Similarity- Similarity occurs when an object is the same as another object except in a different scale (size) then the original. In triangles, two are only similar if they have all the same angles or their sides are proportional to each other. Squares are always similar and rectangles must have proportional sides as well.

Gnomons- A gnomon in math terms is an object G that fits together with another object A but remains similar to object A just on a different scale.

Disks and Circles are Always similar under every circumstance. A circle could only be an object A but never a gnomon because of its properties.

Circular Rings would be the object A and the gnomon would be the other shape but it does have a gnomon. The shapes of the inner and outer radii however have to be proportional or it is not similar.

Rectangles can be the object A but not the gnomon and only if the gnomon that fits on to it has sides corresponding to that of the rectangle being used for object A.

Circular Disks The O shaped ring would be the gnomon to the smaller filled in circle and that circles diameter would have to also be proportional to the gnomons thickness.

Squares once again the square must be the Object A and the L shaped figure would have to be the proportional gnomon.

Triangles Object A and the gnomon can be any type of triangle as long as it ends up having the same angle sizes or side lengths as triangle object A

Note: A rectangle can not be its on gnomon because you cant separate a rectangle from a rectangle without leaving an L shaped figure behind and that L shaped figure would not be proportional to the rectangle that object A and the gnomon would form when combined together.

The Golden Rectangle is the special rectangle that is just the perfect balance between being too skinny and too squarish that appeals most naturally to us as humans in nature and occurs in all of our modern appliances and objects in our world. It is...

...COMPARATIVE ANALYSIS BETWEEN GREEK AND ROMAN ARCHITECTURE
Author : John Vincent C. Munoz
Bs Architecture
Rizal Technological University, Mandaluyong, Philippines
Abstract
The content of this topic is about comparing the ancient greek architecture and ancient roman architecture, the topic said in this comparative analysis is not all about structure,designing a building . I’ts all about compairing the characteristics of greek and roman architecture. And its all about religion beliefs, different materials they’ve use to do a structure.
Keyword
Ancient Greek Architecture, Ancient Roman Architecture
Introduction
The context of this paper is about the ancient structure, different similar concepts. And about the history in ancient greek architecture and ancient roman architecture. Roman architecture is essentially a hybrid composed of elements inherited from the estruscans combined with the outside influences of the greeks. The native etruscan building traditions can be recognized and the early substructures of the capitoline temple in rome. The temple can be identified as the type described by vitrivius as typically etruscan, consisting basically of a wide structures with a deep porch supported by columns. The temple of apollo at pompeii, probably built in a late second century b.c.e.. is a typical example of a temple that exhibit greek influenced in its plan. Etruscan and early roman art and architecture were very...

...Axel Krizza A. Cabalhug
2012-31400
Term Paper Proposal: Broad Subject – Unit Circle
I would like to explore the unit circle and how it is essential in the field of Mathematics especially in Trigonometry and Calculus. I, myself, am a Math enthusiast and I have heard many people complaining as to why Unit Circle is part of the curriculum when it is just a circle with a radius of one. I would like to know if there is a relevant relationship with how developed a student’s understanding of the unit circle is to the student’s comprehension of the major topics in Trigonometry and Calculus. Perchance an established knowledge of the unit circle could help students appreciate and understand better related topics in Trigonometry and Calculus and eventually grasp the wonders of Mathematics.
Analysis Questions
1. What is a unit circle?
2. Why is it important to master such basic idea?
3. What are its main uses, specifically in Trigonometry and Calculus?
4. What are the possible causes that students do not understand the unit circle?
5. How is mastering the unit circle help students understand trigonometry better?
6. Are there unique definitions of the unit circle in other fields?
7. Can the unit circle be applied directly in real life?
Sentence Outline
The Unit Circle and Its Uses
I. The history of trigonometry had arrived at unit circle as the major topic.
II. The unit circle is a circle with a radius of one....

...Similarity and congruence
Two triangles are said to be similar if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion, and this property is also sufficient to establish similarity.
A few basic theorems about similar triangles:
* If two corresponding internal angles of two triangles have the same measure, the triangles are similar.
* If two corresponding sides of two triangles are in proportion, and their included angles have the same measure, then the triangles are similar. (The included angle for any two sides of a polygon is the internal angle between those two sides.)
* If three corresponding sides of two triangles are in proportion, then the triangles are similar.
Two triangles that are congruent have exactly the same size and shape: all pairs of corresponding interior angles are equal in measure, and all pairs of corresponding sides have the same length. (This is a total of six equalities, but three are often sufficient to prove congruence.)
Some sufficient conditions for a pair of triangles to be congruent are:
* SAS Postulate: Two sides in a triangle have the same length as two sides in the other triangle, and the included angles have the same measure.
* ASA: Two interior angles and the included side in a triangle have the same measure and length, respectively, as those in the...

...criminal, a thought which should be suppressed, but he is unable to. The pain is real, so real that one is instantly taken to a dark place. A deed, so vile, once done, can never be undone.
Although the people are allowed to get married and have kids, they are strictly not allowed to fall in Love. People get married to bear children for The Party. They are doing a service to The Party, a service to society.
Doublethink. Doublethink is believing and at the same time not believing. If Oceania is at war with Eastasia, it was always at war with Eastasia, even though that few weeks ago Oceania was at Eurasia. If The Party vaporises someone, they cease to exist – not only on paper but people’s minds. There will be no reference to him in any of the official documents, his name is stricken off every piece of paper, his memory is to be deleted in everyone’s mind by an unwritten commandment. Wives are to forget their husbands; Sons their Mothers. Doublethink is the ability to contort one’s mind, actions and most importantly thought to suit the convenience of The Party.
The Thought Police ensure all thoughtcriminals are caught and punished. They track everyone, every word and every action; they are relentless; they will ultimately win. Public confessions followed by executions are common place.
If you want to keep a secret, you must also hide it from yourself.
There are no individuals in Oceania, there is only The Party and The Enemy(War for Oceania...

...X CBSE Paper March 2012
Time : 3 Hrs. M.M. : 80
1. If 1 is a root of the equation ay2 + ay + 3 = 0 and y2 + y + b = 0, then ab equals :
(a) 3 (b) (c) 6 (d) 3
2. The sum of first 20 odd natural numbers is :
(a) 100 (b) 210 (c) 400 (d) 420
3. In fig., the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and
AC = 11 cm, then the length of BC (in cm) is :
(a) 11
(b) 10
(c) 14
(d) 15
4. In fig., a circle touches the side DF of EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm, then the perimeter of EDF (in cm) is :
(a) 18
(b) 13.5
(c) 12
(d) 9
5. If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is :
(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1
6. If the area of the circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is :
(a) 34 (b) 26 (c) 17 (d) 14.
7. The length of shadow of a tower on the plane ground is times the height of the tower. The angle of elevation of sun is :
(a) 45 (b) 30 (c) 60 (d) 90.
8. If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (2, 5), then the...

...Sample Paper – 2013
Class – XI
Subject – MATHEMATICS
Time Duration: 3 hours M.M.100
Section - A
(Question No 1 Compulsory and Attempt five other questions)
Question 1 [10 X 3 = 30]
(i) If .Show that
(ii) Differentiate the function x3 + 4x2 + 7x + 2 with respect to x
(iii) How many words can be formed with or without meaning by the letters of the word ‘ALLAHABAD’.
(iv) Prove that:
(v) If f : R R and g : R R are defined f(x) = 2x + 3 and g(x) =X2 + 7, then find the Values of x for which (fog) (x) = 25
(vi) Evaluate:-
(vii) If the angle between two lines is and the slope of one of the lines is , find the slope of the other line.
(viii) Using the principle of mathematical induction. Prove that:-
(ix) Find the equation of circle whose centre is ( 4, -3 ) and radius is 10.
(x) Prove that :
Question 2
(a) Find the sum of n terms of the series
[4]
(b) If the coefficient of in the expansion of are in A.P.prove that [6]
Question 3
(a) Find the value of the constant K so that function is continuous at x=0 [5]
Show that is continuous at x=0
(b) If [5]
Question 4
(a) Find General solution of Ө for the equation [5]
(b) If ,prove that [5]
Question 5
(a) Find the equation(s) of tangent (s) to the curve y = x3 + 2x + 6 which is...

... I am writing a paper on the similarities of the setting between two books, The Giver and Gathering Blue both by the same author Lois Lowry. To start off, in both of the books they have annual gatherings each year that start in the morning, are multiple hours long, have lunch and resting breaks and continue into the afternoon. During these gatherings or celebrations the celebrate their past and their maturity and age. Another likeness is that they both have a committee of elders or the people that make most of the decisions for the community. The elders create the rules, decide whether they will be be realesed or sent to the field. Both of the communities have a special building, where the annual gathering is, where they hold trials, where the committee lives. The communities also share the idea of forgetting death, they both have a way of forgetting it, murmurs and not caring but in all it is supposed to be out of their minds and forgotten. In the books the author infers that it is in the future because there would have to be very high technology to do all of that stuff. In either community they do not want imperfect people, such as, twisted/broken anything, mental problems, hearing/vision loss, very weak, light, if they have anything of the above they will either be sent to the field or be released. Together what they both share is that there is no true love, yes they care about each other, they mourn when the die, they take care of...

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