Канал: Dr Barker

Functional Equation Problem: Find f(4)

Functional Equation Problem: Find f(4)

Beyond ½ a b sin(C)

Beyond ½ a b sin(C)

A Trick for Multiplication by 7

A Trick for Multiplication by 7

A Short Combinatorics Problem

A Short Combinatorics Problem

Powers of Non-Diagonalisable Matrices

Powers of Non-Diagonalisable Matrices

Why Is This Almost An Integer?

Why Is This Almost An Integer?

Intuition Behind The Cayley Hamilton Theorem

Intuition Behind The Cayley Hamilton Theorem

A Recurring Decimal Problem

A Recurring Decimal Problem

A Short Functional Equation Problem

A Short Functional Equation Problem

Integers as Sums of Fibonacci Numbers

Integers as Sums of Fibonacci Numbers

A Nested Square Root Problem

A Nested Square Root Problem

Which is Bigger? Tetration Edition

Which is Bigger? Tetration Edition

Can A Function Be Continuous At Only One Point?

Can A Function Be Continuous At Only One Point?

A Fibonacci Series Problem

A Fibonacci Series Problem

Gaussian Integral: Infinite Series Approach

Gaussian Integral: Infinite Series Approach

A Limit With A Cube Root

A Limit With A Cube Root

A Factorial Product Problem

A Factorial Product Problem

A Functional Equation Problem

A Functional Equation Problem

A Fun Exponential Equation

A Fun Exponential Equation

What Lies Above Pascal's Triangle?

What Lies Above Pascal's Triangle?

An Amazing Floor & Square Root Identity

An Amazing Floor & Square Root Identity

The Best Diagram for Angle Sum Identities

The Best Diagram for Angle Sum Identities

A Factor Tree Puzzle

A Factor Tree Puzzle

Convergence of an Interesting Series

Convergence of an Interesting Series

A Tricky Roots of Cubics Problem

A Tricky Roots of Cubics Problem

A Satisfying Divisibility Proof

A Satisfying Divisibility Proof

Finding the Area of a Region

Finding the Area of a Region

More Minimising Without Calculus

More Minimising Without Calculus

Finding the Range of a Function

Finding the Range of a Function

A Short Number Theory Proof

A Short Number Theory Proof

A Floor & Ceiling Equation

A Floor & Ceiling Equation

Minimising Without Calculus

Minimising Without Calculus

Two Neat Properties of Cardioids

Two Neat Properties of Cardioids

A Fun Twist on a Familiar Problem

A Fun Twist on a Familiar Problem

My Favourite Golden Ratio Fact

My Favourite Golden Ratio Fact

The Quadratic Formula No One Taught You

The Quadratic Formula No One Taught You

Can You Solve Without Finding x & y?

Can You Solve Without Finding x & y?

A Short Number Theory Problem

A Short Number Theory Problem

Similar Triangles in the Complex Plane

Similar Triangles in the Complex Plane

Proving A Crazy GCD Identity

Proving A Crazy GCD Identity

A Satisfying Number Theory Proof

A Satisfying Number Theory Proof

Median of Medians Puzzle

Median of Medians Puzzle

A Unique Proof Without Induction

A Unique Proof Without Induction

Solving a Matrix Equation

Solving a Matrix Equation

The Most Satisfying Proof: Product of 4 Consecutive Integers is not Square

The Most Satisfying Proof: Product of 4 Consecutive Integers is not Square

Solving a Compound Inequality

Solving a Compound Inequality

Solve & Sketch the Region

Solve & Sketch the Region

Two Proofs of a Useful Inequality

Two Proofs of a Useful Inequality

A Quick Solution Using Complex Numbers

A Quick Solution Using Complex Numbers

A Simple Sequence, with Fun Consequences

A Simple Sequence, with Fun Consequences

Equation of a Line in the Complex Plane

Equation of a Line in the Complex Plane

Why Your Ruler is Inefficient

Why Your Ruler is Inefficient

Evaluating an Infinite Series

Evaluating an Infinite Series

Find all Real Solutions

Find all Real Solutions

A Neat Application of Complex Numbers

A Neat Application of Complex Numbers

Can You Solve This Inequality?

Can You Solve This Inequality?

A Fun Definite Integral

A Fun Definite Integral

A Satisfying Property of Diagonals

A Satisfying Property of Diagonals

A Neat Product Inequality

A Neat Product Inequality

How Many Ways Are There To Draw This Graph?

How Many Ways Are There To Draw This Graph?

Factorisation using Matrices

Factorisation using Matrices

A 3D Lattice Problem

A 3D Lattice Problem

Rationalising the Denominator with a Cube Root

Rationalising the Denominator with a Cube Root

Domain & Range Problem: Solve for a

Domain & Range Problem: Solve for a

A Satisfying Combinatorics Problem

A Satisfying Combinatorics Problem

Find all Integer Solutions - A Modular Arithmetic Trick

Find all Integer Solutions - A Modular Arithmetic Trick

Summing Along Subsequences of the Exponential Function's Power Series

Summing Along Subsequences of the Exponential Function's Power Series

Proof Using Euler's Theorem: Rational Implies Recurring

Proof Using Euler's Theorem: Rational Implies Recurring

Sum of the First n Non-Square Integers

Sum of the First n Non-Square Integers

Another Ridiculous Approximation?

Another Ridiculous Approximation?

How Many Squares does the Diagonal of an m x n Rectangle Cross?

How Many Squares does the Diagonal of an m x n Rectangle Cross?

Find the Coefficient of x^105 in this Product

Find the Coefficient of x^105 in this Product

Two Unusual Proofs: Partial Sum of a Geometric Series

Two Unusual Proofs: Partial Sum of a Geometric Series

An Underrated Trick for Solving Equations | The Half-Angle Substitution

An Underrated Trick for Solving Equations | The Half-Angle Substitution

Can You Sketch This Region?

Can You Sketch This Region?

Where Did This Result Come From?

Where Did This Result Come From?

Interior & Boundary Points of Convex Sets in ℝ²

Interior & Boundary Points of Convex Sets in ℝ²

Can Numbers Like These Be Square?

Can Numbers Like These Be Square?

Solve this Complex Equation

Solve this Complex Equation

Are There Any Integer Solutions?

Are There Any Integer Solutions?

How Many Points Uniquely Define a Triangle?

How Many Points Uniquely Define a Triangle?

How Many Solutions? A General Approach

How Many Solutions? A General Approach

Can You Sketch This Graph?

Can You Sketch This Graph?

Arithmetico-Geometric Sequences

Arithmetico-Geometric Sequences

Last Digits of Fifth Powers

Last Digits of Fifth Powers

Polar Equations of Polygons

Polar Equations of Polygons

Consecutive Powers of 2 & 3

Consecutive Powers of 2 & 3

Counting Paths in Trees

Counting Paths in Trees

Find all Positive Integer Solutions

Find all Positive Integer Solutions

$Differentiating x^{1/n} from First Principles without Power Series$

Differentiating x^{1/n} from First Principles without Power Series

How to Avoid the Fibonacci Numbers

How to Avoid the Fibonacci Numbers

A Neat Simplification using Complex Numbers

A Neat Simplification using Complex Numbers

How Do They Come Up With This Stuff?

How Do They Come Up With This Stuff?

Find all Integer Solutions

Find all Integer Solutions

Very Special Triangles

Very Special Triangles

Easily Remember These Exact Values of Trig Functions

Easily Remember These Exact Values of Trig Functions

What about this Definition?

What about this Definition?

How Many Real Solutions?

How Many Real Solutions?

Angle Sum Formulae: Proof using Ptolemy's Theorem

Angle Sum Formulae: Proof using Ptolemy's Theorem

Fermat's Proof with Geometric Series: Integral of x^n

Fermat's Proof with Geometric Series: Integral of x^n

A Different Geometric Interpretation for the Scalar Triple Product

A Different Geometric Interpretation for the Scalar Triple Product

How to Sum the Factors of any Number

How to Sum the Factors of any Number

Proof using Complex Numbers: Ptolemy's Theorem

Proof using Complex Numbers: Ptolemy's Theorem

A Neat Property of Logarithmic Spirals

A Neat Property of Logarithmic Spirals

Differentiating the Scalar Triple Product

Differentiating the Scalar Triple Product

Solving a Quintic Equation

Solving a Quintic Equation

Trig Functions of Complex Numbers

Trig Functions of Complex Numbers

Generating Functions of (Eventually) Constant Sequences

Generating Functions of (Eventually) Constant Sequences

A Comparison of Methods

A Comparison of Methods

Fibonacci Variants

Fibonacci Variants

Reconstructing a Matrix from its Minors

Reconstructing a Matrix from its Minors

Find all Integer Solutions

Find all Integer Solutions

A Ridiculous Approximation

A Ridiculous Approximation

A Fun Way to Solve Cubics: Vieta's Substitution

A Fun Way to Solve Cubics: Vieta's Substitution

A Fun Problem from Hungary

A Fun Problem from Hungary

Finding Points at Rational Distances

Finding Points at Rational Distances

Solving a Complex Equation

Solving a Complex Equation

Understanding The Third Derivative Geometrically

Understanding The Third Derivative Geometrically

A Partial Sums Problem

A Partial Sums Problem

A Controversial Polynomial

A Controversial Polynomial

Slick Solutions to Functional Equations

Slick Solutions to Functional Equations

A Tricky Sum to Evaluate

A Tricky Sum to Evaluate

This Equation Describes all Circles in ℝ²

This Equation Describes all Circles in ℝ²

Solving an Unusual Equation

Solving an Unusual Equation

Sums of Digits of Square Numbers

Sums of Digits of Square Numbers

Rounding with the Floor Function

Rounding with the Floor Function

Taylor Series of Even/Odd Functions

Taylor Series of Even/Odd Functions

Divisibility Rules: Why are 3 & 9 Special?

Divisibility Rules: Why are 3 & 9 Special?

A Nice Property of Sums of Reciprocals

A Nice Property of Sums of Reciprocals

A Minimum/Maximum Puzzle

A Minimum/Maximum Puzzle

Proofs in Different Bases: √2 is Irrational

Proofs in Different Bases: √2 is Irrational

Area of a Triangle from Polar Coordinates

Area of a Triangle from Polar Coordinates

My New Favourite Trig Function

My New Favourite Trig Function

Create Your Own Arctan Problem

Create Your Own Arctan Problem

If I Rotate This, is it Still a Function?

If I Rotate This, is it Still a Function?

Cauchy-Schwarz: Proof using Jensen's Inequality

Cauchy-Schwarz: Proof using Jensen's Inequality

A Complex Proof of the Harmonic Addition Theorem

A Complex Proof of the Harmonic Addition Theorem

Wait... does this not work?

Wait... does this not work?

A Nice Geometry Problem

A Nice Geometry Problem

What are base -10 numbers?

What are base -10 numbers?

A Nice Trigonometry Problem

A Nice Trigonometry Problem

A Very Special Data Set

A Very Special Data Set

Sum of the First 1000 Integers Not To Contain the Digit 9

Sum of the First 1000 Integers Not To Contain the Digit 9

A Limit with an Elegant Solution

A Limit with an Elegant Solution

How is this Function Related to Square Numbers? (An Introduction to Generating Functions)

How is this Function Related to Square Numbers? (An Introduction to Generating Functions)

Evaluating a Limit using the Central Limit Theorem

Evaluating a Limit using the Central Limit Theorem

Volume of a Cone - An Unusual Proof

Volume of a Cone - An Unusual Proof

Midpoints Between Squares of Consecutive Integers

Midpoints Between Squares of Consecutive Integers

Solving a Combinatorics Problem with the First Moment Method

Solving a Combinatorics Problem with the First Moment Method

sin(n) does not converge - the subsequence approach

sin(n) does not converge - the subsequence approach

Squares Ending in Repeating Digits

Squares Ending in Repeating Digits

The Set of Convex Functions is Convex

The Set of Convex Functions is Convex

A Fun Number Theory Problem

A Fun Number Theory Problem

Fun with Mutual/Pairwise Independence

Fun with Mutual/Pairwise Independence

When is (m^6 + 27n^6)/(m^2 + 3n^2) prime?

When is (m^6 + 27n^6)/(m^2 + 3n^2) prime?

All Cubics have Rotational Symmetry

All Cubics have Rotational Symmetry

Binomial Distribution/Expansion - A Neat Connection

Binomial Distribution/Expansion - A Neat Connection

Test Your Intuition about Bijections

Test Your Intuition about Bijections

Infinitely Nested Integral Problem

Infinitely Nested Integral Problem

Lesser Known Formula for Sample Variance

Lesser Known Formula for Sample Variance

Why is the answer not e?

Why is the answer not e?

Create Your Own Jug Puzzle

Create Your Own Jug Puzzle

Can 3 Skew Lines be Equidistant?

Can 3 Skew Lines be Equidistant?

The Method No One Taught You - Finding the Tangent to a Curve

The Method No One Taught You - Finding the Tangent to a Curve

Galileo's Paradox of the Bowl

Galileo's Paradox of the Bowl

How can you tell that a Fixed-Point Iteration will Converge?

How can you tell that a Fixed-Point Iteration will Converge?

Evaluating a Limit of the Riemann Zeta Function

Evaluating a Limit of the Riemann Zeta Function

Can 3 Variables all be Negatively Correlated?

Can 3 Variables all be Negatively Correlated?

A Fibonacci AND Geometric Sequence

A Fibonacci AND Geometric Sequence

Every Random Variable is a Transformation of U[0,1] (Inverse Transform Sampling)

Every Random Variable is a Transformation of U[0,1] (Inverse Transform Sampling)

Tail Integral Formula for Moments (Integrated Tail Formula)

Tail Integral Formula for Moments (Integrated Tail Formula)

Infinite Dimensional Hypercube Graphs are Bipartite (feat. the Axiom of Choice)

Infinite Dimensional Hypercube Graphs are Bipartite (feat. the Axiom of Choice)

Tail Integral Formula for Expectation (Integrated Tail)

Tail Integral Formula for Expectation (Integrated Tail)

Reversing the Order of a Probability Tree Diagram

Reversing the Order of a Probability Tree Diagram

A Very Cool Trigonometric Identity

A Very Cool Trigonometric Identity

Tail Sum Formula for Expectation

Tail Sum Formula for Expectation

Geometric proof of sin(cos(x)) ≤ cos(sin(x))

Geometric proof of sin(cos(x)) ≤ cos(sin(x))

sin(cos(x)) ≤ cos(sin(x)) proof

sin(cos(x)) ≤ cos(sin(x)) proof

Proving Inequalities using Linear Algebra

Proving Inequalities using Linear Algebra

Can a Quadrilateral have Exactly 3 Lines of Symmetry?

Can a Quadrilateral have Exactly 3 Lines of Symmetry?

Sine Rule for Quadrilaterals

Sine Rule for Quadrilaterals

sin(314159...)

sin(314159...)

Hypercube Graphs are Bipartite

Hypercube Graphs are Bipartite

Borel's Paradox - Conditional Probability is not Well-Defined

Borel's Paradox - Conditional Probability is not Well-Defined

Intro to Hypercubes: A Coordinate Approach

Intro to Hypercubes: A Coordinate Approach

The Inspection Paradox Explained (Waiting Time Paradox)

The Inspection Paradox Explained (Waiting Time Paradox)

A Statistical Paradox? Different conclusions from the same data

A Statistical Paradox? Different conclusions from the same data

Differentiating sin and cos - a mechanics proof

Differentiating sin and cos - a mechanics proof

Same Integral, Different '+c'?

Same Integral, Different '+c'?

sin(n) does not converge - an elementary proof

sin(n) does not converge - an elementary proof

The Arithmetic-Geometric Mean: agm(x,y)

The Arithmetic-Geometric Mean: agm(x,y)

When Should I use the Geometric Mean?

When Should I use the Geometric Mean?

Binomial + Uniform = Uniform Distribution!

Binomial + Uniform = Uniform Distribution!

Definite Integral of arcsin(1/(x^2-1))

Definite Integral of arcsin(1/(x^2-1))

Who wins? e^e^n vs n^n

Who wins? e^e^n vs n^n

Geometry Problem: Find the Radius of the Smallest Circle.

Geometry Problem: Find the Radius of the Smallest Circle.

Euler Product Formula: A Proof using Probability

Euler Product Formula: A Proof using Probability

Exponential + Poisson = Geometric Distribution!

Exponential + Poisson = Geometric Distribution!

Definite Integral of sin(x+sin(x+sin(x)))

Definite Integral of sin(x+sin(x+sin(x)))

Geometry Problem: Find the Radius of the Small Circles.

Geometry Problem: Find the Radius of the Small Circles.