A Guide to Writing Mathematics

This is a math class! Why are we writing?
There is a good chance that you have never written a paper in a math class before. So you might be wondering why writing is required in your math class now.
The Greek word mathemas, from which we derive the word mathematics, embodies the
notions of knowledge, cognition, understanding, and perception. In the end, mathematics is about ideas. In math classes at the university level, the ideas and concepts encountered are more complex and sophisticated. The mathematics learned in college will include concepts which cannot be expressed using just equations and formulas. Putting mathemas on paper will require writing sentences and paragraphs in addition to the equations and formulas.
Mathematicians actually spend a great deal of time writing. If a mathematician wants
to contribute to the greater body of mathematical knowledge, she must be able
communicate her ideas in a way which is comprehensible to others. Thus, being able to
write clearly is as important a mathematical skill as being able to solve equations.
Mastering the ability to write clear mathematical explanations is important for
non-mathematicians as well. As you continue taking math courses in college, you will come to know more mathematics than most other people. When you use your mathematical
knowledge in the future, you may be required to explain your thinking process to another person (like your boss, a co-worker, or an elected official), and it will be quite likely that this other person will know less math than you do. Learning how to communicate mathematical ideas clearly can help you advance in your career

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Surface Area and Volume of square Pyramid and Triangular Prism

Surface Area and Volume of a square Pyramid
A pyramid is any three-dimensional structure where the upper surfaces are triangular and converge on one point. The base of pyramids are usually quadrilateral or trilateral (but generally may be of any polygon shape), meaning that a pyramid usually has three or four sides. The measurements of these triangles uniformly classify the shape as isosceles and sometimes equilateral.



Surface Area and Volume of a Isosceles Triangular Prism
The volume of a prism is the product of the [area] of the base and the distance between the two base faces, or the height (in the case of a non-right prism, note that this means the perpendicular distance)

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Surface Area and Volume

Sphere
A sphere is a perfectly symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface. In mathematics, a sphere is the set of all points in three-dimensional space (R3) which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere. The fixed point is called the center or centre, and is not part of the sphere itself. The special case of r = 1 is called a unit sphere.
Surface Area and Volume of a Cone
A cone is a three-dimensional geometric shape bounded by a simply connected region of a plane (the base) and a surface (the lateral surface) described by the locus of all line segments joining the perimeter of the base to a point (the apex or vertex) lying off the plane of the base. In common usage in elementary geometry, "cone" usually means a right circular cone (see below).



Surface Area and Volume of a Cylinder



Surface Area and Volume of a Rectangular Prism

In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All cross-sections parallel to the base faces are the same. A prism is a subclass of the prismatoids.

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