S
Scalene Triangle
Scalene Triangle is a triangle, wherein, all the sides of the triangle are unequal or of different lengths.
Scalar
A scalar is the one with magnitude, but with no definite direction. Examples of scalars are length, temperature and mass. Mathematically, a scalar is said to be any real number or any quantity that can be measured by using a single real number.
Solid Geometry
Solid geometry is a term used for the surfaces and solids in space. It includes the study of spheres, cones, pyramids, cylinders, prism, polyhedra, etc. It also involves the study of related lines, shapes, points and regions.
Segment
A segment constitutes all points between two given points, including those two points.
Segment of a Circle
Segment of a circle is any internal region of a circle, that is bounded by an arc or a chord.
SAS Similarity
SAS similarity is side-angle-side similarity. When two triangles have corresponding angles as congruent and corresponding sides with equal ratios, the triangles are similar to each other.
SSS Congruence
When two triangles have corresponding sides congruent, the triangles are said to be in SSS congruency.
Semicircle
Semicircle is a half circle, with a 180 degree arc.
Spherical Trigonometry
Spherical trigonometry is a term used for the study of triangles on the surface of any sphere. The sides of these triangles are arcs of great circles. This study is useful for navigation purposes.
Solving Analytically
A technique of solving a mathematics problem, by using numeric or algebraic methods. This technique does not involve the use of a graphic calculator.
Solve Graphically
A technique of solving a mathematics problem, by using graphs and picture. Graphic calculators are used to solve a problem graphically.
Spheroid
Spheroid actually refers to an oblate spheroid. But, in some cases, it refers to an ellipsoid that looks more or less like a sphere.
Scalene Triangle
Scalene Triangle is a triangle, wherein, all the sides of the triangle are unequal or of different lengths.
Scalar
A scalar is the one with magnitude, but with no definite direction. Examples of scalars are length, temperature and mass. Mathematically, a scalar is said to be any real number or any quantity that can be measured by using a single real number.
Solid Geometry
Solid geometry is a term used for the surfaces and solids in space. It includes the study of spheres, cones, pyramids, cylinders, prism, polyhedra, etc. It also involves the study of related lines, shapes, points and regions.
Segment
A segment constitutes all points between two given points, including those two points.
Segment of a Circle
Segment of a circle is any internal region of a circle, that is bounded by an arc or a chord.
SAS Similarity
SAS similarity is side-angle-side similarity. When two triangles have corresponding angles as congruent and corresponding sides with equal ratios, the triangles are similar to each other.
SSS Congruence
When two triangles have corresponding sides congruent, the triangles are said to be in SSS congruency.
Semicircle
Semicircle is a half circle, with a 180 degree arc.
Spherical Trigonometry
Spherical trigonometry is a term used for the study of triangles on the surface of any sphere. The sides of these triangles are arcs of great circles. This study is useful for navigation purposes.
Solving Analytically
A technique of solving a mathematics problem, by using numeric or algebraic methods. This technique does not involve the use of a graphic calculator.
Solve Graphically
A technique of solving a mathematics problem, by using graphs and picture. Graphic calculators are used to solve a problem graphically.
Spheroid
Spheroid actually refers to an oblate spheroid. But, in some cases, it refers to an ellipsoid that looks more or less like a sphere.
T
Takeout Angle
The angle cut out from a piece of paper, so that the paper can be rolled into a right circular cone is called as the takeout angle.
Tan
The trigonometric function known as the tangent function, gives the ratio of opposite and adjacent side of a triangle.
Tan-1
The angle that has tangent equal to 1, therefore, tan-1 = 45º. In radians tan-1 = Π/4
Tangent Line
A tangent line touches the curve instead of just crossing it. A tangent line can also be defined as a line that intersects the differential curve at a point.
Tautochrone
Tautochrone is a Greek word that means at the same time. Tautochrone has a shape of cycloid hanging downwards. The peculiar feature of a tautochrone is that a bead sliding down the frictionless wire will always take the same time irrespective of the fact that how high or low is the release point.
Taylor Polynomial
The Taylor polynomial is a partial sum of Taylor series. Using the Taylor's polynomial a function can be approximated to a very close value provided the function possess sufficient number of derivatives.
Taylor Series
Taylor series is given by: f(a) + f'(a)(x - a) + f''(a)/2(x - a)2 + f'''(a)/3(x – a)3+.........+ fn(a)/n(x – a)n.
Term
The parts of a mathematical sequence or operations separated by addition or subtraction.
Tetrahedron
Tetrahedron is a polyhedron with four triangular faces. It can be viewed as a pyramid with triangular base.
Three Dimensional Coordinates
The right handed system of coordinates that is used to locate a point in the three dimensional space.
Torus
If we revolve a circle (In 3-D) about a line that does not intersect the circle, then the surface of revolution creates a doughnut shaped figure called as torus.
Transpose of a Matrix
The matrix which is formed by turning all the rows of the matrix into columns or vice-versa.
Transversal
A line that cuts two or more parallel lines.
Trapezium
A quadrilateral with one pair of parallel sides is referred to as trapezium.
Triple (Scalar) Product
Multiplication of vectors using dot product.
If a, b and c are three vectors then triple scalar product is a. (b x c)
Trivial
Trivial solutions are the simple and obvious solutions of a equation. For example, consider the equation x + 2y = 0, here x= 0, y =0 are the trivial solutions and x = 2, y = -1 are the non-trivial solutions.
Truncated Cone or Pyramid
A cone or pyramid whose apex is cut off by intersecting plane. If the cutting plane is parallel to the base it is called as the frustum.
Truncated Cylinder or Prism
A cylinder or prism that is cut by a parallel or oblique plane to the bases. The other base remains unaffected by the cutting of the base.
Truncating a Number
A method of approximation wherein the decimals are dropped after a certain point instead of rounding. For example, 3.45658 would be approximated to 3.4565.
Twin Primes
Prime numbers that have a difference of two between each other. For example, 3 and 5.
Takeout Angle
The angle cut out from a piece of paper, so that the paper can be rolled into a right circular cone is called as the takeout angle.
Tan
The trigonometric function known as the tangent function, gives the ratio of opposite and adjacent side of a triangle.
Tan-1
The angle that has tangent equal to 1, therefore, tan-1 = 45º. In radians tan-1 = Π/4
Tangent Line
A tangent line touches the curve instead of just crossing it. A tangent line can also be defined as a line that intersects the differential curve at a point.
Tautochrone
Tautochrone is a Greek word that means at the same time. Tautochrone has a shape of cycloid hanging downwards. The peculiar feature of a tautochrone is that a bead sliding down the frictionless wire will always take the same time irrespective of the fact that how high or low is the release point.
Taylor Polynomial
The Taylor polynomial is a partial sum of Taylor series. Using the Taylor's polynomial a function can be approximated to a very close value provided the function possess sufficient number of derivatives.
Taylor Series
Taylor series is given by: f(a) + f'(a)(x - a) + f''(a)/2(x - a)2 + f'''(a)/3(x – a)3+.........+ fn(a)/n(x – a)n.
Term
The parts of a mathematical sequence or operations separated by addition or subtraction.
Tetrahedron
Tetrahedron is a polyhedron with four triangular faces. It can be viewed as a pyramid with triangular base.
Three Dimensional Coordinates
The right handed system of coordinates that is used to locate a point in the three dimensional space.
Torus
If we revolve a circle (In 3-D) about a line that does not intersect the circle, then the surface of revolution creates a doughnut shaped figure called as torus.
Transpose of a Matrix
The matrix which is formed by turning all the rows of the matrix into columns or vice-versa.
Transversal
A line that cuts two or more parallel lines.
Trapezium
A quadrilateral with one pair of parallel sides is referred to as trapezium.
Triple (Scalar) Product
Multiplication of vectors using dot product.
If a, b and c are three vectors then triple scalar product is a. (b x c)
Trivial
Trivial solutions are the simple and obvious solutions of a equation. For example, consider the equation x + 2y = 0, here x= 0, y =0 are the trivial solutions and x = 2, y = -1 are the non-trivial solutions.
Truncated Cone or Pyramid
A cone or pyramid whose apex is cut off by intersecting plane. If the cutting plane is parallel to the base it is called as the frustum.
Truncated Cylinder or Prism
A cylinder or prism that is cut by a parallel or oblique plane to the bases. The other base remains unaffected by the cutting of the base.
Truncating a Number
A method of approximation wherein the decimals are dropped after a certain point instead of rounding. For example, 3.45658 would be approximated to 3.4565.
Twin Primes
Prime numbers that have a difference of two between each other. For example, 3 and 5.
U
Unbounded Set of Numbers
Unbounded set of numbers can be defined as the set of numbers which is not bounded, either by a lower bound or by an upper bound.
Under determined System of Equations
Under determined System of Equations is defined to be a linear system of equations, wherein the equations are comparatively less than the variables. The system might be consistent or inconsistent. This depends upon the equations in it.
Uniform
Uniform means same, constant, or in the same pattern.
Undecagon
A polygon having 11 sides is called undecagon.
Unit Circle
Unit circle is defined to be a circle with radius one and is centered at the origin on the x-y plane.
Uncountable
Uncountable is a set that has comparatively more elements than the set of integers. It is an infinite set, in which one cannot put its elements into a one-to-one correspondence with its set of integers.
Upper Bound of a Set
Upper bound of a set is defined to be a number which is greater than or equal to all the elements present in a set. For instance, 4 is a upper bound of the interval [0,1], similarly 3,2 and 1 also are the upper bounds of this interval.
u-Substitution
u-Substitution is a method of integration, that necessarily involves the use of the chain rule in its reverse form.
Union of Sets
Union of sets is defined as the combination of the elements of two sets or more than that. The union is denoted by the U symbol.
Unit Circle Trigonometry Definitions
Unit circle trig definitions is the set of all the six trigonometry functions such as the sine, cosine, tangent, cosecant, secant, and cotangent.
Unbounded Set of Numbers
Unbounded set of numbers can be defined as the set of numbers which is not bounded, either by a lower bound or by an upper bound.
Under determined System of Equations
Under determined System of Equations is defined to be a linear system of equations, wherein the equations are comparatively less than the variables. The system might be consistent or inconsistent. This depends upon the equations in it.
Uniform
Uniform means same, constant, or in the same pattern.
Undecagon
A polygon having 11 sides is called undecagon.
Unit Circle
Unit circle is defined to be a circle with radius one and is centered at the origin on the x-y plane.
Uncountable
Uncountable is a set that has comparatively more elements than the set of integers. It is an infinite set, in which one cannot put its elements into a one-to-one correspondence with its set of integers.
Upper Bound of a Set
Upper bound of a set is defined to be a number which is greater than or equal to all the elements present in a set. For instance, 4 is a upper bound of the interval [0,1], similarly 3,2 and 1 also are the upper bounds of this interval.
u-Substitution
u-Substitution is a method of integration, that necessarily involves the use of the chain rule in its reverse form.
Union of Sets
Union of sets is defined as the combination of the elements of two sets or more than that. The union is denoted by the U symbol.
Unit Circle Trigonometry Definitions
Unit circle trig definitions is the set of all the six trigonometry functions such as the sine, cosine, tangent, cosecant, secant, and cotangent.
V
Variable
The independent quantity in an algebraic expression is called as variable.
Varignon Parallelogram of a Quadrilateral
The parallelogram formed by joining the midpoints of the adjacent sides of any quadrilateral.
Vector
A quantity drawn as an arrow that has both magnitude and direction.
Vector Calculus
The problems involving calculus principles (derivatives, integrals etc) of the three dimensional figures.
Venn Diagrams
Venn diagrams are the pictorial representation of the set operations.
Verify a Solution
We verify a solution by putting the obtained values of the variables and checking if those values satisfy the expression.
Vertex
For a triangle, the meeting end of two sides is called a vertex.
Vertex of an Ellipse
The points on the ellipse where the ellipse takes a sharp turn. Mathematically, vertices of an ellipse are the points that lie on the line through the foci (or the major axis)
Vertex of a Hyperbola
The points at which the hyperbola takes its sharpest turns. Vertices of a hyperbola are the points that lie on the line through the foci.
Vertex of a Parabola
The point at which the hyperbola takes a sharp turn. The vertex of a parabola lies midway between the focus and directrix.
Vertical Angles
Vertical angles are the opposite angles that are formed due to the intersection of two lines.
Vertical Compression
Vertical shrinking of a geometrical figure is called as vertical compression.
Vertical Dilation
Enlargement of a geometrical figure vertically is called as vertical dilation.
Vertical Line Equation
The equation x = a is called the vertical equation of line.
Vertical Line Test
It is used to test if a relation is a function. It is a fact that if a vertical line cuts the graph of a relation at more than one point then the given relation is not a function.
Vertical Reflection
A reflection in which a plane figure is vertically flipped. For a vertical reflection the axis of reflection is always horizontal.
Vertical Shift
Shifting a geometrical figure vertically is called as vertical shift.
Vertical Shrink
Vertical shrink is the shrink in which the plane figure is distorted vertically.
Vertical Stretch
Stretching the dimensions of a figure by a constant factor K in the vertical direction is called vertical stretch.
Vinculum
The horizontal line that is used in a fraction or radical.
Variable
The independent quantity in an algebraic expression is called as variable.
Varignon Parallelogram of a Quadrilateral
The parallelogram formed by joining the midpoints of the adjacent sides of any quadrilateral.
Vector
A quantity drawn as an arrow that has both magnitude and direction.
Vector Calculus
The problems involving calculus principles (derivatives, integrals etc) of the three dimensional figures.
Venn Diagrams
Venn diagrams are the pictorial representation of the set operations.
Verify a Solution
We verify a solution by putting the obtained values of the variables and checking if those values satisfy the expression.
Vertex
For a triangle, the meeting end of two sides is called a vertex.
Vertex of an Ellipse
The points on the ellipse where the ellipse takes a sharp turn. Mathematically, vertices of an ellipse are the points that lie on the line through the foci (or the major axis)
Vertex of a Hyperbola
The points at which the hyperbola takes its sharpest turns. Vertices of a hyperbola are the points that lie on the line through the foci.
Vertex of a Parabola
The point at which the hyperbola takes a sharp turn. The vertex of a parabola lies midway between the focus and directrix.
Vertical Angles
Vertical angles are the opposite angles that are formed due to the intersection of two lines.
Vertical Compression
Vertical shrinking of a geometrical figure is called as vertical compression.
Vertical Dilation
Enlargement of a geometrical figure vertically is called as vertical dilation.
Vertical Line Equation
The equation x = a is called the vertical equation of line.
Vertical Line Test
It is used to test if a relation is a function. It is a fact that if a vertical line cuts the graph of a relation at more than one point then the given relation is not a function.
Vertical Reflection
A reflection in which a plane figure is vertically flipped. For a vertical reflection the axis of reflection is always horizontal.
Vertical Shift
Shifting a geometrical figure vertically is called as vertical shift.
Vertical Shrink
Vertical shrink is the shrink in which the plane figure is distorted vertically.
Vertical Stretch
Stretching the dimensions of a figure by a constant factor K in the vertical direction is called vertical stretch.
Vinculum
The horizontal line that is used in a fraction or radical.
W
Washer
The region between two concentric circles is called as washer. The radii of the two concentric circles different.
Washer Method
Washer method is used to determine the volume of solid of revolution.
Weighted Average
A type of arithmetic mean calculation in which one of the sets among the various sets of observation carries more importance than others (weight).
Whole Numbers
The numbers 0, 1, 2, 3, 4, 5....etc.
Washer
The region between two concentric circles is called as washer. The radii of the two concentric circles different.
Washer Method
Washer method is used to determine the volume of solid of revolution.
Weighted Average
A type of arithmetic mean calculation in which one of the sets among the various sets of observation carries more importance than others (weight).
Whole Numbers
The numbers 0, 1, 2, 3, 4, 5....etc.
X
x-intercept
The point at which a graph intersects the x-axis.
x-y Plane
The plane formed by the x and y axis of the coordinate system.
x-z Plane
The plane formed by the x and z axis of the coordinate system.
x-intercept
The point at which a graph intersects the x-axis.
x-y Plane
The plane formed by the x and y axis of the coordinate system.
x-z Plane
The plane formed by the x and z axis of the coordinate system.
Y
y-intercept
y-intercept is defined as a point where the graph intersects the y-axis.
y-z Plane
y-z plane is simply defined as the plane formed by the y-axis and z-axis.
y-intercept
y-intercept is defined as a point where the graph intersects the y-axis.
y-z Plane
y-z plane is simply defined as the plane formed by the y-axis and z-axis.
Z
z-intercept
The point at which a graph intersects the z-axis.
Zero
Zero is a digit and plays a crucial role in mathematics. Zero is considered as a neutral number as it is neither positive nor negative. It is also an additive identity.
Zero Dimensions
When we talk of zero dimensions it means that no motion is possible without leaving that point.
Zero Matrix
A matrix all whose elements are zero.
Zero of a Function
If f(x) = 0, then the value of x which gives f(x) = 0, is called zero of a function.
Zero Slope
Any horizontal line has a slope equal to zero. A horizontal line has same y-coordinate so from the formula (y2 - y1)/(x2 - x1), we get the slope equal to zero.
Zero Vector
A vector with no magnitude and direction is called as a zero vector.
z-intercept
The point at which a graph intersects the z-axis.
Zero
Zero is a digit and plays a crucial role in mathematics. Zero is considered as a neutral number as it is neither positive nor negative. It is also an additive identity.
Zero Dimensions
When we talk of zero dimensions it means that no motion is possible without leaving that point.
Zero Matrix
A matrix all whose elements are zero.
Zero of a Function
If f(x) = 0, then the value of x which gives f(x) = 0, is called zero of a function.
Zero Slope
Any horizontal line has a slope equal to zero. A horizontal line has same y-coordinate so from the formula (y2 - y1)/(x2 - x1), we get the slope equal to zero.
Zero Vector
A vector with no magnitude and direction is called as a zero vector.
X-Y-Z plane
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