Author Archives: mzspivey

Infinite Series Expressions for Pi, E, Phi, and Gamma

Recently I was trying to find infinite series expressions for some famous mathematical constants, and I thought I would record what I found here.  This post considers , Euler’s constant e, the golden ratio , and the Euler-Mascheroni constant . … Continue reading

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Minimum Number of Wagons to Connect Every City in Ticket to Ride – Europe

How many wagons would you need to create a route network in the board game Ticket to Ride – Europe so that every city is connected to every other city through the network?  If you could do this you could potentially … Continue reading

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The Max Flow-Min Cut Theorem via Linear Programming Duality

The Max Flow-Min Cut Theorem states that the maximum flow from the source node to the sink node through a capacitated network is equal to the capacity of the minimum cut that separates that source node from the sink node.  … Continue reading

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Solving Second-Order Difference Equations with Constant Coefficients: Part II

In this post we’ll discuss the missing case from last month’s derivation of the solution for second-order difference equations with constant coefficients; namely, the case in which the characteristic equation has a repeated root rather than two distinct roots. Once … Continue reading

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Solving Second-Order Difference Equations with Constant Coefficients

Suppose you have a linear, homogeneous second-order difference equation with constant coefficients of the form .  The solution procedure is as follows: “Guess” a solution of the form .  Then substitute this guess into the difference equation to obtain .  … Continue reading

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Adventures in Fine Hall

The Princeton Alumni Weekly has a great article up about the mathematicians at Princeton and the Institute for Advanced Study in the 1930s and 1940s.  I’ve heard a lot of anecdotes about mathematicians over the years, but I had not … Continue reading

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A Quasiperfect Number Must Be an Odd Perfect Square

Let be the sum of divisors function.  For example, , as the divisors of 5 are 1 and 5.  Similarly, , as the divisors of 6 are 1, 2, 3, and 6. A perfect number is one that is equal … Continue reading

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