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- an exact copy of something, especially a document: A PDF file is an electronic facsimile of a printed document.
dictionary.cambridge.org/dictionary/english/facsimile-of
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Mathematical Proofs. How to Write a Proof. Synthesizing definitions, intuitions, and conventions. Proofs on Numbers. Working with odd and even numbers. Universal and Existential Statements. Two important classes of statements. Proofs on Sets. From Venn diagrams to rigorous math. What is a Proof?
A facsimile is intended to be a replica rather than a copy; facsimiles reproduce the form of a text rather than just the content.
An explicit formula for this arithmetic sequence is given by an = a + (n −1)b, n ∈ N, a recursive formula is given by a1 = a and an = an−1 + b for n > 1. Here are some examples of arithmetic sequences, see if you can determine a and b in each case: 1, 2, 3, 4, 5, ... 2, 4, 6, 8, 10, ... 1, 4, 7, 10, 13, ...
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- e.g.
- Annulus
- Horizontal axis
- 10 11 100 101 110 111 1000 1001 1010 Base 2
- e.g.
- c d is ad – bc.
- Gradient = v
- e.g. 5
- Polyhedron (Plural Polyhedra) A three dimensional shape made up of flat faces
- Positive Rotation
- Pyramid A three dimensional shape whose base is a polygon and whose other
- Sector
- Regular Octagons leave small squares between
- e.g. π (Pi)
- Transversal
- Union
- On a Venn Diagram:
If two circles are concentric, the space between them is called an
www.mathsphere.co.uk Anticlockwise The opposite way to the way the hands on a clock turn. Apex The point directly opposite the base of a two dimensional or three dimensional shape. Apex Apex Base Base Triangle Hexagonal based pyramid
Axis of Symmetry A line through the middle of a shape so that one side of the line is a reflection of the other side: One axis of symmetry
Bisect To cut something in half. In geometry this is normally a line or an angle. www.mathsphere.co.uk Bisector A line that is normally drawn to cut a line or an angle in half. Bisector Line to be bisected. Bisector
Mrs Jones bought 12 Kilos of potatoes today. Centre Another word for 'middle'. The centre of a circle is the point which is the same distance from all points on the circumference. Centre of Rotation A point about which a shape is rotated. The centre of rotation may be on the shape being rotated (perhaps even the centre of the shape) or it may be of...
Diagonal A straight line going across a polygon from one vertex to another.
h Graph A way of showing a relationship on a diagram. The most common types of graph are block graphs, line graphs and pie charts. www.mathsphere.co.uk Grid A sequence of (normally) horizontal and vertical intersecting lines used to draw patterns or graphs. Heptagon A polygon with seven sides. Hexagon A polygon with six sides.
www.mathsphere.co.uk Inscribed circle A circle drawn inside a polygon (normally a triangle) so that it just touches each of the sides of the polygon. In a triangle the centre of this circle is obtained by bisecting each angle and putting the compass point at the place where the three bisectors meet.
only. e.g. Cube, cuboid, tetrahedron, dodecahedron etc are all polyhedra. A sphere is not a polyhedron because its surface is curved.
An anti-clockwise rotation. www.mathsphere.co.uk Power The number of times a quantity is multiplied by itself.
edges meet at a point (apex). Pythagoras' Theorem A theorem that states: In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. Square B
www.mathsphere.co.uk Segment A part of a circle cut off by a chord. Semicircle Half a circle.
www.mathsphere.co.uk Tetrahedron A polyhedron with four faces, each being a triangle. A regular tetrahedron has equilateral triangles for all its faces. Therefore Shown by the sign , therefore indicates the next logical step in a proof or explanation. e.g. 6p = 18 p = 3 Three Dimensional A three dimensional shape is a shape that has length, ...
Translation The movement of a shape in a straight line. This can be in any direction and any distance.
AA line crossing two (normally parallel) lines. Trapezium A quadrilateral with two parallel sides. www.mathsphere.co.uk Travel Graph A graph with time on the horizontal axis and distance travelled on the vertical axis. Trial and Improvement Method A method used for solving problems where the exact answer is not easy to find straight away. Firs...
The process of joining together two or more sets. e.g. A = {red, green, blue, orange, pink} and B = {yellow, pink, black} A B = {red, green, blue, orange, pink, yellow, black}
The shaded area represents A B Unit (i) The last digit in a whole number. The figure before the decimal point. We talk about the 'units column'. (ii) A standard quantity used for measurement. EG. metre, newton, gram, second. (iii) The number of items that are sold together or packaged together. e.g. 'These light bulbs are sold in units ...
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The original document is scanned at the sending station, converted into an analog or digital representation, and sent over a communication channel to the receiving station, which constructs a duplicate image on paper; this image is referred to as a facsimile.
A function is a rule which maps a number to another unique number. In other words, if we start off with an input, and we apply the function, we get an output. For example, we might have a function that added 3 to any number. So if we apply this function to the number 2, we get the number 5.
A function is typically represented in a table, by points on a coordinate graph, or by a rule such as an equation. For example, for a function with the rule “Double,” 1 is paired with 2, 2 is paired with 4, 3 is paired with 6, and so on. In symbols, y = 2 ∗ x or y = 2 x.
