Many numbers, if you repeatedly add them to the number formed by reversing their own digits, will eventually lead to a palindrome. For example: \begin{align} 7326 + 6237 &= 13563 \\ 13563 + 36531 &= 50094 \\ 50094 + 49005 &= 99099 \end{align} For most numbers, this happens with in fewer than 10 iterations. However, Wade in…
Puzzlebomb – December 2015
Puzzlebomb is a monthly puzzle compendium. Issue 48 of Puzzlebomb, for December 2015, can be found here: Puzzlebomb – Issue 48 – December 2015 The solutions to Issue 48 can be found here: Puzzlebomb – Issue 48 – December 2015 – Solutions Previous issues of Puzzlebomb, and their solutions, can be found at Puzzlebomb.co.uk.
Happy 200th Birthday, Ada Lovelace!
Today marks computing and maths pioneer Ada Lovelace’s 200th birthday. In celebration we’ve rounded up a few Ada-based links from around the internet. Ada Lovelace was a 19th-century mathematician and early computer scientist, during an era when it was uncommon for women to do such things, and worked alongside Charles Babbage. His incredible Analytical Engine,…
Aperiodvent, Day 10: The Basel Problem
Today’s entry is a Theorem of the Day: The Basel Problem: \[ \sum_{k=1}^\infty \frac{1}{k^2} = 1 + \frac{1}{4} + \frac{1}{9} + \cdots = \frac{\tau^2}{24} \] Originally posed in the 1640s, the value of this series was unknown until 1734 when it was solved by Euler. Many beautiful proofs exist; for some examples and more information,…
Aperiodvent, Day 9: Platonic solid decorations
This superb set of printable nets for platonic solids features a variety of Christmas-themed designs, including santa, snowflakes, and even the Baby Jesus (not sure what that has to do with Christmas, but ok). You can print, cut out and assemble the cubes, tetrahedra, octahedra, dodecahedra and icosahedra, and the tabs can be taped or…
Aperiodvent, Day 8: House of Graphs
The House of Graphs is a database of interesting graphs (not charts, plots or diagrams – but proper graphs with nodes and arcs). Searchable by a huge range of invariants, either for a specific value, or a range, or just that having an interesting value – plus, there’s a funky search tool where you can…
Aperiodvent, Day 7: Counterexamples
Pictured here is a connected but not locally-connected space, from the endlessly counter-intuitive blog, Math Counterexamples. It’s full of counterexamples that will challenge your preconceptions about everything from geometry to algebra to Fubini’s theorem. This is part of the Aperiodical Advent Calendar. We’ll be posting a new surprise for you each morning until Christmas!