Measuring Solid Angles Beyond Dimension Three

Measuring Solid Angles Beyond Dimension Three

The dot product formula allows one to measure an angle determined by two vectors, and a formula known to Euler and Lagrange outputs the measure of a solid angle in R3 given its three spanning vectors. However, there appears to be no closed form expression for the measure of an n-dimensional solid angle for n > 3. We derive a multivariable (infinite) Taylor series expansion to measure a simplici...

Bounds for solid angles of lattices of rank three

We find sharp absolute constants C1 and C2 with the following property: every well-rounded lattice of rank 3 in a Euclidean space has a minimal basis so that the solid angle spanned by these basis vectors lies in the interval [C1, C2]. In fact, we show that these absolute bounds hold for a larger class of lattices than just well-rounded, and the upper bound holds for all. We state a technical c...

Improved technique for measuring small angles.

Based on the total-internal-reflection effect and heterodyne interferometry, an improved technique for measuring small angles is proposed. This technique not only expands the measurement range but it also improves measurement performances. Its validity is demonstrated.

Measuring Neutrino Mixing Angles at Lhc

We study an MSSM model with bilinear R-parity violation which is capable of explaining neutrino data while leading to testable predictions for ratios of LSP decay rates. Further, we estimate the precision with which such measurements could be carried out at the LHC.

Computing Solid Angles by Barycentric Subdivision ∗