The Imaginary Power Tower: Part II

This is a continuation of last week's post: LINK The complex power tower is defined by an `infinite tower' of exponents: $latex \displaystyle Z(z) = {z^{z^{z^{.^{.^{.}}}}}} \,. &fg=000000$ The sequence of successive approximations to this function is $latex z_0 = 1 \qquad z_{1} = z \qquad z_{2} = z^{z} \qquad \dots \qquad z_{n+1} = z^{z_n} … Continue reading The Imaginary Power Tower: Part II →

The Imaginary Power Tower: Part I

The function defined by an `infinite tower' of exponents, $latex \displaystyle y(x) = {x^{x^{x^{.^{.^{.}}}}}} &fg=000000$ is called the Power Tower function. We consider the sequence of successive approximations to this function: $latex \displaystyle y_0 = 1 \qquad y_1 = x \qquad \dots \qquad y_{n+1} = x^{y_n} \,. &fg=000000$ As $latex {n\rightarrow\infty}&fg=000000$, the sequence $latex {\{y_n\}}&fg=000000$ converges for … Continue reading The Imaginary Power Tower: Part I →

Computus: Dating the Resurrection

Whatever the weather, St Patrick's Day occurs on the same date every year. In contrast, Easter springs back and forth in an apparently chaotic manner. The date on which the Resurrection is celebrated is determined by a complicated convolution of astronomy, mathematics and theology, an algorithm or recipe that fixes the date in accordance with … Continue reading Computus: Dating the Resurrection →

Peano Music

The links between mathematics and music are manifold. Mathematics can be set to music in a simple but surprising manner. For the award ceremony of the Gödel Medal in 2014, a musical interpretation of Gödel's incompleteness Theorems was written by Danish composer Niels Marthinsen. It encodes the basic axioms of number theory that form the … Continue reading Peano Music →

The Abel Prize – The Nobel Prize for Mathematics

There is no Nobel Prize for mathematics, but there is a close equivalent: The prestigious Abel Medal is awarded every year for outstanding work in mathematics [TM086, or search for “thatsmaths” at irishtimes.com]. This years winner, or winners, will be announced soon. When Alfred Nobel's will appeared, the absence of any provision for a prize … Continue reading The Abel Prize – The Nobel Prize for Mathematics →