We demonstrate theoretically and experimentally how highly multimodal high index contrast waveguides with micron-scale cores can be bent, on an ultra-broad band of operation, with bending radii below 10 µm and losses for the fundamental mode below 0.02 dB/90°. The bends have been designed based on the Euler spiral and fabricated on 4 µm thick SOI. The proposed approach enabled also the realization of 180° bends with 1.27 µm effective radii and 0.09 dB loss, which are the smallest low-loss bends ever reported for an optical waveguide. These results pave the way for unprecedented integration density in most semiconductor platforms.