or in space by their invariance under a group of transformations. Conversely, the application of a group of transformations to simple designs or spatial objects automatically generates beautifully symmetric patterns and forms.

InBrewster's newly-invented kaleidoscope demonstrated the power of the laws of reflection in automatically generating eye-catching rosettes from jumbles of colored shards between two mirrors.

Periodic tessellations, whether geometric or Escher-like, can be automatically generated by computer programs [R12] or by hand, following recipes that employ isometries. Art illuminates mathematics When mathematical patterns or processes automatically generate art, a surprising reverse effect can occur: Who could have guessed the mathematical nuggets that might otherwise be hidden in a torrent of symbolic or numerical information?

The process of coloring allows the information to take on a visual shape that provides identity and recognition. Who could guess the limiting shape or the symmetry of an algorithmically produced fractal? With visual representation, the mathematician can exclaim "now I see!

But there are examples in which the artist's main purpose is to express, even embody mathematics. Several prints by M. Escher are the result of his attempts to visually express such mathematical concepts as infinity, duality, dimension, recursion, topological morphing, and self-similarity.

From toJohnson produced over abstract oil paintings, each a representation of a mathematical theorem.UC Berkeley Haas MBA Application Essay Tips & Deadlines Facebook Tweet Google+ Pin Email Haas, like several top MBA programs, is looking for a new dean to replace its dynamic, innovative dean, Richard Lyons, on July 1.

Top Successful College Essays. Get into the college of your dreams! We hope these essays inspire you as you write your own personal statement. Just remember to . These University of California - Berkeley college application essays were written by students accepted at University of California - Berkeley.

All of our sample college essays include the question prompt and the year written. Please use these sample admission essays responsibly. Very recently I. Introduction This essay contains a description of several famous malicious computer programs (e.g., computer viruses and worms) that caused extensive harm, and it reviews the legal consequences of each incident, including the nonexistent or lenient punishment of the program's author.

To illustrate the process, here is a sample exam question. EXAMPLE ESSAY QUESTION. Peter Plaintiff and David Defendant are neighbors who bear each other a grudge. The essay questions for the Berkeley-Haas full-time MBA app are: Tell us a six-word story that reflects a memorable experience in your life-to-date. Elaborate on why it is meaningful to you. Kellogg MBA Essay Example #1 Question: Describe a situation where your values, ethics, or morals were challenged. How did you handle the situation?

About Art Sawyer. Art graduated magna cum laude from Harvard University, where he was the top-ranked liberal arts student in his class. Art pioneered the one-on-one approach to test prep in California in and co-founded Compass Education Group in in order to bring the best ideas and tutors into students' homes and computers.

The following essay was submitted to the Wharton MBA program by our client. The client was accepted to the program.

Upon graduation I wish to lead the fiber-optics product management team in one of the world’s largest optical communication companies (such as Alcatel-Lucent and AT&T), supervising a .

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