"The Little Book of Scientific Principles, Theories, & Things" by Surendra Verma

• A postulate (or axiom) claims something is true or is the basis for an argument. A theorem is a proven proposition, which is a statement with logical constraints.
• Archimedes Principle explains why things float. If an object is less dense than the fluid that surrounds it (that is, it weighs less than an equal volume of the fluid), it will float, since the apparent loss of weight will be greater than its weight in air. If it is denser than the fluid, the apparent loss in weight will be less than its weight in air and it will sink.
• All circles are similar and the ratio of the circumference to the diameter of a circle is always the same number, known as the constant pi.
• It is impossible to find the exact value of pi; however, the value can be calculated to any required degree of accuracy.
• Fibonacci numbers: A series of numbers in which each successive term is the sum of the preceding two. The ratio of successive terms approaches the number 1.618. This ratio is known as the golden ratio and is denoted by the Greek letter phi.
• Ockham’s Razor: This guiding principle in developing scientific ideas insists that you should prefer the simplest explanation to fit the facts. In other words, the explanation requiring the fewest assumptions is most likely to be correct.
• Scientific laws must be based on observations and experiments.
• The essence of his [Bacon’s Scientific Method] is as follows: collect masses of facts by observations and experiments, analyze facts by drawing up tables of negative, affirmative, and variable instances of the phenomenon, draw hypotheses from the evidence, collect further evidence to proceed toward a more general theory. The most important aspect of this method was the idea of drawing up tentative hypothesis from available data and then verifying them by further investigations.
• Refraction is the change in direction of a ray of light when it crosses the boundary between two media. It happens because light has different speeds in different media.
• Pascal’s Law: When pressure is applied anywhere to an enclosed fluid, it is transmitted uniformly in all directions.
• Light, but not sound, can travel through a vacuum.
• Calculus has now become an important branch of mathematics dealing with the behavior of functions.
• Newton’s Law of Gravitation: Any two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
• Newton’s Laws of Motion:
• An object at rest will remain at rest and an object in motion will remain in motion at that velocity until an external force acts on the object.
• The sum of all the forces (F) that act on an object is equal to the mass (m) of the object multiplied by the acceleration, or F = ma.
• To every action, there is an equal and opposite reaction.
• We now know that biological clocks are an internal timing system that regulates metabolism in all forms of life.
• Hundreds of cellular, physiological, and behavioral patterns have been observed to follow a 24-hour cycle in humans. For this reason the biological clock is also called circadian rhythm (from the Latin circa diem, about a day).
• Bernoulli’s Principle: As the velocity of a liquid or gas increases, its pressure decreases; and when the velocity increases, its pressure increases. It can be summed up simply as the faster the flow the lower the pressure.
• The Celsius Temperature Scale: The temperature difference between the freezing point and the boiling point of water is a hundred degrees.
• The mnemonic, My Very Educated Mother Just Served Us Nine Pizzas, may help you to remember the order of nine planets, outwards from the sun.
• In an arithmetic series of numbers there is common difference between any number and its successor, while in a geometric series each number is a constant multiple of the preceding number.
• Young’s Principle of Interference: Interference between waves can be constructive or destructive. Two identical waves traveling together either reinforce each other (constructive interference) or cancel each other out (destructive interference).
• Oersted’s Theory of Electromagnetism: Electric current produces a magnetic field.
• The distant galaxies are moving away from us at a speed so high that it diminishes the intensity of light we receive from them.
• Ampere’s Law: Two current-carrying wires attract each other if their currents are in the same direction, but repel if their currents are opposite. The force of attraction or repulsion is directly proportional to the strength of the current and inversely proportional to the square of the distance between them.
• Ohm’s Law: The electric current in a conductor is proportional to the potential difference.
• Faraday’s Law of Induction: A changing magnetic field around a conductor produces an electric current in the conductor. The size of the voltage is proportional to the rate of change of the magnetic field.
• Gases have no fixed volume; they expand to fill the entire volume of their container.
• Gauss’ Law: The electric flux through a closed surface is proportional to the sum of the electric charges within the surface.
• Doppler Effect:; Any source of sound or light moving away from an observer changes in frequency with reference to the observer.
• First Law of Thermodynamics: Heat is a form of energy and energy is conserved. It’s simply a restatement of the law of conservation of energy: energy is neither created nor destroyed, but may be changed from one form to another.
• Kirchhoff’s Laws:
• At any junction point in an electrical circuit, the sum of all currents entering the junction must equal the sum of all currents leaving the junction.
• For any closed loop in an electrical circuit, the sum of the voltages must add up to zero.
• Second Law of Thermodynamics: Heat does not flow spontaneously from a colder to a hotter body.
• The third law of thermodynamics dictates that it is impossible to cool an object to a temperature of absolute zero.
• Boolean Logic: Logical operations can be expressed in mathematical symbols rather than words and can be solved in a manner similar to ordinary algebra.
• Boolean algebra has three main logical operations: NOT, AND, OR.
• Darwin’s Theory of Evolution: All present-day species have evolved from simpler forms of life through a process of natural selection.
• Evolution through natural selection is opportunistic and it takes place steadily.
• Four equations [Maxwell’s Equations] that express mathematically the way electric and magnetic fields behave.
• The equations [Maxwell’s Equations] are complex, but in simple words they describe:
• a general relationship between electric field and electric charge
• a general relationship between magnetic field and magnetic poles
• how a changing magnetic field produces electric current
• how an electric current or a changing electric field produces a magnetic field
• Radio waves can be produced by electric sparks. They have the same speed as light and behave the same as light. We are now familiar with all the types of electromagnetic waves that make up the complete electromagnetic spectrum they all travel with the speed of light and differ from each other in their frequency -- and we measure this frequency in hertz (Hz), a unit named in Hertz's honor.
• The transmission of high-voltage alternating current (AC) over long distances is more efficient than the transmission of direct current (DC).
• Quantum Theory: Energy is not a continuous quantity but it is quantized, that is, it flows in discrete bundles or quanta (singular quantum). When particles emit energy they do so only in quanta.
• Special Theory of Relativity
• The relativity principle: All laws of science are the same in all frames of reference.
• Constancy of the speed of light: The speed of light in a vacuum is constant and is independent of the speed of the observer.
• The theory [Special Relativity] says that time is not an absolute quantity. Our measurements of time are affected by our motion.
• The theory [Special Relativity] also says that the mass of a moving object increases as its speed increases. At the speed of light, which is about 186,300 miles per second, the mass becomes infinite and therefore nothing can move faster than light.
• The energy of a body (E) equals its mass (m) times the speed of light (c) squared.
• Mass and energy are mutually convertible under certain conditions.
• The mass-energy equation is a consequence of Einstein’s theory of special relativity.
• Superconductivity: At very low temperature, some materials conduct electricity without any resistance; that is, virtually without any loss of energy.
• Theory of General Relativity: Objects do not attract each other by exerting pull, but the presence of matter in space causes space to curve in such a manner that a gravitational field is set up. Gravity is the property of space itself.
• In quantum mechanics, elementary particles can, in some instances, behave like waves. The waves - which are really waves of probability - describe where a particle is most likely to be at a given moment.
• Heisenberg’s Uncertainty Principle: It is impossible to determine exactly both the position and momentum of a particle (such as an electron) simultaneously.
• Dirac’s Antimatter Theory: Every fundamental particle has an antiparticle -- a mirror twin with the same mass but opposite charge.
• When antimatter and ordinary matter meet, they annihilate each other and disappear in a violent explosion in which mass is converted into energy as dictated by Einstein’s equation E = mc^2.
• Hubble’s Law: Galaxies are moving away from us and each other at an ever-increasing rate. The more distant the galaxy, the faster it is moving away.
• Asimov’s Three Laws of Robotics
• A robot may not injure a human being or, through inaction, allow a human being to come to harm.
• A robot must obey orders given it by human beings, except where such orders would conflict with the first law.
• A robot must protect its own existence as long as such protection does not conflict with the first or second law.
• Radiocarbon Dating: The radioactive isotope of carbon, carbon-14, is present in all living things. When life stops carbon-14 begins to decay. From the rate of decay, the age (or time of death) of an organism can be calculated.
• The Big Bang Theory: The universe began when a single point of infinitely dense and infinitely hot matter exploded spontaneously.
• Murphy’s Law: If anything can go wrong, it will.
• Moore’s Law: The number of transistors on a computer chip doubles every 18 months or so.
• The Scientific Method involves the following:
• observations and search for data
• hypothesis to explain observations
• experiments to test hypothesis
• formulation of theory
• experimental confirmation of theory
• mathematical or empirical confirmation of theory into scientific law
• use of scientific law to predict behavior of nature
• Hypothesis -- a tentative explanation of observed facts. Every theory or law in science begins as a hypothesis.
• Theory -- a theory is a hypothesis that has been tested by experiments, and to which exceptions have been found.
• Scientific Law -- a theory that has been verified mathematically.