Mathematics

This page is a list of mathematics articles in Mathematics and Multimedia. You might also want to check the Post List page which contains the newest posts in major categories.

The complete list of posts arranged by month can be found in the Archives page.

NUMBERS/NUMBER THEORY

  1. Division by 0
  2. Rational and Irrational Numbers
  3. Counting the Infinite: A Glimpse at Infinite Sets
  4. Is 0.999… really equal to 1?
  5. Prime Series 1: Introduction to Prime Numbers
  6. Prime Series 2: The Intuition Behind the Infinitude of Primes
  7. Prime Series 3: Proof of the Infinitude of Primes
  8. Making Sense of Exponential Growth
  9. Counting the Real Numbers
  10. Young Gauss and the Sum of the First n Positive Integers
  11. Dominoes and Mathematical Induction
  12. Pythagorean Triple 1: The Infinitude of Pythagorean Triples
  13. Pythagorean Triple 2: Generating Pythagorean Triples
  14. Large Numbers and One Million
  15. Light Year and the Mathematics of the Stars
  16. The Geometry of Commutativity
  17. The Distributive Property
  18. The Commutativity of Real Numbers
  19. Military Drills and the Closure Property of Real Numbers
  20. Finger Math 1: Finger Multiplication
  21. Finger Math 2: Why Finger Multiplication Works
  22. Understanding Fermat’s Last Theorem
  23. Irrational Numbers as Decimals
  24. Order of Operations: 360 or 354?
  25. The mysterious 495
  26. The mystery of 495 exlpained
  27. The Golden Ratio
  28. The Kaprekar constant 6714
  29. Operations on Integers – Addition
  30. Operations on Integers – Subtraction
  31. Real Numbers: A summary
  32. Is 0 a natural number?
  33. Multiplication of Fractions
  34. Linking sum of counting numbers to triangle area
  35. Pi to 10 Trillion Digits
  36. Using Area to Prove the Arithmetic Mean-Geometric Mean Inequality
  37. Another Proof of the Sum of the First n Positive Integers
  38. Counting the Number of Squares on a Chess Board
  39. Prime or Not: Determining Primes Through Square Root
  40. Triangular Numbers and the Sum of the First n Positive Integers
  41. Introduction to Clock Arithmetic and Modular Systems
  42. Clock Arithmetic and Modular Systems Part 2
  43. Introduction to Number Bases
  44. Why Expressions with Negative Exponents Equal their Reciprocals
  45. Finding the General Formula for the kth Polygonal Number
  46. Why are Non-terminating, Repeating Decimals Rational
  47. Are all objects with irrational lengths measureable?
  48. Approximating Square Root of Numbers by Averaging
  49. How Big is Infinity?
  50. The Definition of Congruence in the Modular Systems
  51. The Clock Arithmetic and Modular Systems Series
  52. Guest Post: An Interesting Property of Prime Numbers
  53. Why The Addition Number Trick Works
  54. Properties of Addition and Multiplication of Real Numbers
  55. Are all fractions rational numbers?

Complex Numbers Series

  1. What is i? What are imaginary numbers?
  2. Complex Numbers and Their Properties
  3. Demystifying Complex Conjugates
  4. Introduction to the Complex Plane

 The Divisibility Series

ALGEBRA

  1. Making Connection Between Distance and Absolute Value
  2. Letters, Variables and Algebraic Expressions
  3. Matchsticks, Linear Relations, and Multiple Representations
  4. Equation of a line: The derivation of y = mx + b
  5. Slope Concept 1 – Understanding the Basic Concepts of Slope
  6. Slope Concept 2 – Slope of the Graph of a Linear Function
  7. Slope Concept 3 – Slopes of Vertical and Horizontal Lines
  8. Arithmetic Sequences and Linear Functions
  9. Derivation of the Quadratic Formula
  10. Understanding the Meaning of Discriminant
  11. Geometric Sequences and Series
  12. Why do we reverse the inequality sign?
  13. Why is any number raised to 0 equals 1?
  14. Why is zero factorial equals 1?
  15. How to use the summation symbol
  16. Compound Interest and the Irrational Number e
  17. Functions 1: Introduction to the Concept of Functions
  18. Functions 2: Basic Concepts of Functions
  19. Vectors, Parallelograms and Commutativity
  20. Simon’s Favorite Factoring Trick
  21. Addition of Coordinates
  22. The Handshake Problem and Its Multiple Solutions
  23. The Multiplication Parabola
  24. Mathematical Equations and Their Properties
  25. The 12 days of Christmaths and the Triangular Numbers
  26. Why is the slope of a vertical line undefined?
  27. Deceptive and Misleading Mathematical Patterns
  28. Visualizing the Difference of Two Squares
  29. Why is negative times negative equals positive?
  30. Guest Post: Why Study Algebra
  31. The Polynomials that Generate Prime Numbers

GEOMETRY

  1. Chess and Axiomatic Systems
  2. Angle Sum of Polygons
  3. Why is the angle sum of the interior angles of a triangle equal to 180 degrees?
  4. Parallel Lines and Transversals
  5. The Exterior Angle Theorem
  6. Is there an SSA Congruence?
  7. Making Connections among Pythagorean Theorem, Distance Formula and Equation of a Circle.
  8. The Algebraic and Geometric Proof of Pythagorean Theorem
  9. Tessellation: The Mathematics of Tiling
  10. Is a square a rectangle?
  11. The Inscribed Angle Theorem
  12. Demystifying Triangle Inequality
  13. Constructing Segments with Irrational Lengths
  14. Similarity 1: Introduction to Similarity
  15. Similarity 2: Properties of Similar Triangles 1
  16. Similarity 3: Properties of Similar Triangles Part 2
  17. A Closer Look at the Midpoint Formula
  18. Eratosthenes and the Earth’s Circumference
  19. Platonic Solids: Why only five of them?
  20. Regular Tessellations: Why only three of them?
  21. The Seven Bridges of Konigsberg
  22. Discovering Properties of Parallelograms
  23. The Marvels of the Nine-Point Circle
  24. Introduction to Coordinate Geometry
  25. Undefined terms: What are they?
  26. Diagonals of a Parallelogram
  27. A US President’s Proof of the Pythagorean Theorem
  28. Which is the most pleasing rectangle?
  29. Understanding the Meaning of Correspondence
  30. Introduction to Geometric Construction

Area Tutorial Series

  1. Area Tutorial 1 – Introduction to the Concept of Area
  2. Area Tutorial 2 – Area of a Triangle
  3. Area Tutorial 3 – Area of a Parallelogram
  4. Area Tutorial 4 – Area of a Circle
  5. Area Tutorial 5 – Area of a Trapezoid

TRIGONOMETRY AND PRECALCULUS

  1. Demystifying Degree and Radian Measures
  2. An elementary proof of the cosine law
  3. Folding a Hyperbola
  4. The Complements Theorem
  5. Pi and the Circle
  6. Jeepneys and Step Functions
  7. The Proof of the Tangent Half-Angle Formula
  8. Understanding Decreasing and Increasing Functions

Curve Sketching (New!)

  1. Graph Sketching 1: 4 Easy Ways to Graph a Linear Function
  2. Curve Sketching 2: Graphing Quadratic Functions
  3. Curve Sketching 3: Understanding Vertical and Horizontal Asymptotes
  4. Curve Sketching 4: Identifying Oblique Asymptotes

CALCULUS

  1. An Intituive Introduction to Limits
  2. An extensive explanation about the \epsilon-\delta definition of limits
  3. Limit by \epsilon-\delta proof: Example 1
  4. Limit by \epsilon-delta proof: Example 2
  5. Derivative Concept 1: The Algebraic and Geometric Meaning of Derivative
  6. Derivative Concept 2: Derivative in Real Life Context
  7. Derivative Concept 3: Derivative and the Maximum Area Problem
  8. Calculating the Area Under a Curve: An Intuitive Introduction

The Calculus Primer Series

  1. Motion and Graphs: A Calculus Primer
  2. A Calculus Primer Part 2
  3. A Calculus Primer Part 3

STATISTICS, PROBABILITY AND COMBINATORICS

  1. Introduction to Permutations
  2. Introduction to Combinations
  3. Binomial Theorem Series 1: Milkshakes, Beads, and Pascal’s Triangle
  4. Binomial Theorem Series 2: The Binomial Expansion
  5. A Gentle Introduction to Probability
  6. The Unfinished Game Problem
  7. Using Mathematics to Win the Lottery
  8. Storytelling and Statistics at their finest
  9. Ben Goldacre and Bad Statistics
  10. Understanding the Multiplication Principle
  11. Probability Terminologies and Notations
  12. Wedding Guests and Circular Permutations
  13. Understanding Sample Space and Sample Points
Experimental and Theoretical Probability Series

PROOFS

  1. Proof Tutorial 1: Introduction to Mathematical Proofs
  2. Proof Tutorial 2: Proving the Irrationality of Square Root of 2 by  Contradiction
  3. More examples of Proof by Contradiction
  4. Proof that log 2 is irrational
  5. Proof by Contradiction: Knights and Liars
  6. Another Proof of the Sum of the First n Positive Integers
  7. The Proof of the Tangent Half-Angle Formula
  8. A Simple Proof of the Arithmetic Mean Geometric Mean Inequality
  9. Using Similarity to Prove the Pythagorean Theorem
  10. Proof of the Sum of Square Numbers
  11. Mathematical Proofs Without Words: What are they?
  12. A Proof that the Vertex Angle Sum of a Pentagram is 180 degrees
  13. Proof without Words: Odds and Squares
  14. Understanding If Then Statements and Counterexamples

MATH LITE (Fun, Games, Puzzles, Trivia)

  1. Funny Math – 10 Steps you Need to Solve a Calculus Problem
  2. The Square Root of Three
  3. Why Mathematics Teachers Drink Part 1
  4. Why Mathematics Teachers Drink Part 2
  5. Men, Women, and Mathematics
  6. Amazing Number Patterns
  7. Simba sings math
  8. Math is …
  9. Nature by Numbers: Watch and fall in love with math
  10. Potato chips and mathematics
  11. Math Easter Egg
  12. Calculus Rhapsody
  13. Three
  14. Math Words in Filipino
  15. Calculating the volume of a pizza
  16. Math, Santa and Venn Diagrams
  17. Tangled and the Mathematics of Hairdressing
  18. The Beauty of Narcissistic Numbers
  19. Heart Graph for the Mathematically In Love
  20. Would you have given a different mark?
  21. Why Every Proof that 0.999… = 1 is Wrong
  22. Mathematics and Perspective
  23. Can you solve the hardest Sudoku puzzle yet?
  24. 11 Mathematical Proof Techniques Liberal Arts Majors Should Know
  25. Apple and the Golden Ratio?
  26. The Musical Beauty of Tau
  27. The Magic Circle Puzzle
  28. Teaching Math Like a Boss
  29. Who’s the Winner
  30. The Sound of Pi
  31. Grading Test Papers Like a Boss
  32. Watch Exceptional Fast-Paced Math Videos at Vi Hart
  33. How many squares are there?
  34. Pi In The Sky, Literally
  35. What if your paycheck…
  36. Matchsticks and Squares
  37. Origami and Its Surprising and Stunning Applications
  38. The Mathematics of Christmas Wrapping
  39. Taylor, Mathematics, and Perspective
  40. The Cycloid and the Pendulum Clock

MISCELLANEOUS Math Word Problem Solving Series Age Problems

  1. Solving Age Problems Part 2
  2. Solving Age Problems Part 3

Motion Problems

  1. Solving Motion Problems Part 1
  2. Solving Motion Problems Part 2
  3. Solving Motion Problems Part 3

Vedic Mathematics (by Sanjay Gulati)

  1. Introduction to Vedic Mathematics
  2. Squaring Numbers in 5
  3. Multiplication with a series of 9s
  4. Nikhilam Method of Multiplication
  5. Nikhilam Method of Multiplication 2
  6. Squaring Numbers: Part 1

Paper Folding

  1. Getting the square root of any  number on a number line
  2. Paper Folding: Extracting the cube root of a number
  3. Paper Folding: The proof of the cube root applet
  4. Origami and GeoGebra — a slightly different version

Set Theory

  1. Sets: A Gentle Introduction
  2. Subset: A set contained in a set
  3. Sets: Terminologies,  Notations, and Operations
  4. Counting the Number of Subsets in a Set
  5. Are all infinities created equal?

General Information/Miscellany

  1. The Mystery Behind the Proof of 1 = 2
  2. The Search for Magic Squares
  3. The definition of Undefined
  4. Is mathematics and exact science?
  5. Steven Strogatz
  6. Making Mathematicians I
  7. How do mathematicians greet happy valentines?
  8. SOMEBODY up there pushed me
  9. Would you have made it into Harvard in 1869?
  10. All time Top Mathematics Posts
  11. A Hundred Years Down the Road
  12. The man who conned a mathematician
  13. 10 Ways to Think Like a Mathematician
  14. Applying Mathematics to Web Design
  15. Mathematics and the Love of God?
  16. 25 Signs You’re a Future Mathematician
  17. Who Owns the Zebra?
  18. Lottery Math — If you play, you should know your odds
  19. The Mathematics of Leap Years Explained
  20. The 10 Misfortunes of Evariste Galois
  21. Where is the Nobel Prize in Mathematics?
  22. Millenium Prize Problems: Problems Worth $1M Each
  23. 7 Extraordinary Mathematicians You Should Know About
  24. The Actual Fermat-Pascal Correspondence

MATH RESOURCES/FREEBIES

  1. More than 20,000 contest problems and solutions
  2. 8000+ Math, Physics, and Engineering applets
  3. Calculus 1 Video Lectures
  4. 8 Free Online Graphing Tools
  5. Mu Alpha Theta: 10,000+ Math Contest Problems with Solutions
  6. Wholemovement and The Art of Folding Circles
  7. The Prime Composite Dance

MATH TEACHING AND PEDAGOGY

  1. Math Exercise, Problem Solving, and Investigation
  2. The Inverted Classroom
  3. Conrad Wolfram: Teaching kids real math with computers
  4. When do mathematical definitions matter?
  5. Exploring Computational Thinking
  6. Math Curriculum Makeover
  7. What is Universal Design Learning
  8. Popularizing Lesson Study
  9. Using Paper Folding to Introduce the Notion of Proof
  10. 10 Tips in Studying School Mathematics
  11. Constructing Open -Ended Math Problems
  12. A Mathematician’s Lament
  13. 10 Reasons Why Mathematics Teachers Should Blog
  14. An Open Letter to New Teachers
  15. Common Errors in MDAS Operations
  16. PEMDAS and the Common Errors in the Order of Operations
  17. 4 Common Errors in Calculating Expressions with Exponents
  18. The Trigonometric Ratio Hexagon

14 thoughts on “Mathematics

  1. Why 0.999999999… = 1?
    This equality usually surprises everybody. This is a short explanation:
    Clearly
    0.3333333333… = 1/3
    Multiply both members by 3:
    3*0.3333333333… = 0.99999999999… = 3*(1/3) = 1

  2. Another way to go…
    x = 0.999999999…
    10x = 9.999999999…
    Subtract the two and the infinite decimals cancel out
    10x – x = 9x =9
    x = 1
    Hence 0.999999999… = 1

  3. sir saan po b pwede ma view ung mga sagot sa questionare ng math sa ALL-UP workers uniion CSC review..

    maraming salamat po!

  4. I am a Math Teacher and I want to learn more tricks and new techniques in teaching mathematics. So that, I can make teaching and learning more fun and enjoyable. Through this website you really help us teachers learn more and make learning mathematics easier to our students. Good job!

  5. To Whom It May Concern,

    BSE grad po ako major in Math…To be honest po..tagal ko na pong di nagturo ..last turo ko po ay year 2000 pa and di ko pa po nagagamit ang major ko sa pagtuturo..Nag try po ako na mag apply sa public para magturo but they have told me na I need to take refresher course….I was thinking na instead of taking refresher course…will enter private school, and when I’ve found this site…so thankful …dahil malaki pong bagay ang ginawa niya to those teachers na need ng references na mapagaaralan…oo nga po pala..may teaching demo po ako this coming Tuesday (April 29, 2014)..the lesson is about ” SOLVING QUADRATIC EQUATION BY FACTORING”…dahil sa tagal ko na po di nagturo…yung style po ng lesson plan na alam ko ay old style na po..puwede niyo po ba ako i guide..for sample lesson plan about this topic? Your help would be highly appreciated..About po dun sa lesson…alam ko na po yung subject…kaya lang po ung outline ng lesson plan ang wala ho ako idea…Please do help me..thanks po

    • Ms. Carmela,

      Honestly, I don’t have any idea of what kind of lesson plans DepEd requires. I don’t teach in basic education, I am working in a teacher training institute, so our lesson plans are really for training and not for classroom use. In my opinion, hindi naman ganun ka-crucial ang lesson plan sa demo, ang importante siguro ay madeliver nyo ng maayos. However, if you are concerned about it, maybe you can ask high school teachers.

      If I will be observing you, siguro hahanapin ko sa lesson plan mo ang problem, possible solutions, at guide questions na itatanong mo during the demo. Hindi ko lang alam kung ganon dun ang iniisip ng magoobserve sayo. 🙂

      Guillermo

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