Mathematics and art

For my Algebra 2 students, I gave them a list of exponent rules. We wrote a word summary of what type of problem each exponent rule would help us with. My marker choice was not good for photographing They were really struggling with applying these to the problems we were simplifying. They kept claiming that they just didn’t know where to start. Eventually, I broke down and gave them an order of steps to follow. This helped them a lot. Though, I wish they could solve these problems without me writing out step by step directions.


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Line Graphs of Weather Forecasts (students learn to interpret data; make and read a line graph, understand plotting points on an X-Y axis, and round numbers); Take a Road Trip (students integrate map reading, math, library research skills and writing).

Bring fact-checked results to the top of your browser search. The techniques of astronomy Astronomical observations involve a sequence of stages, each of which may impose constraints on the type of information attainable. Radiant energy is collected with telescopes and brought to a focus on a detector, which is calibrated so that its sensitivity and spectral response are known.

Accurate pointing and timing are required to permit the correlation of observations made with different instrument systems working in different wavelength intervals and located at places far apart. The radiation must be spectrally analyzed so that the processes responsible for radiation emission can be identified. Since that time, telescopes have become central to astronomy. Having apertures much larger than the pupil of the human eye , telescopes permit the study of faint and distant objects.

In addition, sufficient radiant energy can be collected in short time intervals to permit rapid fluctuations in intensity to be detected. Further, with more energy collected, a spectrum can be greatly dispersed and examined in much greater detail. Aerial view of the Keck Observatory’s twin domes, which are opened to reveal the telescopes. Keck II is on the left and Keck I on the right. Keck Observatory Optical telescopes are either refractors or reflectors that use lenses or mirrors , respectively, for their main light-collecting elements objectives.

Refractors are effectively limited to apertures of about cm approximately 40 inches or less because of problems inherent in the use of large glass lenses. These distort under their own weight and can be supported only around the perimeter; an appreciable amount of light is lost due to absorption in the glass.

How Good are those Young

Science and Its Times: Bibliography of Primary Sources Apollonius of Perga. This work consisted of 8 books with some theorems. In this great treatise, he set forth a new method for subdividing a cone to produce circles, and discussed ellipses, parabolas, and hyperbolas—shapes he was the first to identify and name.

In place of the concentric spheres used by Eudoxus, Apollonius presented epicircles, epicycles, and eccentrics, concepts that later influenced Ptolemy’s cosmology. Even more significant was his departure from the Pythagorean tendency to avoid infinites and infinitesimals:

This step paves the way for the general solution of the cubic and quartic equations (material dating back to Descartes’s earliest studies)and leads to a general discussion of the solution of equations, in which the first method outlined is that of testing the various factors of the constant term, and then other means, including approximate.

The physics is discussed in two subsections: Descartes apparently received the stimulus to study these works from Isaac Beeckman ; his earliest recorded thoughts on mathematics are found in the correspondence with Beeckman that followed their meeting in As Descartes wrote in his Rules for the Direction of the Mind ca. Yet each problem will be solved according to its own nature, as, for example, in arithmetic some questions are resolved by rational numbers, others only by irrational numbers, and others finally can be imagined but not solved.

I cannot imagine anything that could not be solved by such lines at least, though I hope to show which questions can be solved in this or that way and not any other, so that almost nothing will remain to be found in geometry 6. Descartes sought, then, from the beginning of his research a symbolic algebra of pure quantity by which problems of any sort could be analyzed and classified in terms of the constructive techniques required for their most efficient solution.

These superscripts, he argued in rule XVI , resolved the serious conceptual difficulty posed by the dimensional connotations of the words they replaced. That is, since 1: Although the Greek mathematicians had established the correspondence between addition and the geometrical operation of laying line lengths end to end in the same straight line, they had been unable to conceive of multiplication in any way other than that of constructing a rectangle out of multiplier and multiplicand, with the result that the product differed in kind from the elements multiplied.

Division and the remaining operations are defined analogously. As Descartes emphasized, these operations do not make arithmetic of geometry, but rather make possible an algebra of geometrical line segments. The problem states in brief:


I celebrate myself, and sing myself, And what I assume you shall assume, For every atom belonging to me as good belongs to you. I loafe and invite my soul, I lean and loafe at my ease observing a spear of summer grass. My tongue, every atom of my blood, form’d from this soil, this air, Born here of parents born here from parents the same, and their parents the same, I, now thirty-seven years old in perfect health begin, Hoping to cease not till death.

Creeds and schools in abeyance, Retiring back a while sufficed at what they are, but never forgotten, I harbor for good or bad, I permit to speak at every hazard, Nature without check with original energy.

PSYCHOLOGICAL SCIENCE Research Report THE LOSS OF POSITIONAL CERTAINTY IN LONG-TERM MEMORY James S. Nairne The filled circles display subject perfor-mance and represent the proportions The “Dating” Curves Another way to represent the data of.

Basic concepts covered include double-entry bookkeeping and examination of basic financial reports such as the balance sheet, statement of owner’s equity and income statement. Emphasis on cash receipts, cash disbursements, accounts receivable and accounts payable. Some assignments made using general ledger accounting software.

Intended to be the first accounting course for students who have not taken high school accounting or have no accounting experience. ACT or high school accounting strongly recommended Introduction to financial accounting, through the theory and logic underlying accounting procedures as well as the measurement and presentation of financial data. Brief review of the basic accounting cycle. Development of fundamental concepts in determination of income and presentation of financial position of business firms.

Exposure to partnership accounting as well as coverage of corporation accounting including stocks, stockholder equity transactions, and bonds. Introduction to international accounting as well as statement of cash flows. Exposure to some of the most popular accounting software used in the marketplace by small and medium sized businesses. Computer application packages include Quickbooks, Peachtree, and Microsoft Excel.

ACT Introduction to relevant costs for decision making, controlling, contribution approach to decision-making, and absorption costing versus direct costing effect on income. Coverage of segment profitability, budgeting, capital projects, selection and subsequent evaluation, cost volume and allocation involving joint costs decentralization, and performance measurement and transfer pricing. Emphasis on performance standards, activity-based costing, variance analysis, and responsibility accounting.

How to use the distance formula to find the radius of a circle

Mathematics in ancient Egypt The introduction of writing in Egypt in the predynastic period c. By virtue of their writing skills, the scribes took on all the duties of a civil service: Young men enrolled in scribal schools to learn the essentials of the trade, which included not only reading and writing but also the basics of mathematics.

One of the texts popular as a copy exercise in the schools of the New Kingdom 13th century bce was a satiric letter in which one scribe, Hori, taunts his rival, Amen-em-opet, for his incompetence as an adviser and manager. Answer us, how many bricks are needed? This problem, and three others like it in the same letter, cannot be solved without further data.

Quizzes There will be regular short quizzes (5 minutes or less) at the beginning of class throughout the semester. The quizzes will be over graphs of functions and trigonometric identities and will begin.

Posted on May 24, by The Physicist The original question was: Does this occur due to centripetal force and the lack of friction to stop the Earth from spinning? If so, where did this centripetal force come from? The same is true of stellar nebulae the gigantic clouds of gas and dust that condense to form stars and planets. They always have at least a little bit of swirl and spin.

As the cloud that became our solar system collapsed inward, the mass settled into a spinning disc with a big bump in the middle the Sun , and that disk began collapsing even more to form the planets. This process is called accretion, and you can see it at work over and over again. When stuff collapses it tends to form a central ball and a disk. How fast and in exactly what direction a planet will end up spinning is a fiendishly complicated problem.

Since the Earth orbits the sun in the same direction that it rotates, when it’s morning 6 am you’re standing on the “front side” of the Earth. But once the ball gets rolling so to speak you find yourself with a solar system full of big rocks on slightly different orbits slamming into each other, and changing each others rotations. That impact, as well as tidal effects from the moon itself, have radically changed the length of the day on Earth.

Bibliography of Primary Sources

I have been a teacher, administrator, supervisor, ICU nurse, and medical advise nurse. I have worked in home health and the medical information industry. I have two medical patents. I have also assisted nurses who did not pass the first time. I have helped them to understand the test taking process for this type of exam. I show students how to review for each section type, analyze practice questions and answers, and develop critical thinking skills.

It uses concepts such as abstraction and logic, numbering and calculation, measurement of volume and distance, and the quantification of shape and motion (which includes speed) (1).

Play media By placing a metal bar in a container with water on a scale, the bar displaces as much water as its own volume , increasing its mass and weighing down the scale. The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius , a votive crown for a temple had been made for King Hiero II of Syracuse , who had supplied the pure gold to be used, and Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith.

While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible, [19] so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained.

Illustrative Mathematics

History of Technology Heroes and Villains – A little light reading Here you will find a brief history of technology. Initially inspired by the development of batteries, it covers technology in general and includes some interesting little known, or long forgotten, facts as well as a few myths about the development of technology, the science behind it, the context in which it occurred and the deeds of the many personalities, eccentrics and charlatans involved.

You may find the Search Engine , the Technology Timeline or the Hall of Fame quicker if you are looking for something or somebody in particular. Scroll down and see what treasures you can discover.

Teacher guide Sorting Equations of Circles 1 T-2 BEFORE THE LESSON Assessment task: Going Round in Circles (15 minutes) Give this task, in class or for homework, a few days before the formative assessment lesson.

Babylonian mathematics refers to any mathematics of the peoples of Mesopotamia modern Iraq from the days of the early Sumerians through the Hellenistic period almost to the dawn of Christianity. The first few hundred years of the second millennium BC Old Babylonian period , and the last few centuries of the first millennium BC Seleucid period. Later under the Arab Empire , Mesopotamia, especially Baghdad , once again became an important center of study for Islamic mathematics.

In contrast to the sparsity of sources in Egyptian mathematics , our knowledge of Babylonian mathematics is derived from more than clay tablets unearthed since the s. Some of these appear to be graded homework. They developed a complex system of metrology from BC.

Algebra in Simplest Terms

We covered this thoroughly in Algebra 1, but I know they needed to be reminded after two summers plus a year of geometry. I typically use this foldable with my students in Algebra 1, so I wanted something on the quicker and easier side that they hadn’t seen before. I whipped up a quick graphic organizer over graphing ordered pairs.

Bibliography of Primary Sources. Apollonius of (c. b.c.). This work consisted of 8 books with some theorems. In this great treatise, he set forth a new method for subdividing a cone to produce circles, and discussed ellipses, parabolas, and hyperbolas—shapes he was the first to .

Use Tracker software to create a Sine wave. How to use modeling to predict booms and busts. Is Bitcoin going to keep rising or crash? Some nice examples of using polar coordinates to create interesting designs. The use of regression in polling predictions. What would happen to the climate in the event of a nuclear war? The use of game theory in psychology and economics. A good chance to investigate misconceptions in probability and probabilities in gambling. Why does the house always win?

How probability and game theory can be used to explore the the best strategies for bluffing in poker. This chess puzzle asks how many moves a knight must make to visit all squares on a chess board. This topics provides a fascinating introduction to both combinatorial Game Theory and Group Theory.

Write the equation of a circle given the center and a point it passes through