geometry
From a smile to a line drawing by Picasso, curves bring great beauty to our world. But how curvy is a curve? 
Free kicks will deliver much of the drama in the football world cup this summer. But how should strikers approach them and how does the design on the ball impact on its behaviour in flight? Maths can give us answers... 
Imagine a circle with radius 1 cm rolling completely along the circumference of a circle with radius 4 cm. How many rotations did the smaller circle make? Be prepared for a surprise! 
Like spirals and flowers? Then you'll love polar coordinates and the pretty pictures they allow you to draw! 
Saul Schleimer and Henry Segerman show off some of their beautiful 3D printed mathematical structures. 

Did you learn at school that the angles in a triangle always add up to 180 degrees? If yes then your teacher was wrong. Find out why here. 
The Plus team's vehicle of choice is the bicycle, so we're particularly pleased about an announcement that hit the news this month: a clever car mirror that eliminates the dreaded blind spot has been given a patent in the US. The mirror was designed by the mathematician Andrew Hicks, of Drexel University, after years of puzzling over the problem. 
The Jerusalem Chords Bridge, Israel, was built to make way for the city's light rail train
system. Its design took into consideration more than just utility — it is a work of
art, designed as a monument. Its beauty rests not only in the visual appearance of its crisscross
cables, but also in the mathematics that lies behind it. So let's take a deeper look at it.

The only good thing about a washout summer is that you get to see lots of rainbows. Keats complained that a mathematical explanation of these marvels of nature robs them of their magic, conquering "all mysteries by rule and line". But rainbow geometry is just as elegant as the rainbows themselves. 