I am using Ubuntu 12.04 and want to use python 3.4 side by side with python 2.7.
The installation of python 3.4 worked properly. However, I cannot install the numpy
You have not installed the Python 3 development package. Install python3.4-dev:
apt-get install python3.4-dev
The main package never includes the development headers; Debian (and by extension Ubuntu) package policy is to put those into a separate -dev package. To install numpy however, you need these files to be able to compile the extension.