In Euclidean geometry, a parallelogram is a simple (non self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean Parallel Postulate and neither condition can be proven without appealing to the Euclidean Parallel Postulate or one of its equivalent formulations. The three-dimensional counterpart of a parallelogram is a parallelepiped.
The etymology (in Greek παραλληλ-όγραμμον, a shape "of parallel lines") reflects the definition.
A simple (non self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true:12
Two pairs of opposite sides are equal in length.
Two pairs of opposite angles are equal in measure.
The diagonals bisect each other.
One pair of opposite sides are parallel and equal in length.
Adjacent angles are supplementary.
Each diagonal divides the quadrilateral into two congruent triangles.
The sum of the squares of the sides equals the sum of the squares of the diagonals. (This is the parallelogram law.)
It has rotational symmetry of order 2.
The etymology (in Greek παραλληλ-όγραμμον, a shape "of parallel lines") reflects the definition.
A simple (non self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true:12
Two pairs of opposite sides are equal in length.
Two pairs of opposite angles are equal in measure.
The diagonals bisect each other.
One pair of opposite sides are parallel and equal in length.
Adjacent angles are supplementary.
Each diagonal divides the quadrilateral into two congruent triangles.
The sum of the squares of the sides equals the sum of the squares of the diagonals. (This is the parallelogram law.)
It has rotational symmetry of order 2.
What are you studying Jane?
Oh, I am studying quadrilaterals, specifically I am on Chapter 5 proving a quadrilateral is a Parallelogram, Claire.
Oh, I am studying quadrilaterals, specifically I am on Chapter 5 proving a quadrilateral is a Parallelogram, Claire.
by david faustino December 18, 2012
by david faustino April 22, 2012
Logic (from the Greek λογική, logikē)1 refers to both the study of modes of reasoning (which are valid and which are fallacious)2 and the use of valid reasoning. In the latter sense, logic is used in most intellectual activities, including philosophy and science, but in the first sense, is primarily studied in the disciplines of philosophy, mathematics, semantics, and computer science. It examines general forms that arguments may take. In mathematics, it is the study of valid inferences within some formal language.3 Logic is also studied in argumentation theory.4
Logic was studied in several ancient civilizations, including India,5 China,6 and Greece. In the west, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric.
Logic is often divided into three parts, inductive reasoning, abductive reasoning, and deductive reasoning.
Logic was studied in several ancient civilizations, including India,5 China,6 and Greece. In the west, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric.
Logic is often divided into three parts, inductive reasoning, abductive reasoning, and deductive reasoning.
What are you working on Charles?
Oh, I am doing logic homework!
What is it about?
Oh, its a subject about reasoning in a logical manner, I am doing a proof that involves the transitive property of equality.
Oh, I am doing logic homework!
What is it about?
Oh, its a subject about reasoning in a logical manner, I am doing a proof that involves the transitive property of equality.
by david faustino November 07, 2012
Russell Carrington Wilson (born November 29, 1988) is an American football quarterback for the Seattle Seahawks of the National Football League (NFL). Wilson was selected by the Seahawks with the 12th pick in the third round (75th overall) of the 2012 NFL Draft.2
Drew Brees is his idol to look up to growing up.
Wilson played college football for the University of Wisconsin during the 2011 season, in which he set the single season FBS record for passing efficiency (191.8) and led the team to a Big Ten title and the 2012 Rose Bowl.3 Wilson received the Big Ten Quarterback of the Year award and was named a consensus first-team All-Big Ten and third-team All-American by Yahoo! Sports.4
Wilson played football and baseball for North Carolina State University before transferring to Wisconsin. In 2008, he was named the ACC Rookie of the Year in football and became the first freshman quarterback to receive first team All-ACC honors. Wilson also played minor league baseball for the Tri-City Dust Devils in 2010 and the Asheville Tourists in 2011 as a second baseman.5
Wilson signed a four-year, $2.99 million contract with the Seattle Seahawks on May 7, 2012 and was named the team's starting quarterback on August 26, 2012.67 In his rookie season Wilson led the Seahawks to a 11-5 regular season record and the divisional round of the NFL playoffs, and was voted the Pepsi NFL Rookie of the Year.89
Drew Brees is his idol to look up to growing up.
Wilson played college football for the University of Wisconsin during the 2011 season, in which he set the single season FBS record for passing efficiency (191.8) and led the team to a Big Ten title and the 2012 Rose Bowl.3 Wilson received the Big Ten Quarterback of the Year award and was named a consensus first-team All-Big Ten and third-team All-American by Yahoo! Sports.4
Wilson played football and baseball for North Carolina State University before transferring to Wisconsin. In 2008, he was named the ACC Rookie of the Year in football and became the first freshman quarterback to receive first team All-ACC honors. Wilson also played minor league baseball for the Tri-City Dust Devils in 2010 and the Asheville Tourists in 2011 as a second baseman.5
Wilson signed a four-year, $2.99 million contract with the Seattle Seahawks on May 7, 2012 and was named the team's starting quarterback on August 26, 2012.67 In his rookie season Wilson led the Seahawks to a 11-5 regular season record and the divisional round of the NFL playoffs, and was voted the Pepsi NFL Rookie of the Year.89
Did you see that touchdown pass from Russel Wilson to Golden Tate in St. Louis?
Yeah, Russell Wilson is the man!
Yeah, Russell Wilson is the man!
by David Faustino December 08, 2013
The greatest center to play in the NBA. He could move like a guard, score, pass, block, rebound, defend. You name it he could do it. He played the majority of his career for the Houston Rockets and then later played and retired with the Toronto Raptors.
by david faustino April 04, 2012
A social network that is superficial and analogous like facebook. People just bullshitting and bragging about what they do have. People trying to see who has more friends and please post a comment on my picture or you will die in 24 hours.
Just an extremely waste of my time. I am glad I left that website. Moreover, I am wasting my time right now acknowledging myspace, but its worth it to show my perspective so other future users will not waste their time. Life is too short and precious, enjoy the outdoors instead of trying to act cool on myspace.
Just an extremely waste of my time. I am glad I left that website. Moreover, I am wasting my time right now acknowledging myspace, but its worth it to show my perspective so other future users will not waste their time. Life is too short and precious, enjoy the outdoors instead of trying to act cool on myspace.
by david faustino April 04, 2012
A geometric figure.
In mathematics, an annulus (the Latin word for "little ring", with plural annuli) is a ring-shaped geometric figure, or more generally, a term used to name a ring-shaped object. It is also used to describe the area between two concentric circles. The adjectival form is annular (for example, an annular eclipse).
The area of an annulus is the difference in the areas of the larger circle of radius R and the smaller one of radius r:
A = \pi R^2 - \pi r^2 = \pi(R^2 - r^2)\,.
In mathematics, an annulus (the Latin word for "little ring", with plural annuli) is a ring-shaped geometric figure, or more generally, a term used to name a ring-shaped object. It is also used to describe the area between two concentric circles. The adjectival form is annular (for example, an annular eclipse).
The area of an annulus is the difference in the areas of the larger circle of radius R and the smaller one of radius r:
A = \pi R^2 - \pi r^2 = \pi(R^2 - r^2)\,.
by David Faustino November 24, 2012