Search results for: circle

Undecagon|Definition & Meaning Definition An undecagon is an 11-sided polygon referred to as a hendecagon or an undecagon. Regular undecagons have all sides the same length and vertices that are evenly placed around a circle. Visualizing an Undecagon Undecagon has 11 sides and 11 angles, all of the sides and angles are equal. It also […]

Ellipse|Definition & Meaning Definition A regular oval shape called an ellipse can be created by a point moving in a plane in a way that the summation of its distances from the foci remains constant or by cutting a cone with an oblique plane that does not cross its base. Ellipse is a conic section […]

Decompose|Definition & Meaning Definition Decompose means to break the words or numbers. As there are terms in math like add, which means joining numbers to get the result, and subtracting, which means subtracting or taking away numbers from a number, decompose is also a term of math which means taking or writing numbers apart. If […]

Csch|Definition & Meaning Definition If y is a real number, the csch or hyperbolic cosecant function can be defined with the help of the following equation: [ operatorname {csch}(mathrm {y}) =frac{2} {e^y – e^{-y}} ] The hyperbolic functions can be thought of as being analogous to either the trigonometric functions or the circular functions. In […]

Cross Section|Definition & Meaning Definition The cross-section is defined in geometry as the shape formed by the intersection of a solid and a plane. A three-dimensional cross-section is a two-dimensional geometric shape. In other words, a cross-section is a shape formed by cutting a solid parallel to the base. Cross Section A cross-section represents an […]

Convex|Definition & Meaning Definition Convex is defined as having a surface or contour that is curled like the rim of a sphere or circle in an upward direction. Convex Sets and Their Importance in Optimization In geometry, a subset of an affine space over the reals, or more broadly a subset of Euclidean space, is […]

Converse (Logic)|Definition & Meaning Definition In mathematical logic, the converse of a statement is what you get by swapping (reversing) the position of the antecedent and the consequent. For example, in implicational logic, if A $boldsymbolto$ B is the statement where A is the hypothesis and B is the consequent, then A $boldsymbolleftarrow$ B is […]

Cone|Definition & Meaning Definition A cone is a three-dimensional geometric structure that starts from a circular base and converges as you move up to a point known as the apex. It can also be described as a circle that is moving up while continuously decreasing in radius till it reaches zero. The circle part of […]

17TH CENTURY MATHEMATICS Logarithms were invented by John Napier, early in the 17th Century In the wake of the Renaissance, the 17th Century saw an unprecedented explosion of mathematical and scientific ideas across Europe, a period sometimes called the Age of Reason. Hard on the heels of the “Copernican Revolution” of Nicolaus Copernicus in the […]

HELLENISTIC MATHEMATICS The Sieve of Eratosthenes By the 3rd Century BCE, in the wake of the conquests of Alexander the Great, mathematical breakthroughs were also beginning to be made on the edges of the Greek Hellenistic empire. In particular, Alexandria in Egypt became a great centre of learning under the beneficent rule of the Ptolemies, […]

PREHISTORIC MATHEMATICS The Ishango bone, a tally stick from central Africa, dates from about 20,000 years ago Our prehistoric ancestors would have had a general sensibility about amounts, and would have instinctively known the difference between, say, one and two antelopes. But the intellectual leap from the concrete idea of two things to the invention […]

Construction of a 45 Degree Angle – Explanation and Examples Since a 45-degree angle is half of a 90-degree angle, constructing one requires first creating a right angle and then dividing it in half. Remember, though, that in pure geometry, we would refer to a 45-degree angle as half of a right angle. This lesson […]

Construct an Angle Bisector – Explanation and Examples Given an angle ABC, it is possible to construct a line BF that divides the angle into two equal parts using only a straightedge and compass. Such a line is called an angle bisector. Constructing an angle bisector requires that we construct an isosceles triangle BDE inside […]

Construct a 60 Degree Angle – Explanation and Examples The easiest way to construct a 60-degree angle is to construct an equilateral triangle, which will have three angles with 60 degrees each. The construction of an equilateral triangle was Euclid’s first proposition in book 1 of his Elements. Knowing how to construct one can also […]

    Construct Parallel Lines – Explanation and Examples Constructing a line parallel to a given line that goes through a given point involves knowing some facts about parallel lines and copying angles. To do this, we will need to construct a transversal. This is a line that crosses two parallel lines. Several pairs of […]

Constructing Perpendicular Bisectors – Explanation and Examples Constructing a perpendicular bisector with a compass and straightedge requires that we first find the center of a line segment and then construct a line perpendicular to that point. To do this requires constructing an equilateral triangle on the line segment. Before moving on, review the construction of […]

    Construct a Line Segment – Explanation and Examples To construct a line segment connecting two points, you need to line up a straightedge with two points and trace. Constructing a new line segment congruent to another involves creating an equilateral triangle and two circles. The construction of a line segment between any two […]

Acute Angle – Explanation and Examples An acute angle is an angle larger than a zero angle and smaller than a right angle. In degrees, an acute angle measures greater than $0$ degrees and less than $90$ degrees. In radians, an acute angle is one with a measure greater than $0$ radians and less than […]

GREEK MATHEMATICS & MATHEMATICIAN – Numerals and Numbers Ancient Greek Herodianic numerals As the Greek empire began to spread its sphere of influence into Asia Minor, Mesopotamia and beyond, the Greeks were smart enough to adopt and adapt useful elements from the societies they conquered. This was as true of their mathematics as anything else, […]

Not Equal|Definition & Meaning Definition A synonym for unequal is the sign that says not equal. The symbol for “inequality” is represented by the not equal sign. The purpose of this is to demonstrate a juxtaposition of the two quantities, which are not equal and therefore represent inequality among themselves. When a number does not […]

Degree Algebra|Definition & Meaning Definition Degree Algebra is defined as the highest valued power of a variable in a polynomial expression while ignoring the coefficients. We can also find the sum of all the variables to get the highest degree of the expression. Significance of Degree Algebra Degree Algebra is the highest power of any […]

Compass (Drawing)|Definition & Meaning Definition A compass is a drawing instrument used in geometry to draw circles, and arcs and measure distances. Design of Compass Compasses typically have two legs that connect at a joint and are constructed of metal. The circle’s or arc’s size can be adjusted by moving legs apart depending upon the […]

Closed Intervals|Definition & Meaning Definition Closed intervals represent a range of numeric values. The numerical endpoint values specified in a range are included in the closed intervals. Closed intervals are represented by [ ]. For example, the range 1 $leqslant$ x $leqslant$ 10 represents an [1, 10] interval. Other intervals are any singleton, the set […]

Circumradius|Definition & Meaning Definition In polygons, the circumradius equals the radius of the circle that touches the vertices of the polygon or the circle in which the polygon can be inscribed. When a triangle is circumscribed by a circle, then the circumradius is the radius of that circle. Due to the cyclical nature of triangles, […]

Clockwise|Definition & Meaning Definition Two-dimensional rotation can happen in two possible orientations. The direction of the clock’s hands is the direction the  Clockwise motion follows. Starting from the top and swinging to the right, then down, then moving to the left, and then again moving to the top. The opposing sense of rotation or trajectory […]

Circumference|Definition & Meaning Definition A circle’s circumference is the length of its perimeter. The circle circumference can be determined by using length units such as centimeters, meters, or kilometers by opening a circle and measuring the boundary in the same way that we would measure a straight line. A circle’s perimeter is known as its […]

Circumcenter|Definition & Meaning Definition The circumcenter is the middle point of the circumcircle tempted around a polygon. The polygon’s circumcircle is the circle that crosses through all of its vertices and the middle of that circle is named the circumcenter. All polygons which have circumcircles are comprehended as cyclic polygons. Only standard polygons like triangles […]

Chord|Definition & Meaning Definition A chord of a circle is defined to be a line segment formed by two points on the circumference of a circle. This resulting line segment is also known as a straight line with endpoints on a circular arc. Any straight line that passes through the center of the circle and […]

Center|Definition & Meaning Definition A center is generally a point at the center of an object in geometry. Centers may or may not exist depending on the definition of the term taken into consideration. The center is defined as the point where all the isometries that move the object onto itself have a fixed point […]

Brackets|Definition & Meaning Definition Brackets are such symbols that are used in pairs to group terms together. They include terms such as constants or variables with coefficients and separate them from the rest to carry out mathematical operations in order. Figure 1 shows different types of brackets in a numeric expression. Note that each bracket […]

Boundary|Definition & Meaning Definition A boundary is a line that outlines an object’s shape or a polygon. The total length of the boundary is called the perimeter. The boundary is different for all shapes. A boundary allows us to identify the shape of an object or image and is necessary for separating one shape from […]

Bisector|Definition & Meaning Definition In geometry, a bisector is any shape or line that cuts a line segment, an angle, or a curve into two equal parts. This can be explained by bisecting a line segment using a bisector, where a line cuts a line segment AB into two equal pieces. It means that the […]

Bisect|Definition & Meaning Definition In geometry, to bisect is to split something into two equal parts. For example, if you cut a line segment at its midpoint, you end up with two line segments of equal length. Therefore, you have bisected the line segment! A bisection usually involves two geometrical objects cutting into each other: […]

Benchmark Angles|Definition & Meaning Definition Benchmark angles are such angles that are used as a reference or standard to estimate other angles such as acute and obtuse angles closer to them. These angles have exact values of trigonometric ratios which makes the calculations easier with chances of fewer errors. Figure 1 shows a demonstration of […]

Bearing|Definition & Meaning Definition Bearings can be defined as the angles used to measure direction, with the north being taken as a point of reference. What Are Bearings? Bearings are a source to express the angle between two things. Bearings must be computed and expressed according to a set of criteria. Measurements must always be taken […]

Axiom|Definition & Meaning Definition An axiom is a statement assumed to be true to start a new argument or theory. It is considered the starting point of reasoning and proof. The word itself originated from the greek meaning “to be worthy” and is regarded as a universal truth in terms of mathematics. Axiom Synopsis An […]

Array|Definition & Meaning Definition A structured arrangement of different items or things following a definite pattern or flow is known as an array. The things and items could be arithmetic numbers, any object, or pictures while the definite pattern could be columns or rows. The basic aim of arrays is to demonstrate the concept of […]

Area|Definition & Meaning Definition The area of any 2D object is defined as the amount of space taken in any plane. The area is used to express the region’s size on any surface. We calculate Area by its square units which are cm2 and m2. We can find the area of any closed-region object by […]

Arc|Definition & Meaning Definition An arc may be defined as a piece or segment of a circle’s circumference. In other words any curved path or segment which may be fitted on a circle is called an arc. The concept of arc is a is a very fundamental idea commonly used in geometry. An arc is any […]