They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli’s scheme and theorem, the ...

PDF for mathematics from the official Punjab Board website. Access chapter-wise details for mathematics with the link to ...

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380-year-old Descartes circle problem finally solved with help from physics Researchers explained that spinors, commonly used in quantum mechanics, played a key role in cracking the ancient puzzle ...

Left, a 3-flower. Right, a 5-flower. Credit: Journal of Geometry and Physics, 10.1016/j.geomphys.2025.105458 Monash University researchers have extended Descartes’ Circle Theorem by finding a general ...

Recent experiments in circuit quantum electrodynamics and electric circuit networks have demonstrated the coherent propagation of wave-like excitations on hyperbolic lattices. The negative curvature ...

Schertz, R. (2006) On the Generalized Principal Ideal Theorem of Complex Multiplication. Journal de Thorie des Nombres de Bordeaux, 18, 683-691.

The theorem of Thales and the theorem of Pythagoras do not escape the rule, and they seem to have been preceded by several millennia. Asking the true paternity of those geometrical realities makes it ...

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