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March 17^{th} is celebrated by many as St. Patrick's Day, in honour of none other than the patron saint of Ireland, William Rowan Hamilton, who drove the discretization requirement out of classical mechanics... or something like that.
So listen to Finnegan's Wake Topology or some Danny Boy Surface, wear your Green's Function with pride else face a pinch point, have a pint of Beer–Lambert law, and enjoy a scholarly St. Patrick's Day. 
In knot theory, the trefoil (or cloverleaf) knot is the simplest nontrivial knot. Being the unique prime knot with three crossings, the cloverleaf knot has many exciting properties that make a little recreational knot theory perfect for St. Patrick's Day. The cloverleaf knot cannot be deformed continuously into its mirror image without tearing it, but it is invertible. It is the intersection of the unit 3sphere S^{3} in C^{2} with the complex plane curve of zeroes for the complex polynomial z^{2} + w^{3}. It can be described as a (2,3)torus knot and its complement in S^{3} is a fiber bundle over the circle S^{1}.
If you're looking for some knot(y) suggestions, and the trefoil is too boring on it's own, consider playing with its homotopic form or projection. Turning a penrose triangle inside out, Thaddeus M. Cowan, Journal of Mathematical Psychology. Volume 26, Issue 3, December 1982, Pages 252262. doi:10.1016/00222496(82)900049
The knotted hexagon, Adrian Baddeley, Lecture Notes in Mathematics; Combinatorial Mathematics V. 1977, Pages 5560. doi:10.1007/BFb0069176 If knot theory isn't your style, physicists have been making use of the trefoil for years. It turns out, the cloverleaf/trefoil leads to some beautiful equipotential designs. For more pages of pretty pictures: Cutoff space of cloverleaf resonators with electric and magnetic walls, J. Helszajn and D.J. Lynch, IEEE Transactions on Microwave Theory and Techniques, Volume 40, Issue 8, 1992, Pages 16201629. doi:10.1109/22.149540 If you want a little combination knot theory and condensed matter physics: LEFT: Observation of laserinduced microscale knotted and unknotted vortex filaments on vaporizing tantalum surface, S. Lugomer, Physical Review B, Volume 54, Issue 7, 1996, Pages 44884491. doi:10.1103/PhysRevB.54.4488 For a more natural feel, electron spin resonance spectroscopy even allows for some actual clover visuals. RIGHT: SURF_ER—surface electron spin resonance (ESR) of the surface domain of large objects, Th. Herrling, J. Rehberg, K. Jung and N. Grotha, Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, Volume 58, Issue 6, April 2002, Pages 13371344. doi:10.1016/S13861425(01)007235
If a little relativity and analogies are more your speed, consider a circular “Lineland” (a closed, 1D space); with singularities, it happens to look an awful lot like a clover. LEFT: Geometry, relativity, and the fourth dimension, Rudy von Bitter Rucker, Dover Publications, 1977. ISBN10: 0486234002 And that's not all the St. Patrick's themed fun from physics... 
So maybe a good integral kernel doesn’t scream “Happy St. Patrick’s Day” to you, but well all right, you’re probably not alone there. There are some mathematical functions, however, that do instill the spirit of the holiday: spherical harmonics, for example.
While an electron can technically be found at any distance from its associated atom, there are regions where the probability of finding it is greater. These regions are the familiar boundary surfaces (shown here in festive green). It is the Azimuthal quantum number (or the orbital angular momentum quantum number), l, that determines an orbital's shape (ie. it’s boundary surface) with the 3dimensional spherical harmonics, and the magnetic quantum number, m_{l}, that determines its orientation. The first four “shapes” are known as the s (l = 0), p, (l = 1), d, (l = 2), and f (l = 3), orbitals. The relevant St. Patrick’s Day orbitals are obviously the five “d” orbitals. They are sometimes described as “dumbbells” or, often more accurately, as the “cloverleaf” orbitals. In honour of the holiday, instead of using the tired mnemonic “some poor dumb fool” to remember the atomic orbital order, I think “St. Patrick’s Day Fun” might be more appropriate. 
March 17^{th}, 1764, Leonhard Euler wrote his final letter addressed to Christian Goldbach, finishing the famous 196 letter EulerGoldbach correspondance series [ref]. Euler may or may not have been aware that it was also St. Patrick's Day. In case the death of the patron saint of Ireland wasn't enough for you to throw a party, March 17^{th} holds many important anniversaries in the mathematical/physical sciences too.

Remember, like most holidays, St. Patrick’s Day is best celebrated with beer, a substance that is historically well appreciated by physicists. While the story of Donald Glaser being inspired by seeing the bubbles in a pint of beer to build the first Bubble Chamber is now known to be apocryphal, some of the early Bubble Chamber prototypes did actually use beer as the superheated liquid. Unfortunately for beer and Bubble Chamber enthusiasts, Glaser’s “experiments with beer left nothing but a stench in the room and raised a few eyebrows.”^{ [ref] }
Personally, I still think beer’s greatest achievement in physics was the 1920s opening of the Niels Bohr's Institute for Theoretical Physics, which was sponsored by the Carlsberg Brewery. The Carlsberg Foundation also paid for Bohr’s travel to England in 1911 to study with J.J. Thomson. 