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The article discusses several unequal tangent problems. The author examines whether there exist a pair of simple closed curves and asserts that when dealing with a smooth curve, a chord determines the tangent directions at its end-points. It states that a binormal chord automatically gives a bitangent circle with its center concurring with the midpoint of the chord, which gives a point at infinity on the equitangent locus.

The article presents the computation of Σ 1/n2 by solving triangles. A geometric method for determining the exact value of Σ 1/n2 is through basic trigonometry using the sine rule for triangles in combination with area-preserving maps. It presents a computation that uses the bipolar coordinates and the (co)sine rule, and spreading and piling of squares. Theorems include the Jacobian determinant of the area-preserving map, area-preserving bijective map permutes the amoeba subsets, and others.

The article explains the several connections between Sudoku puzzle and various parts of mathematics and statistics. It also defines gerechite designs, how they can be enumerated and describes their use in statistics and the kinds and properties that statisticians require of the designs they use. The authors note that the solution to a Sudoku puzzle is a special case of a gerechte designs, in which an n x n grid is partitioned into n regions with n square each, and each of the number symbols occurs once in each row, column or region. Some of the special types of Sudoku solution and generalizations are described.

The article presents information on a simplified mathematical approach which is used to measure differentiation in mathematics. This approach uses a local maximal function developed and employed by researchers to deal with limit theorems in various mathematics setting. The principal device of this approach is to differentiate a local maximal function defined in terms of a finite Borel measure and Lebesgue measure. This approach has cut almost half the time spent by researchers in covering mathematical topics.

The article offers an annotation to the mathematical congruence (mdnd) ≡ (mn) (modq). Mathematical problems that involve binomial coefficients modulo a prime power have been the focus of many great mathematicians of the 19th century. These mathematicians have derived different theorems that could be easily proved. One of these theorems is the congruence (mdnd) ≡ (mn) (modq). The author presented a partial converse theorem based on this established equation and observed that the same products of binomial coefficients are established on the right of Lucas's theorem.

The article presents the mathematical analysis of q-analogue of wolstenholme's harmonic series congruence. It is stated that congruence is considered over the ring of the polynomials in the variable q with integral coefficients.

Provides a solution for a three-point characterization of central symmetry curve. Theorem for the characterization of centrally symmetric curve; Proof of the equation; Method to check the equation and satisfy three-point property.