The Geometer's Sketchpad
Encyclopedia
Arsh is a popular commercial interactive geometry software program for exploring Euclidean geometry
, algebra
, calculus
, and other areas of mathematics
. It was created by Nicholas Jackiw.
It is designed to run on Windows 95
or Windows NT 4.0
or later and Mac OS 8.6
or later (including Mac OS X
). It also runs on Linux
under Wine
with few bugs.
Geometer's Sketchpad includes the traditional Euclidean tools of classical Geometric constructions; that is, if a figure (such as the pentadecagon
) can be constructed with compass and straight-edge, it can also be constructed using this program. However, the program also allows users to employ transformations to "cheat," creating figures impossible to construct under the traditional compass-and-straight-edge rules (such as the regular nonagon). Objects can also be animated. The program also allows the determination of the midpoint
and midsegments of objects.
Geometer's Sketchpad also allows to measure lengths of segments
, measures of angles
, area
, perimeter
, etc. Some of the tools one can use include; construct function, which allows the user to create objects in relation to selected objects. The transform function allows the user to create points in relation to objects, which include distance, angle, ratio, and others. With these tools, one can create numerous different objects, measure them, and potentially figure out hard-to-solve math problems.
and Canada
. NCTM (National Council of Teachers of Mathematics
) had identified one of its six principles as a technology principle, stating that "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning." Geometer's Sketchpad is one of these examples. The program comes with program files to help deepen students' understanding of such concepts as slope
, geometric transformations, and arithmetic on integer
s.
Euclidean geometry
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...
, algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
, and other areas of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
. It was created by Nicholas Jackiw.
It is designed to run on Windows 95
Windows 95
Windows 95 is a consumer-oriented graphical user interface-based operating system. It was released on August 24, 1995 by Microsoft, and was a significant progression from the company's previous Windows products...
or Windows NT 4.0
Windows NT 4.0
Windows NT 4.0 is a preemptive, graphical and business-oriented operating system designed to work with either uniprocessor or symmetric multi-processor computers. It was the next release of Microsoft's Windows NT line of operating systems and was released to manufacturing on 31 July 1996...
or later and Mac OS 8.6
Mac OS 8
Mac OS 8 is an operating system that was released by Apple Computer on July 26, 1997. It represented the largest overhaul of the Mac OS since the release of System 7, some six years previously. It puts more emphasis on color than previous operating systems...
or later (including Mac OS X
Mac OS X
Mac OS X is a series of Unix-based operating systems and graphical user interfaces developed, marketed, and sold by Apple Inc. Since 2002, has been included with all new Macintosh computer systems...
). It also runs on Linux
Linux
Linux is a Unix-like computer operating system assembled under the model of free and open source software development and distribution. The defining component of any Linux system is the Linux kernel, an operating system kernel first released October 5, 1991 by Linus Torvalds...
under Wine
Wine (software)
Wine is a free software application that aims to allow computer programs written for Microsoft Windows to run on Unix-like operating systems. Wine also provides a software library, known as Winelib, against which developers can compile Windows applications to help port them to Unix-like...
with few bugs.
Pentadecagon
In geometry, a pentadecagon is any 15-sided, 15-angled, polygon.- Regular pentadecagon:A regular pentadecagon has interior angles of 156°, and with a side length a, has an area given by...
) can be constructed with compass and straight-edge, it can also be constructed using this program. However, the program also allows users to employ transformations to "cheat," creating figures impossible to construct under the traditional compass-and-straight-edge rules (such as the regular nonagon). Objects can also be animated. The program also allows the determination of the midpoint
Midpoint
The midpoint is the middle point of a line segment. It is equidistant from both endpoints.-Formulas:...
and midsegments of objects.
Geometer's Sketchpad also allows to measure lengths of segments
Line segment
In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment...
, measures of angles
Angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...
, area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...
, perimeter
Perimeter
A perimeter is a path that surrounds an area. The word comes from the Greek peri and meter . The term may be used either for the path or its length - it can be thought of as the length of the outline of a shape. The perimeter of a circular area is called circumference.- Practical uses :Calculating...
, etc. Some of the tools one can use include; construct function, which allows the user to create objects in relation to selected objects. The transform function allows the user to create points in relation to objects, which include distance, angle, ratio, and others. With these tools, one can create numerous different objects, measure them, and potentially figure out hard-to-solve math problems.
Educational benefits
Geometer's Sketchpad is used in many secondary mathematics classrooms throughout the United StatesUnited States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
and Canada
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
. NCTM (National Council of Teachers of Mathematics
National Council of Teachers of Mathematics
The National Council of Teachers of Mathematics was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally....
) had identified one of its six principles as a technology principle, stating that "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning." Geometer's Sketchpad is one of these examples. The program comes with program files to help deepen students' understanding of such concepts as slope
Slope
In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....
, geometric transformations, and arithmetic on integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
s.
Further reading
- Kimberling, Clark. Geometry in Action: A Discovery Approach Using The Geometer's Sketchpad. Key College Publishing, Emeryville, California, (2003), ISBN 1-931914-02-8.
- Scher, Daniel. Lifting the Curtain: The Evolution of The Geometer's Sketchpad Mathematics Educator, v10 n2 p42-48 Sum 2000