Notes, summaries, assignments, exams, and problems for Secondary education

Projecting Points and Shapes

Projecting points onto a plane involves rays passing through the points and intersecting the plane. These intersections are called projections. Projecting a shape involves projecting its vertices.

Projection Systems

There are two main systems of projection:

Perspective Projection

When the rays originate from a single point, the system is called perspective projection. The resulting shape is proportionally smaller or larger.

Parallel Projection

When the rays are parallel, the system is called parallel projection. The resulting shape is congruent (same shape and size). There are two variations:

1. Oblique Projection: The rays are oblique to the projection plane.

2. Orthographic Projection: The rays are perpendicular to the projection

The Urbanization Process

The urbanization process consists of concentrating population and the most dynamic economic and cultural activities within cities.

Antiquity

In Europe, the urbanization process began around the third millennium BC with the creation of cities in the Eastern Mediterranean by trading civilizations like Crete. However, the definitive push toward urbanization came in the 8th century BC, first with the Greeks and then with Roman rule, which spread cities all across the empire.

In Spain, the first cities (Cádiz and Ampurias) emerged in the 8th century BC thanks to colonization by Mediterranean peoples (Phoenicians and Greeks). The number of cities increased during the period of Roman rule, when numerous cities were founded, such... Continue reading "The Urbanization Process: From Ancient Cities to Modern Metropolises" »

The Suburbs

In the 20th century, particularly between the 1950s and 1980s, urban growth led to the creation of vast suburban outskirts adjacent to historical cities. These areas were subject to characteristic zoning laws that segregated them into residential, industrial, and service-sector zones.

Residential Zones

Residential zones vary based on residents' buying power, resulting in social segregation: slums for disadvantaged or marginalized groups; tower block neighborhoods of varying sizes and qualities for the middle and lower classes; and exclusive single-family housing developments for the upper classes.

Industrial Zones

Industrial zones house factories that have relocated from city centers, as well as new industries seeking lower land prices... Continue reading "Suburbanization: Urban Growth and the Creation of Rural-Urban Areas" »

Audition 1: Beethoven's Symphony No. 5

Work and Composer

Symphony No. 5 by Ludwig van Beethoven. He was born on December 16, 1770, and died on March 26, 1827.

Genre

Instrumental and secular because it is a symphony.

Style

Between Classicism and a middle period called the Heroic Period.

Texture

Counterpoint: Musical phrases develop independently of one another.

Movement

Allegro

Rhythm

Short figures (predominantly)

Timbre

Orchestra with brass and percussion

Character

Nervous, intriguing

Context

To be filled with a mysterious story.

Text

No text can be found as it is an instrumental work.

Audition 2: Dvorak's New World Symphony

Work and Composer

New World Symphony by Antonin Dvorak. He was born on September 8, 1841, and died on May 1, 1904.

Genre

Instrumental and secular... Continue reading "Classical Music Analysis: Beethoven, Dvorak, Verdi, Vives" »

Core Principles Governing Insurance Contracts

Utmost Good Faith (Uberrimae Fidei)

The principle of Utmost Good Faith requires the insured party to disclose all material information to the insurance company (insurer).

• Material information is any data that would affect the insurer’s decision to provide coverage and/or determine the premium charged.
• When completing the proposal form (application form), all questions must be answered truthfully.
• If the insurer discovers that material information was withheld (e.g., during a claim), the contract becomes null and void, resulting in no compensation.

The Principle of Insurable Interest

Insurable Interest dictates that you can only insure something in which you have a legal relationship and a personal financial... Continue reading "5 Essential Principles of Insurance Law and Claims" »

Classical Music

Transformation from the Early Modern Period to the Contemporary Age

Music between 1730 and 1820

The Rest of the Arts

Neo-classicism. 18th Century: The Age of Enlightenment. Music started to get closer to private houses and public concerts.

Classical Composers

• Liberal artists
• Wanted to reach out to new audiences
• Music: human, natural, pleasant for everyone
• Predominated formal clarity and melodic simplicity

Secular Vocal Music

• Most important: Classical Opera
• Opera underwent a change during the Classicism, which made it tend towards naturalness. It eliminates the excess of the Baroque and took the plots and the characters closer to the new audience.
• Opera Seria: Most important composer C.W. Gluck, who laid the foundation of the new opera in

The Olympic Games

The Olympic Games are an international sporting event celebrated every four years. They are organized by the International Olympic Committee (IOC). All countries are invited to participate under two flags: their national flag and the Olympic flag, which is composed of five interconnected rings of different colors. Each ring represents one of the five continents.

Historical Periods

The Games are historically divided into two periods:

• The Ancient Olympic Games (776 BC - 393 AD)
• The Modern Olympic Games (1896 to present)

The Ancient Olympic Games

The Ancient Games were celebrated in Olympia, located on a Greek island called "Katakolon." To participate, athletes needed to meet three requirements:

1. Be Greek
2. Be a man (women were not allowed

Population

Population is the number of people who inhabit a particular place. Population is influenced by physical environment, settlement patterns, economic activities, and the history of an area.

Before the 19th Century

• Climate changes around 10,000 years ago led to the Neolithic Revolution. As agriculture developed and population became more sedentary, towns and cities were established. Population grew slowly because it was dependent on the resources available.
• Wars, epidemics, and large-scale migration also either limited or promoted population growth. In the first century A.D. the world population was about 256 million. It increased until the Black Death of 1342. By the mid-17th century, the world population surpassed 500 million, and in 1800

Classification of Mechanisms

Transmission of Motion

• Linear transmission: lever, pulley, block and tackle
• Rotary transmission: friction wheels, belt drive, gears

Transformation of Motion

• Rotary to linear: wheel, rack and pinion, nut and bolt
• Reciprocating: crank and rod, crankshaft, cam

Motion Control

• Direction control: ratchet, freewheel
• Speed reduction: brake

Energy Accumulation

• Absorption/dissipation: spring

Connection

• Linkage: clutch
• Support: plain bearing

Levers

Class 1: Levers can do both of those things; the fulcrum is between the force and resistance.

Class 2: Levers increase the force that we apply; the resistance is between the fulcrum and the force.

Class 3: Levers increase the distance that the end of the lever moves; the force is between the fulcrum... Continue reading "Mechanical Systems and Motion Transmission Principles" »

English Vocabulary and Grammar

Phrasal Verbs and Vocabulary

Breathtaking (asombroso), look into, look out for (tener cuidado), flock (birds), herd (elephants), pack (dogs), pride (lion), school (dolphin), troop (monkey), dam (manada), once you've done it. Come across (cruzar), get away (irse), get off (bajar), see off (despedir), set off (activar), speed up, stop over, take off (despegar), blizzard (ventisca), breeze (brisa), drizzle (llovizna), frost, gale (vendaval), hailstorm, mist (niebla), sleet (aguanieve), score, be in a league of their own, neck and neck, no match for, get off to a good start, put up a good fight, be about to (a punto de).

Agree, complain (quejarse), reply, amateur (aficionado), newcomer, script (guion), sketch, spotlight,... Continue reading "English Vocabulary and Grammar: Key Concepts" »