**The Twelve Days of Christmas and Tetrahedral Numbers**

- The Twelve Days of Christmas and Tetrahedral Numbers
- Computing tetrahedral numbers
- Triangular number formula (Challenge #8)
- Binomial coefficients
- Challenge #8 solution
- Binomial coefficients and Pascal’s triangle
- Tetrahedral numbers, exposed!

**Fibonacci numbers and the golden ratio**

- Golden ratio properties (Challenge #10)
- Challenge #10 Solution
- Golden powers
- Explicit Fibonacci numbers

**Perfect numbers**

- Perfect numbers, part I
- Perfect numbers, part II
- Perfect numbers, interlude (Challenge #11)
- Perfect numbers, part III

**Recounting the Rationals**

- Recounting the Rationals, part I
- Recounting the Rationals, part II (fractions grow on trees!)
- Recounting the Rationals, part III
- Recounting the Rationals, part IV
- Recounting the Rationals, part IVb: the Euclidean Algorithm
- Challenge #12: sums of powers of two
- Challenge #12 solution, part II
- More hyperbinary fun
- Hyperbinary conjecture seeking proof for a good time, long walks on the beach
- The hyperbinary sequence and the Calkin-Wilf tree

**Rational and irrational numbers**

- Rational and irrational numbers
- Rational numbers and decimal expansions
- Decimal expansion zoo
- More on decimal expansions
- More on repetend lengths

**Predicting Pi**

**Irrationality of pi**

- Irrationality of pi
- Irrationality of pi: the unpossible function
- Irrationality of pi: derivatives of f
- Irrationality of pi: curiouser and curiouser
- Irrationality of pi: the impossible integral
- Irrationality of pi: the integral that wasn’t

**Decadic numbers**

- A curiosity
- An invitation to a funny number system
- What does “close to” mean?
- The decadic metric
- Infinite decadic numbers
- More fun with infinite decadic numbers
- A self-square number
- u-tube
- Computing with decadic numbers

**A combinatorial proof**

- Differences of powers of consecutive integers
- Differences of powers of consecutive integers, part II
- Combinatorial proofs
- Making our equation count
- How to explain the principle of inclusion-exclusion?
- PIE Day
**More to come…**

**What I Do**

- What I Do: Part 0
- What I Do, Part 1: Programming languages
**More to come…**

**MaBloWriMo 2015: The Lucas-Lehmer Test and Group Theory**

- The Lucas-Lehmer test
- Mersenne composites
- Mersenne composites in binary
- not all prime-index Mersenne numbers are prime
- The Lucas-Lehmer Test
- The Proof Begins
- s via omega
- definition of s and mod
- omega and its ilk
- Groups
- Examples of Groups
- Groups and Order
- Elements of finite groups have an order
- Element orders are no greater than group size
- One more fact about element orders
- Recap and outline
- X marks the spot
- X is not a group
- groups from monoids
- the group X star
- the order of omega, part I
- the order of omega, part II
- contradiction!
- Bezout’s identity
- Subgroups
- Left cosets
- From subgroups to equivalence relations
- Equivalence relations are partitions
- Equivalence classes are cosets
- Cyclic subgroups

**The chocolate bar game**

- Visualizing nim-like games
- The chocolate bar game
- The chocolate bar game: losing positions in binary
- The chocolate bar game: losing positions characterized
- The chocolate bar game: losing positions proved
- The chocolate bar game: variants

**Fibonacci numbers and golden numbers**

- Testing Fibonacci numbers
- Testing Fibonacci numbers: the proofs
- Fibonacci numbers are golden
- Golden numbers are Fibonacci

**Apollonian gaskets and Descartes’ theorem**

- Post without words #6
- Apollonian gaskets
- Apollonian gaskets and Descartes’ Theorem
- Apollonian gaskets and Descartes’ Theorem II

**Roots of unity and the Möbius function**

- Post without words #10
- A few words about PWW #10
- Post without words #11
- Totient sums
- Complexifying our dots
- Complex multiplication and roots of unity
- Complex multiplication: proof
- Primitive roots of unity
- Sums and symmetry

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