geometry formulas

List of Free Science Books

Here’s an alphabetical list of all available free books. Note that many of the links will bring you to an external page, usually with more info about the book and the download links. Also, the links are updated as frequently as possible, however some of them might be broken. Broken links are constantly being fixed. In case you want to report a broken link, or a link that violates copyrights, use the contact form


  • A Beginner’s Guide to Mathematica
  • A Brief Introduction to Particle Physics
  • A First Course in General Relativity
  • A New Astronomy
  • A No-Nonsense Introduction to General Relativity
  • A Popular History of Astronomy During the Nineteenth Century, Fourth Edition
  • A Review of General Chemistry
  • A Simple Guide to Backyard Astronomy
  • A Text Book for High School Students Studying Physics
  • A Tour of Triangle Geometry
  • About Life: Concepts in Modern Biology
  • Acoustic Emission
  • Adaptive Control
  • Advanced Calculus
  • Advanced Learning
  • Advanced Mathematics for Engineers
  • Advanced Microwave Circuits and Systems
  • Advanced Technologies
  • Advances in Computer Science and IT
  • Advances in Evolutionary Algorithms
  • Advances in Geoscience and Remote Sensing
  • Advances in Haptics
  • Advances in Human Computer Interaction
  • Age of Einstein
  • Aging by Design
  • AMPL:  A Modeling Language for Mathematical Programming
  • An Introduction to Elementary Particles
  • An Introduction to Higher Mathematics
  • An Introduction to Many Worlds in Quantum Computation
  • An Introduction to Mathematical Reasoning
  • An Introduction to Mathematics
  • An Introduction to Proofs and the Mathematical Vernacular
  • An Introduction to Relativistic Quantum Mechanics
  • Analysis 1 (Tao T)
  • Analysis 2 (Tao T)
  • Analytic Functions
  • Astronomical Discovery
  • Astronomy for Amateurs
  • Astronomy Today
  • Astronomy with an Opera-Glass
  • Automation and Robotics


  • Basic Algebra, Topology and Differential Calculus
  • Basic Concepts of Mathematics
  • Basic Concepts of Thermodynamics
  • Basic Concepts of Thermodynamics Chapter 1
  • Basic Ideas in Chemistry
  • Basic Math: Quick Reference eBook
  • Basic Mathematics for Astronomy
  • Basic Physics
  • Basic Positional Astronomy
  • Basic Principles of Classical and Statistical Thermodynamics
  • Basic Principles of Physics
  • Basics of Physics
  • Beginner’s Botany
  • Biochemistry
  • Biochemistry (practice book)
  • Biology
  • Board Notes for Particle Physics
  • Book of Proof


  • Calculus
  • Calculus Based Physics
  • Celestial Navigation, Elementary Astronomy, Piloting
  • Circuit QED — Lecture Notes
  • Classical Dynamics
  • Classical Geometry
  • Classical Mechanics
  • Climate Models
  • Collaborative Statistics
  • College Algebra
  • Complex Analysis
  • Computational Geometry
  • Computational Introduction to Number Theory and Algebra
  • Computational Physics with Python
  • Conceptual Physics
  • Consistent Quantum Theory
  • Cook-Book Of Mathematics
  • College Physics
  • Crude Oil Emulsions- Composition Stability and Characterization
  • Curiosities of the Sky


  • Decoherence: Basic Concepts and Their Interpretation
  • Do We Really Understand Quantum Mechanics?
  • Differential Equations
  • Diophantine Analysis
  • Discover Physics
  • Dr. Donald Luttermoser’s Physics Notes
  • Dynamics and Relativity


  • Earthquake Research and Analysis
  • Earthquake-Resistant Structures – Design, Assessment and Rehabilitation
  • Einstein for Everyone
  • Electromagnetic Field Theory
  • Elementary Mathematical Astronomy
  • Elementary Linear Algebra
  • Elementary Particle Physics in a Nutshell
  • Elementary Particles in Physics
  • Elements of Astrophysics
  • Embedded Systems – Theory and Design Methodology
  • Encyclopaedia of Mathematics
  • Encyclopedia of Astrophysics
  • Engineering Mathematics 1
  • Engineering Mathematics with Tables
  • Essential Engineering Mathematics
  • Essential Physics
  • Exoplanet Observing for Amateurs
  • Experimental Particle Physics


  • Fields
  • Foundations of Nonstandard Analysis
  • Frequently Asked Questions about Calendars
  • Fundamental Concepts of Mathematics
  • Fundamentals of Analysis (Chen W.W.L)
  • Further Mathematical Methods
  • Fusion Physics


  • General Chemistry
  • General Relativity
  • General Relativity
  • Geometric Asymptotics
  • Geometry and Group Theory
  • Geometry and Topology
  • Geometry Formulas and Facts
  • Geometry Study Guide
  • Geometry, Topology and Physics
  • Geometry, Topology, Localization and Galois Symmetry
  • Great Astronomers


  • Handbook of Formulae and Physical Constants
  • High School Mathematics Extensions
  • Higher Mathematics for Engineers and Physicists
  • History of Astronomy
  • Homeomorphisms in Analysis
  • How to Use Experimental Data to Compute the Probability of Your Theory


  • Intelligent Systems
  • Intrinsic Geometry of Surfaces
  • Introduction to Astronomy and Cosmology
  • Introduction to Cancer Biology
  • Introduction to Chemistry
  • Introduction to Cosmology
  • Introduction to Elementary Particles
  • Introduction to General Relativity
  • Introduction To Finite Mathematics
  • Introduction to Particle Physics Notes
  • Introduction to PID Controllers
  • Introduction to Quantum Mechanics with Applications to Chemistry
  • Introduction to Quantum Noise, Measurement and Amplification
  • Introduction to Social Network Methods
  • Introduction to String Field Theory
  • Introduction to the Time Evolution of Open Quantum Systems
  • Introduction to Quantum Mechanics
  • Introductory Computational Physics
  • Introductory Physics 1
  • Introductory Physics 2


  • Kinetic Theory


  • Laboratory Manual for Introductory Physics
  • Laws of Physics
  • Learn Physics Today
  • Lecture Notes in Discrete Mathematics
  • Lecture Notes in Quantum Mechanics
  • Lecture Notes in Nuclear and Particle Physics
  • Lecture Notes in Particle Physics
  • Lecture Notes on General Relativity
  • Lectures on Astronomy, Astrophysics, and Cosmology
  • Lectures on Particle Physics
  • Lectures on Riemann Zeta-Function
  • Light and Matter


  • Mag 7 Star Atlas Project
  • Many Particle Physics
  • Math Alive
  • Mathematical Analysis I(Zakon E)
  • Mathematical Biology
  • Mathematical Methods
  • Mathematical Methods 1
  • Mathematical Methods for Physical Sciences
  • Mathematical Methods of Engineering Analysis
  • Mathematics, Basic Math and Algebra
  • Mathematics for Computer Science
  • Mathematics for Computer Science
  • Mathematics for Computer Scientists
  • Mathematics For Engineering Students
  • Mathematics Formulary
  • Motion Mountain
  • Music: A Mathematical Offering
  • Mysteries of the Sun


  • Natural Disasters
  • New Frontiers in Graph Theory
  • Noise Control, Reduction and Cancellation Solutions in Engineering
  • Nondestructive Testing Methods and New Applications
  • Nonlinear Optics
  • Notes on Coarse Geometry
  • Notes on Elementary Particle Physics
  • Notes on Quantum Mechanics


  • Observing the Sky from 30S
  • On Particle Physics
  • Operating Systems: Three Easy Pieces


  • Particle Physics Course Univ. Cape Town
  • Particle Physics Lecture Notes
  • People’s Physics Book
  • Perspectives in Quantum Physics: Epistemological, Ontological and Pedagogical
  • Photons, Schmotons
  • Physics Lectures
  • Physics Tutorials
  • Physics Study Guides
  • Pioneers of Science
  • Practical Astronomy
  • Practical Astronomy for Engineers
  • Preparing for College Physics
  • Primer Of Celestial Navigation
  • Principal Component Analysis – Multidisciplinary Applications
  • Publications of the Astronomical Society of the Pacific Volume 1


  • Quantum Dissipative Systems
  • Quantum Field Theory
  • Quantum Fluctuations
  • Quantum Information Theory
  • Quantum Magnetism
  • Quantum Mechanics
  • Quantum Mechanics
  • Quantum Mechanics: A Graduate Course
  • Quantum Mechanics: An Intermediate Level Course
  • Quantum Notes
  • Quantum Physics Notes
  • Quantum Theory of Many-Particle Systems
  • Quantum Transients


  • Recreations in Astronomy
  • Relativistic Quantum Dynamics
  • Relativity: The Special and General Theory
  • Review of Basic Mathematics
  • Riemann Surfaces, Dynamics and Geometry Course Notes


  • Short History of Astronomy
  • Sintering of Ceramics – New Emerging Techniques
  • Solitons
  • Some Basic Principles from Astronomy
  • Special Relativity
  • Spherical Astronomy
  • Star-Gazer’s Hand-Book
  • Statistical Physics
  • Street-Fighting Mathematics
  • String Theory
  • Structures of Life
  • Supernova Remnants: The X-ray Perspective
  • Superspace: One Thousand and One Lessons in Supersymmetry
  • System of Systems


  • The Astrobiology Primer: An Outline of General Knowledge
  • The Astronomy and the Bible
  • The Astronomy of the Bible: An Elementary Commentary on the Astronomical References of Holy Scripture
  • The Basic Paradoxes of Statistical Classical Physics and Quantum Mechanics
  • The Beginning and the End
  • The Beginning and the End of the Universe
  • The Complete Idiot’s Guide to the Sun
  • The Convenient Setting of Global Analysis
  • The Eightfold Way: The Beauty of Klein’s Quartic Curve
  • The General Theory of Relativity
  • The Geology of Terrestrial Planets
  • The Geometry of the Sphere
  • The Handbook of Essential Mathematics
  • The Moon: A Full Description and Map of its Principal Physical Features
  • The Open Agenda
  • The Origin of Mass in Particle Physics
  • The Particle Detector Brief Book
  • The Physics Hypertextbook
  • The Physics of Quantum Mechanics
  • The Planet Mars
  • The Small n Problem in High Energy Physics
  • The Story of Eclipses
  • The Story of the Heavens
  • The Structure of Life
  • The Wonder Book of Knowledge
  • The World According to the Hubble Space Telescope
  • The Zij as-Sanjari of Gregory Chioniades (June 27, 2009)
  • Three Dimensional Geometry


  • Understanding Physics
  • Unfolding the Labyrinth
  • Utility of Quaternions in Physics
  • Uses of Astronomy

Hello, tumblr!

Today, I’m going to talk about AP Calculus! It has a reputation as one of the hardest AP courses, not without desert; it is heavy with concepts and requires a high degree of proficiency in all the math that comes before it. It is also enormously useful for a variety of fields, from architecture to medicine, and can be a lot of fun to do! Some tips:


  • Most AP Calc courses come after a substantial list of prerequisites: Algebra 1 and 2, Geometry, Trigonometry, and whatever your school calls the mish-mash of topics falling under pre-calculus. It is imperative to be comfortable with these when you start; calculus uses all of them.
  • Specifically:
    • Know. The. Trigonometric. Circle. Know it like the back of your hand (if you are someone who studies each detail of your hand carefully like the weirdo who came up with this saying)
    • Make sure you know the trigonometric identities too, back and forth.
    • You will need the formulas from Geometry. These aren’t as hairy as the trigonometric ones imo, but still good to know so you don’t have to relearn them later.
    • Make sure you are comfortable with algebraically changing expressions from one form to another. Factoring and reducing expressions will be super important.
  • If you have a hard time with any of these, it’s ok; you can review them! If you find that you have forgotten anything you need during your course, see if you can find some excercises in it online or in a book, and do a few so that you are comfortable with it.


  • AP Calc involves some proofs, but most of the course is about learning how to do specific types of operations. The best way to prepare is to just do the problems you are assigned for homework, then do more as time passes or if you have a hard time with a particular one.
  • Memorize formulas as they are introduced. Review them often. Do problems with them.
  • If you do not understand a concept:
    • Try to break down why. Do you understand part of it? Write down what you know. See what it is that is stopping you.
    • Try drawing a picture. Label it. See if you can relate your problem to the visual geometry.
    • Try working a problem. See where you stop understanding it. Ask yourself why you are doing each step. See if you can explain to yourself.
    • Look at a worked problem. Explain each step to yourself. See where you stop understanding.
    • If there a proof involved? Work through the proof, making sure you understand each step. This can give you a solid foundation.
    • Go to your teacher or a friend with specific questions.
  • The FRQs and MCQs from previous tests are a goldmine. Do every one you can get your hands on. For FRQs, compare your answers to the model answers given on the College Board website. Mark everything you do wrong. Try to remember it and do it right next time you do a similar problem.
  • FRQs are great because they tend to incorporate multiple concepts, giving you practice, and they also follow similar patterns. Getting used to those patterns is really helpful.

The Test

  • Do some full practice tests. Time yourself. Note the concepts you get wrong and review them. Ask someone about things that give you trouble.
  • Make sure you know all your formulas well.
  • Make sure you can do everything you will need to with your calculator.
  • Part of the test is no-calculator. Make sure you can do the sort of problems which appear there without your calculator.
  • When you take the test:
    • Sleep.
    • 0/10 do not recommend late night cramming the night or two before the test.
    • Change your calculator’s batteries. Just so you’re certain it won’t die on you.
    • Have something to drink on you.
    • On the MCQs, skip problems you can’t do quickly and come back to them. I recommend:
      • Doing all the easy problems first. The ones that you get instantly. Just read the rest.
      • Come back and do the ones you need some time for. Ignore any if you have no idea how start or take a lot of time.
      • Come back for these on the third pass.
      • They’re all worth the same amount, so don’t worry about specific ones; just get as many as you can right.
    • Show. You. Work. On the FRQs. Write down everything you can.
    • If you don’t know how to do the first part of a problem, but the second part relies on it, just pick a number you think is reasonable for the answer to the first part, and use it. You can still get credit for the second part if you use that number correctly.
    • Don’t stress out too much. Even if you feel terribly, it is quite possible that you did will.
    • For illustration, I took BC, and I literally cried after the test, because I thought I did terribly. I got a five. The percentage you need to get right to do well is low, and how you feel does not predict how you do.
  • Take a bit of time for yourself afterwards. It’s going to be May. The weather will be beautiful. Breathe it in. :)

my posts on:

ap in general

ap english literature

ap us history

The /r/teenagers FAQ Academic Resource Masterpost


This masterpost has links for various academic content, from studying to homework help to assistance on assignments.

As this is 12 pages long, we would say that the “Ctrl + F” keyboard shortcut is your friend.

If you have a link that’s not here (we’re in need of links for the non-American and IB sections), the link given is now behind a paywall (aka you have to pay to see everything) or any of the links are broken, please send a message to the /r/teenagers FAQ ask box.


Keep reading

april 26th  / /  9:26 am

Revising in the most useful way for my extreme visual learning––making math beautiful : ) I gotta kick this exam’s ass to get an A in the class. Even though they’re somewhat redundant formulas I already knew, I can’t let anything slip through! Hopefully after this test I will be able to focus on other subjects I miss.

Ok so @goodluckdetective​ had an idea for an Emergency Services AU aaaaaand it just blew my mind. I started thinking how I would write it and pair things up. I’m trying to think of how Blood Gulch and Armonia would work (thinking city limits debate). It’s honestly really crazy and hilarious to me how it would all work.

Red Team are firefighters. All itching to go on the next call. In the mean time, either taking care of equipment, lazing around, or doing training drills. Haven’t decided if I wanted small city or small town volunteer station.

Sarge - Assistant chief at the local station. Always ‘fixing’ some piece of broken machinery. He’s still waiting on approval from county to get things upgraded. Until then he cobbles it together. He has a love/hate relationship with SOPs (Standard Operating Procedure) and County Command. Sarge LOVES to do practice burns. He’s always overenthusiastic about any fire. Car accident? He’s hoping (but not) it’s on fire. Sees smoke on the horizon? Clearly that’s a brush fire, not someone burning their leaves in their yard; Grif get the truck. Prefers riding Shotgun on the Engine.

Simmons - Simmons actually went to the Fire Academy. He knows the science behind fires, knows a lot about the trucks and pumps, also knows the formulas and geometry needed to calculate pressure loss (Grif gives him shit about being a nerd). He’s all about the SOPs and regulations. He’s usually the one fiddling with the walkies. Later on Simmons goes to get basic paramedic training, so the truck would have a paramedic. However he gets roped into taking a few shifts to help out EMS. Sarge and Grif rag him about being a “Blue traitor”. Simmons is more the “book smart” fighter, but still lacks the “on your feet instinct”. Simmons prefers to drive the Rescue over the Engine. During one bad call, a chunk of a building gets caught on his arm and leg. Thankfully he was on the side that wasn’t on fire. They were damaged to the point of being amputated. However, the skin tissue from the lost limbs as well as a kidney was donated to Grif who was badly injured in the same fire. He was given high grade prosthetics and continued fire fighting. However he usually stays by the trucks and mans the pump and gophers.

Grif - Best Driver for the engine. The most reliable at getting the engine through the tiny back roads however the laziest. Simmons has just giving up on relying on Grif to load the hose back on the truck or if he does it’s the shittiest job imaginable. He does eventually learn when the hose kinks when they were catching a hydrant and dents the fuck out of the bar on the hose bed. He also CONSTANTLY forgets to refill the air tanks and to change out the hose on the dry racks. He’s usually paired with Simmons since they’re pretty good at balancing each other. During the bad call, he was the unlucky one that was caught on the fire side during the collapse. He experienced 3rd degree burns on most of his left side. He went into shock which caused his kidneys to fail. The excess skin from Simmons amputated limbs was grafted to Grif. He makes a full recovery.

Lopez -  (He’s the only one I don’t have a clear idea for) Lopez handles most of the truck maintenance. On car accidents, he’s usually the one wielding the Jaws. He’s bilingual, but refuses to speak English (he thinks the rest of them are a bunch of idiots and doesn’t want to deal with them). He’s usually paired with Donut since Donut’s the only one that can “understand” him. Has a HUGE crush on Sheila, one of the dispatchers.

Donut - Rookie who started volunteering after doing several years of the Explorers program at a different station. Very chipper and enthusiastic about everything. Donut usually takes care of the house chores at the station. He gets caught in a backdraft. He wasn’t wearing a Nomex hood at the time (his program was with a lot of vet fighters who hate the Nomex hoods because their ears are covered and can’t tell when it’s getting too “hot” in a room). He has some really nasty scaring on the right side of his face and lost most of his ear on one side.

Blue Team are EMS. Always bickering over who is driving or just bickering in general. When Washington joins full time, he’s always drilling them. 

Tucker - A people person. Not necessarily a good one. He is known to be mostly professional out in public but makes tons of inappropriate jokes in the truck and at the station. He’s the best at setting up for IVs and spotting locations or people in distress. Tucker tried to get the call number “69″, but was denied several times.

Caboose - is really great with kids and guys who need to be restrained when their insulin is too high. When something goes wrong he blames Tucker. Caboose is also known to accidentally inject his teammates instead of his patients. He really enjoys talking with dispatch over the radio.

Alpha Church - no bed side manner and is impatient as hell. Cannot hit a vein to save his life. He’s usually good at getting vital readings, symptoms for potential drugs, and noticing when a patient is about to crash. Alpha runs into a building trying to get to a patient and dies. Not sure if Alpha and Epsilon should be siblings or cousins with Carolina.

Epsilon Church - After alphas accident, his twin brother Epsilon is transferred to his station. (to the surprise of everyone at the station because Alpha never mentioned a twin). If the group didn’t know any better they would almost swear that twins were the same person. Epsilon however isn’t as high strung as his brother was, and gets along better with the crew, and is a little better with patients. However he can’t hit a vein either.

Freelancers are Police. Something happens with county/state police (haven’t thought this through much). Freelance was contracted to the Blood Gulch crew, but something happens that requires them to pull out. They were all specially trained in basics for firefighting and are at least paramedic status.

Eventually Wash and Carolina take police work at Blood Gulch. They’re always on call since they’re the only two regularly scheduled police officers. Wash gets EMT training and takes shifts with EMS as well as his policing duties (the man never sleeps). Carolina gets hired on as Police/Fire Chief at some point, but also goes and gets EMT training in case it’s needed.

Vic (early days, but mysteriously leaves with no explanation), Sheila, and Fillis are 911 dispatch.

Doc is a “Safety Inspector” from County. He makes a bunch of suggestions and changes that were made either too late are so ridiculous no one listens.

Ok cut below is an explanation of things back from my home. I was raised in a firefighting family in a small town. I know things are probably a lot different now and that other cities and areas would be run differently. 

Feel free to send asks, suggestions, and what not.

Keep reading

anonymous asked:

Can you write one about cuddling with Harry, but you are really inexperienced and dont know how to cuddle?

“Nonsense!” Harry cried out. “Everyone knows how to give a proper cuddle." 

Unfortunately, it was true; you weren’t experienced with cuddling or tangling your limbs with someone without accidentally kneeing them in the groin or poking their eye out with a hand. It seemed all too very complex, like a geometry formula, in which angles had to be properly executed or something would go terribly, terribly wrong (like an extremity being lost in the mangle of bodies or not being able to get up in time when you had to go to the bathroom or — ) 

"Hey,” Harry whispered, tongue poking out of his pursed lips when he caught you thinking too hard. “What’s on your mind?” He tapped his index finger against your temple and brought his arm around your back, tugging you in a little closer to him. 

“Too much thinking going on up there,” he said in the same soft voice, trailing his finger down from his initial resting place until it was scrunching your nose. “Not enough holding me back.”

You tried to protest, “Harry, I don’t know how — “ 

“Nah.” Harry shook his head gently, wisps of haphazardly placed hair falling into his eyes. “Cuddling isn’t about thinking at all. You just do it, yeah? You feel how warm someone is and you just… it just happens, y’know? Don’t think too much. It’s alright.” He takes a short pause to rub a soothing hand up and down your back before; “C’mon, I’ll take good care of you." 

You melt into him while he shifts until he’s up on his back, arm still hooked protectively around your midsection. He murmurs very softly while placing you in the perfect position, so your head is resting in the crook of his elbow and your leg is slotted inbetween his own, arm pulled tight across his chest so you’re as proximate as could be. 

"Alright now?” he double checks, wanting to make sure you’re comfortable and feeling safe and sleepy like him because that’s all cuddling is really supposed to achieve. “No cold toes?" 

You make a small noise in the back of your throat when he drapes the fluffy white blanket over your bodies, but the warmth is nothing compared to the one radiating off his chest. “I think the phrase is ‘cold feet’, Harry.” 

Harry laughs; beautiful and soft and tickling your ear. He hugs you tighter to him and kisses just above your brow. 

"Silly,” he murmurs, “I’m talking about how cold your toes are against my leg and how I really wouldn’t want it any other way.”


i was so please with my religious studies cootie-catcher that i decided to do one for my geometry formulas too! i really like the colours on this one (though they’re a little hard to see) and these are really portable (they easily fold up even smaller than in the first image) and just overall i find them really fun to make!