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The article discusses presents mathematical formulae to show how Greek mathematician Archimedes measured a circle as described in his book, "Measurement of a Circle." Topics include the approximate ratio of circumference to diameter in a circle using Greek philosopher Pythagoras' theorem and modern notation for square roots, how Archimedes provided upper and lower bounds for determining the ratio of a circle's circumference to its diameter, and the limitations he had to overcome.

The article focuses on solution of several mathematical problems. Topics discussed include values of a triangle's coordinates estimated by the use Pythagorean theorem, determination of empty space in a rectangular box filled with candles by subtraction of total volume of candles from total volume of the box, estimation of area of various regions in a triangle and finding area of trapezoid.

The article presents several solution related to mathematical questions including equation of the perpendicular slopes, coordinates of a triangle, and proving Pythagorean theorem.

In this article, the author shares his experience of teaching calculus in the class so that students gets the insights of the problems easily. Topics discussed include optimization of the problems provide a medium to practice a variety of skills in a calculus class, algebraic manipulation for working with multiple variables and time to examine rules and formulas in the proof of the Pythagorean theorem.

The article discusses connections that California State University in Los Angeles, California's mathematics professor Frank Burk's approach and proof to the Pythagorean theorem (PT) offers and inclusion of the proof in the curriculum. Topics discussed include visual aid used by Greek mathematician Euclid in his PT proof, explanation of Burk's proof of PT which involves scaling a right triangle sides' thrice, and classroom activity of making isosceles right triangle to study proof given by Burk.

The article lists solutions of mathematical problems which include standard deviation calculation in District of Columbia's highest point above sea level, area of an equilateral triangle by Pythagorean Theorem and arithmetic progression proof for sides of right triangle.

The article lists mathematical analysis of several questions for media clips which includes mosquito's survival against raindrop and Pythagorean winning percentage for the baseball teams including the Arizona Diamondbacks and the Milwaukee Brewers.

The article focuses on a mathematical problem of finding an infinite series of ever-decreasing circles. Topics include Pythagorean Theorem, infinite geometric series and generalization of n-dimensional objects which are termed as hypercubes or hyperspheres. Other topics include representation of four-dimensional object into two-dimensional and manipulation of numeric and algebraic expressions.

The article presents information on mathematical quizzes related to Pythagorean Theorem.

The article discusses ways for encouraging students to extend the use of Pythagorean triples beyond its traditional applications to triangles. It suggests the introduction of a notation indicating a Pythagorean triple and a point with rational coordinates. It states that students can solve the slope of the line passing through the point (0, -1) and any rational point on the circle. It also emphasizes the importance of following the given process to derive the formulas for Pythagorean triples.

The article presents the mathematical solution and its alternative options to the 2011 November mathematical problems. It solves the total distance which a cowboy must take in order to water his horse at the stream using the Pythagorean theorem. It provides a solution which provides the number of people being interviewed in a company through the use of a Venn diagram.

The article presents a solution related to solving the challenges posed by Pythagorean triples and quadruples. It shows a methods on how to produce integer solution to the equations involving algebraic representation. The article also shows that this solution will produce opposite parity among integers and algebraic equations.

The article investigates the possibility of finding a representation for all Pythagorean triples using triples (1) and (3). It aims to support the validity of using the formula (12a)-(12b) to find Pythagorean Triples. It also discusses the expressions and solutions of calculating Pythagorean Triples.

The article focuses on the theorems in geometry for high school education. It cites the proof of the Pythagorean theorem through the approach of paper folding. It explores the concept of Ceva's theorem which proves the concurrence of medians, angles bisectors, and altitudes of a triangle. It describes the Ptolemy's theorem, which is attributed to Claudius Ptolemaeus of Alexandria, Egypt, and Heron's formula, which is used to identify the area of a triangle. Also, it views on the use of technology in geometric constructions.

The article provides solutions to problems through the use of educated guessing. It is noted then that it is the mean of all five when one of the numbers serves as the mean of the other four. It is also emphasized that such a solution would result and imply that there will be a total of 662, 669, and 399 possibilities. Hence, the use of Pythagorean theorem in finding the length of the hypotenuse of each right triangle, length is found to be the diagonal of the square and thus the area of the square is 40 and 31, respectively.

Several letters to the editor are presented in response to article in the previous issues including "Solving Square Roots," in the October 2005 issue, "Pythagorean Triples," by Anita Schuloff in the September 2005 issue, and problem 9 in "Calendar," in the November 2005 issue.

The article focuses on a new process of teaching trigonometry to school students. It is recommend that the students should be acquainted with the familiar concepts of algebra and geometry before they start studying trigonometry. It is also suggested that the teachers should depend on the concepts of area and the Pythagorean theorem. These concepts will help the students to learn the foundational concept of invariance, which is the foundation of trigonometry. This innovative process breaks down the artificial barriers placed by the students between geometry, algebra and trigonometry and students begin to see the interconnectedness of these three branches of mathematical thought. The simplest mathematical explanation that gives the necessary insight is the best one. The concepts of area of triangle and Pythagorean Theorem are discussed in detail.

Elaborates on various aspects of trapezoids. Definition of trapezoids; Clarifications of the misconceptions associated with the definition; Derivation of a formula for calculating the area of trapezoids; Proof of the Pythagorean theorem with respect to trapezoids.

Describes a situation when proof was meaningful and was the logical outcome of a student's investigation in mathematics. Overview of the Pythagorean theorem; Reason that students should have opportunities to formulate and refine problems; Function of the Geometer's Sketchpad.

Discusses several ideas on mathematics tackled during the High School Teachers Program of the Park City Mathematics Institute. Graphical representation of the Gaussian integers; Application of Gaussian integers in the derivation of Pythagorean numbers; Creation of algorithms for example problems and solutions in algebra.

Presents an approach in the derivation of a mathematical formula to compute for the sine and cosine of the sum of two angles. Use of the Pythagorean calculation method; Definition of the sine and cosine functions; Diagram analysis for the sine of a sum of two angles.

Discusses how to generate Pythagorean triples from harmonic mathematical sequences. Ways by which Pythagorean triples are generated; Mathematical notation used to derive the Pythagorean triples; General mathematical solution on the derivation of Pythagorean triples from harmonic sequences.

Examines some proofs of the Pythagorean theorem. Equations and solutions for analyzing a perpendicular problem using Pythagorean theorem; Information on the collection of proofs of Elisha Scott Loomis; Questions on the infinity of the number of proofs.

Describes a generalized method of constructing any Pythagorean triangle on a geoboard. Two different Pythagorean right triangles; General case for primitive Pythagorean triples generators; Some ideas for use in classrooms.

The article investigates the arc length of a smooth curve. Pythagorean theorem is the basis of the derivation of the formula for arc length, which is typically presented as a definite integral from x = a to x = b. The derivation of the formula is confined to measuring the portion of the graph that begins at x=0. The details of the derivation of the formula of arc length is presented. The explanation to the theory behind the concept of the special form of integrand is also discussed in detail. The author concluded that the investigation of the new function leads to greater understanding of the connection between integrals and area.

Offers information on the Pythagorean theorem. Information on the sequence of mathematics unit in the secondary level; Factors to consider in teaching mathematics; Challenges associated with teaching the Pythagorean theorem; Illustration of an approach to proving the Pythagorean theorem.

Focuses on several issues concerning the teaching of mathematics. Problem in teaching calculus about identifying values that change in a related rate problem and those that remain constant; Way to find primitive Pythagorean triples when the smallest number is a multiple of 4; Alternative definition of a circle.

The article discusses the application of the Pythagorean theorem in finding the diagonal of a given geometric figure. It states that the lengths of the two legs of the right triangle ACD can be solved by identifying the segment AC, which is also the hypotenuse of the right triangle ABC. It also shows how to obtain the n-dimensional distance formula to find the variation in the data set.

The article focuses on the coordinate proofs of Pythagorean theorem such as slopes of perpendicular lines and the right angle inscribed in a semicircle.

A letter to the editor is presented in response to the article "N-Mids Follow-Up," by Robert Ryden in the December 2007-January 2008 issue.

The article presents several questions based on the figure presented in the previous section of this issue of this journal related to Pythagorean Theorem. Develop as many algebric expression as possible for the three triangles APM, PBN and ABC of the figure of the previous section using the Pythagorean theorem. Reevaluate the result tan ζ, the ratio of the perpendicular and base of the two similar right triangles APM and PNB. For a given angle ζ calculating the ratio of the length of the leg adjacent to the angle and the length of the hypotenuse, it is found to be invariant and is called cosine of ζ. Calculating the ratio of the length of the leg opposite to the acute angle ζ to the hypotenuse is also found to be a invariant and is known as the sine of ζ.

Presents a letter to the editor on the experiences of a mathematics teacher while taking a class on pythagorean triples.

Presents views on articles on teaching mathematics. Information on an alternative definition for the circle; Details on an alternative method for Pythagorean triples; Description of a variant for constructing equipartition points.

Explains the reasons for trusting mathematics. Comparison of ancient mathematics with other ancient beliefs; Information on the Pythagorean theorem; Factors that make mathematics reliable.

A letter to the editor is presented in response to the article on Norman architecture wherein practical application of the Pythagorean theorem in construction of an archway is discussed.

The article discusses the construction of a mechanical device De Almeida made up of wood and metal to make the sum of the interior angles of a triangle and the Pythagorean Theorem proved by Greek mathematician Euclid.

A letter to the editor is presented in response to the article "Calendar" in the May 2010 issue.

A personal narrative is presented which explores the author's experience of witnessing activities that aim to explain the concept of Pythagorean theorem.

This article presents information on Pythagorean propositions and ideas. According to the author generating Pythagorean triple other than the tried-and-true 3,4,5 or 5, 12, 13 is as easy as A, B, C. This process gives a triple with a difference of 1 between the hypotenuse and the longer leg. The process is as follows: Pick an odd positive integer, 7, then square it 49 and then determine consecutive integers that have that sum, 24 and 25.

Presents a letter to the editor in response to the article "Reader Reflection: More Patterns of Triple," by Dennis H. Alcock, published in the January 2003 issue of the periodical "Mathematics Teacher."