https://liberty.io/orthogonal-position-and-velocity-vectors.htmlBuzz Spill Dailyen2026-08-11T19:44:25-04:00Orthogonal Position and Velocity Vectorshttps://liberty.io/lower-bound-on-tail-probabilities.htmlBuzz Spill Dailyen2026-08-11T19:44:08-04:00Lower bound on Tail Probabilitieshttps://liberty.io/intuitive-and-memorable-way-to-see-n1-n1-n2-as-distinct-permutations-o.htmlBuzz Spill Dailyen2026-08-11T19:36:17-04:00Intuitive and memorable way to see N1/n1!n2! as distinct permutations of N objects with n1 of one type and n2 of other. N = n1+n2https://liberty.io/eigenspace-definition.htmlBuzz Spill Dailyen2026-08-11T19:34:51-04:00Eigenspace definitionhttps://liberty.io/proving-cos-4-theta-4-cos-2-theta-equiv-8-sin-4-theta-3.htmlBuzz Spill Dailyen2026-08-11T19:25:37-04:00Proving $\cos(4\theta) - 4\cos(2\theta) \equiv 8\sin^4\theta - 3$.https://liberty.io/the-significance-and-acceptance-of-helfgott-s-proof-of-the-weak-goldba.htmlBuzz Spill Dailyen2026-08-11T19:25:09-04:00The significance and acceptance of Helfgott’s proof of the weak Goldbach Conjecturehttps://liberty.io/proof-of-pythagorean-theorem-without-using-geometry-for-a-high-school-.htmlBuzz Spill Dailyen2026-08-11T19:21:40-04:00Proof of Pythagorean theorem without using geometry for a high school student?https://liberty.io/how-is-a-general-case-equivalent-to-a-special-case-and-how-showing-a-s.htmlBuzz Spill Dailyen2026-08-11T19:18:19-04:00How is a general case equivalent to a special case and how showing a special case demonstrates a general case, in the proof of pythagoras theorem?https://liberty.io/is-heat-equation-is-also-called-as-thermal-diffusion-equation.htmlBuzz Spill Dailyen2026-08-11T19:12:24-04:00Is heat equation is also called as thermal diffusion equation?https://liberty.io/proof-of-yet-another-weyl-s-inequality-using-courant.htmlBuzz Spill Dailyen2026-08-11T19:12:23-04:00Proof of yet another Weyl’s inequality using Couranthttps://liberty.io/polar-equation-of-a-circle.htmlBuzz Spill Dailyen2026-08-11T19:08:27-04:00Polar equation of a circlehttps://liberty.io/numerically-calculate-the-second-left-hand-derivative.htmlBuzz Spill Dailyen2026-08-11T19:07:01-04:00Numerically calculate the second "left hand" derivativehttps://liberty.io/divisibility-criteria-of-24-why-is-this.htmlBuzz Spill Dailyen2026-08-11T18:52:47-04:00Divisibility criteria of 24. Why is this?https://liberty.io/differential-topology-versus-differential-geometry.htmlBuzz Spill Dailyen2026-08-11T18:48:31-04:00Differential topology versus differential geometryhttps://liberty.io/derivative-of-integral.htmlBuzz Spill Dailyen2026-08-11T18:41:08-04:00Derivative of Integralhttps://liberty.io/toy-examples-for-kan-extensions.htmlBuzz Spill Dailyen2026-08-11T18:38:24-04:00Toy examples for Kan extensionshttps://liberty.io/parabolic-points-and-curvature.htmlBuzz Spill Dailyen2026-08-11T18:22:40-04:00Parabolic points and curvature.https://liberty.io/find-the-perimeter-of-triangle-abc.htmlBuzz Spill Dailyen2026-08-11T18:21:06-04:00Find the perimeter of Triangle ABChttps://liberty.io/number-of-words-that-can-be-made-using-all-the-letters-of-the-word-w-i.htmlBuzz Spill Dailyen2026-08-11T18:19:20-04:00Number of words that can be made using all the letters of the word W, if Os as well as Is are separated is?https://liberty.io/square-of-a-differential-duplicate.htmlBuzz Spill Dailyen2026-08-11T18:15:33-04:00Square of a differential [duplicate]https://liberty.io/expected-value-of-a-the-estimate-of-bernoulli-distribution.htmlBuzz Spill Dailyen2026-08-11T18:15:10-04:00Expected value of a the estimate of Bernoulli distributionhttps://liberty.io/find-from-the-first-principle-the-derivative-of-sqrt-sin-2x.htmlBuzz Spill Dailyen2026-08-11T18:06:29-04:00Find, from the first principle, the derivative of $\sqrt {\sin (2x)}$https://liberty.io/how-to-find-the-percent-variation-in-y-is-explained-by-x.htmlBuzz Spill Dailyen2026-08-11T18:05:17-04:00How to find the percent variation in Y is explained by X?https://liberty.io/list-of-common-or-useful-limits-of-sequences-and-series.htmlBuzz Spill Dailyen2026-08-11T18:03:51-04:00List of Common or Useful Limits of Sequences and Serieshttps://liberty.io/how-can-you-show-that-the-center-of-mass-of-a-triangle-lies-on-the-med.htmlBuzz Spill Dailyen2026-08-11T17:45:07-04:00How can you show that the center of mass of a triangle lies on the medians?https://liberty.io/finding-maximum-height-with-initial-velocity.htmlBuzz Spill Dailyen2026-08-11T17:44:32-04:00Finding maximum height with initial velocity.https://liberty.io/identity-element-generating-a-cyclic-group.htmlBuzz Spill Dailyen2026-08-11T17:25:02-04:00Identity element generating a cyclic grouphttps://liberty.io/how-to-define-a-relation.htmlBuzz Spill Dailyen2026-08-11T17:14:32-04:00How to define a relationhttps://liberty.io/given-the-function-minimize-the-function-subject-to-the-constraint-lag.htmlBuzz Spill Dailyen2026-08-11T17:14:01-04:00Given the function, minimize the function subject to the constraint. (Lagrange&#039;s Multipliers)https://liberty.io/equation-of-a-line-that-passes-halfway-between-two-points-in-other-wor.htmlBuzz Spill Dailyen2026-08-11T16:59:07-04:00Equation of a line that passes halfway between two points (in other words, divides the space)https://liberty.io/is-there-an-integral-that-proves-pi-333-106.htmlBuzz Spill Dailyen2026-08-11T16:54:43-04:00Is there an integral that proves $\pi > 333/106$?https://liberty.io/curves-with-a-common-tangent-line.htmlBuzz Spill Dailyen2026-08-11T16:29:20-04:00Curves with a common tangent linehttps://liberty.io/solving-for-given-variable-how-to-solve.htmlBuzz Spill Dailyen2026-08-11T16:17:44-04:00Solving For Given Variable - How to Solvehttps://liberty.io/what-is-cumulative-logistic-distribution.htmlBuzz Spill Dailyen2026-08-11T16:11:06-04:00What is cumulative logistic distributionhttps://liberty.io/how-do-you-derive-the-formula-of-sin-a-b-from-cos-a-b-cos-a-cos-b-sin-.htmlBuzz Spill Dailyen2026-08-11T15:38:22-04:00How do you derive the formula of $\sin (a+b)$ from $\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$https://liberty.io/laplace-transform-to-solve-differential-equation-with-ivp-given-at-a-p.htmlBuzz Spill Dailyen2026-08-11T15:34:12-04:00Laplace Transform to solve differential equation (with IVP given at a point different from $0$)https://liberty.io/matrix-by-matrix-derivative-formula.htmlBuzz Spill Dailyen2026-08-11T15:31:07-04:00Matrix-by-matrix derivative formulahttps://liberty.io/the-meaning-of-differentiation-of-x-with-respect-to-y.htmlBuzz Spill Dailyen2026-08-11T15:28:43-04:00The meaning of differentiation of $x$ with respect to $y$https://liberty.io/round-table-seating-probability.htmlBuzz Spill Dailyen2026-08-11T15:26:42-04:00round table seating probabilityhttps://liberty.io/determinant-of-an-elementary-matrix.htmlBuzz Spill Dailyen2026-08-11T15:07:13-04:00Determinant of an elementary matrixhttps://liberty.io/third-order-linear-parabolic-pde.htmlBuzz Spill Dailyen2026-08-11T14:59:52-04:00Third-order Linear Parabolic PDEhttps://liberty.io/solving-system-of-differential-equations-using-runge-kutta-method.htmlBuzz Spill Dailyen2026-08-11T14:52:12-04:00Solving system of differential equations using Runge Kutta methodhttps://liberty.io/proving-that-pi-2x-2-pi-x.htmlBuzz Spill Dailyen2026-08-11T14:46:14-04:00Proving that $\pi(2x) < 2 \pi(x) $https://liberty.io/flipping-a-fraction-within-an-inequality.htmlBuzz Spill Dailyen2026-08-11T14:28:59-04:00Flipping a fraction within an Inequality?https://liberty.io/tetrahedron-packing-in-cube.htmlBuzz Spill Dailyen2026-08-11T14:11:37-04:00Tetrahedron packing in Cubehttps://liberty.io/how-can-you-visually-distinguish-between-a-parabola-and-hyperbola.htmlBuzz Spill Dailyen2026-08-11T14:05:09-04:00How can you visually distinguish between a parabola and hyperbola?https://liberty.io/solution-to-equations-in-3-variable-without-forming-a-cubic-polynomial.htmlBuzz Spill Dailyen2026-08-11T14:04:11-04:00Solution to equations in 3 variable without forming a cubic polynomialhttps://liberty.io/symbol-for-kernel-and-range-of-a-linear-transformation.htmlBuzz Spill Dailyen2026-08-11T13:58:40-04:00Symbol for kernel and range of a linear transformationhttps://liberty.io/what-does-x-2-1-mean.htmlBuzz Spill Dailyen2026-08-11T13:40:49-04:00what does $|x-2| < 1$ mean?https://liberty.io/is-there-a-geometric-interpretation-for-a-function-039-s-alpha-subleve.htmlBuzz Spill Dailyen2026-08-11T13:40:07-04:00Is there a geometric interpretation for a function&#039;s $\alpha$-sublevel set?https://liberty.io/study-according-to-the-values-of-x-the-relative-position-of-line-curve.htmlBuzz Spill Dailyen2026-08-11T13:37:43-04:00Study , according to the values of x , the relative position of line & Curvehttps://liberty.io/finding-all-real-zeros-of-the-polynomial.htmlBuzz Spill Dailyen2026-08-11T13:36:04-04:00Finding all real zeros of the polynomial?https://liberty.io/strategies-for-factoring-expressions-with-four-terms.htmlBuzz Spill Dailyen2026-08-11T13:33:22-04:00Strategies for Factoring Expressions with Four Termshttps://liberty.io/novikoff-039-s-proof-for-perceptron-convergence.htmlBuzz Spill Dailyen2026-08-11T13:25:05-04:00Novikoff &#039;s Proof for Perceptron Convergencehttps://liberty.io/simple-formula-for-a-sieries-like-1-2-5-10-20-50-100.htmlBuzz Spill Dailyen2026-08-11T13:20:43-04:00Simple formula for a sieries like 1, 2, 5, 10, 20, 50, 100, ...https://liberty.io/geometric-interpretation-of-eigendecomposition.htmlBuzz Spill Dailyen2026-08-11T13:18:59-04:00Geometric Interpretation of Eigendecompositionhttps://liberty.io/how-to-determine-the-right-side-of-the-dice.htmlBuzz Spill Dailyen2026-08-11T12:57:09-04:00how to determine the right side of the dicehttps://liberty.io/finding-partial-fractions-involving-complex-numbers-express-h-z-frac-2.htmlBuzz Spill Dailyen2026-08-11T12:56:57-04:00Finding partial fractions involving complex numbers: express $h(z) = \frac{2z + 4i}{z^2 + 2z + 2}$ as partial fractionshttps://liberty.io/cardinality-of-union-of-3-sets.htmlBuzz Spill Dailyen2026-08-11T12:52:28-04:00Cardinality of union of 3 setshttps://liberty.io/continuity-is-required-for-differentiability.htmlBuzz Spill Dailyen2026-08-11T12:48:10-04:00Continuity is required for differentiability?https://liberty.io/how-to-round-0-45-is-it-0-or-1.htmlBuzz Spill Dailyen2026-08-11T12:47:14-04:00How to round 0.45? Is it 0 or 1?https://liberty.io/how-was-this-approximation-of-pi-involving-sqrt-5-arrived-at.htmlBuzz Spill Dailyen2026-08-11T12:46:58-04:00How was this approximation of $\pi$ involving $\sqrt{5}$ arrived at?https://liberty.io/measurable-space-vs-measure-space.htmlBuzz Spill Dailyen2026-08-11T12:46:20-04:00Measurable Space VS Measure Spacehttps://liberty.io/using-conjugates-to-find-a-limit-with-a-cubic-root-lim-h-to-0-frac-sqr.htmlBuzz Spill Dailyen2026-08-11T12:45:30-04:00Using conjugates to find a limit with a cubic root: $\lim_{h\to 0}\frac{\sqrt[3]{h+1}-1}{h}$https://liberty.io/039-imperfect-039-numbers.htmlBuzz Spill Dailyen2026-08-11T12:40:07-04:00&#039;imperfect&#039; numbershttps://liberty.io/proof-with-double-counting.htmlBuzz Spill Dailyen2026-08-11T12:29:16-04:00proof with double countinghttps://liberty.io/evans-pde-5-17.htmlBuzz Spill Dailyen2026-08-11T12:13:45-04:00Evans PDE $5.17$https://liberty.io/eliminate-xy-term-of-conic.htmlBuzz Spill Dailyen2026-08-11T12:12:11-04:00Eliminate xy term of conichttps://liberty.io/proving-the-universal-mapping-property-for-polynomial-rings.htmlBuzz Spill Dailyen2026-08-11T12:09:12-04:00Proving the universal mapping property for polynomial ringshttps://liberty.io/proof-verification-if-the-diagonals-of-a-parallelogram-are-congruent-t.htmlBuzz Spill Dailyen2026-08-11T12:07:36-04:00Proof Verification: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectanglehttps://liberty.io/convolution-of-two-gaussians-is-a-gaussian.htmlBuzz Spill Dailyen2026-08-11T11:58:58-04:00Convolution of two Gaussians is a Gaussianhttps://liberty.io/user-basanta-raj-pahari-mathematics-stack-exchange.htmlBuzz Spill Dailyen2026-08-11T11:55:27-04:00User Basanta Raj Pahari - Mathematics Stack Exchangehttps://liberty.io/intuition-behind-the-ilate-rule.htmlBuzz Spill Dailyen2026-08-11T11:47:51-04:00Intuition behind the ILATE rulehttps://liberty.io/how-is-the-gradient-of-exponential-functions-with-different-bases-in-t.htmlBuzz Spill Dailyen2026-08-11T11:39:34-04:00How is the gradient of exponential functions with different bases (in the included table) worked out?https://liberty.io/a-question-concerning-an-exercise-from-tao-vu.htmlBuzz Spill Dailyen2026-08-11T11:30:34-04:00A question concerning an exercise from Tao Vuhttps://liberty.io/line-integral-vs-arc-length.htmlBuzz Spill Dailyen2026-08-11T11:12:57-04:00Line integral vs Arc Lengthhttps://liberty.io/what-does-it-mean-for-a-matrix-to-be-nearly-singular.htmlBuzz Spill Dailyen2026-08-11T11:01:03-04:00What does it mean for a matrix to be nearly singular?https://liberty.io/convert-rectangular-coordinate-3-0-to-polar-coordinate.htmlBuzz Spill Dailyen2026-08-11T11:00:44-04:00convert rectangular coordinate (-3,0) to polar coordinatehttps://liberty.io/finding-stagnation-points.htmlBuzz Spill Dailyen2026-08-11T10:59:39-04:00Finding Stagnation Pointshttps://liberty.io/how-to-calculate-the-surface-area-of-a-cube-given-a-diagonal.htmlBuzz Spill Dailyen2026-08-11T10:59:26-04:00How to calculate the surface area of a cube given a diagonal?https://liberty.io/how-do-i-get-the-square-root-of-a-complex-number.htmlBuzz Spill Dailyen2026-08-11T10:57:10-04:00How do I get the square root of a complex number?https://liberty.io/trigonometric-identities-like-a-sin-x-b-cos-y-cdots.htmlBuzz Spill Dailyen2026-08-11T10:35:56-04:00Trigonometric Identities Like $A \sin(x) + B \cos(y) = \cdots$https://liberty.io/platonic-solids-in-4d.htmlBuzz Spill Dailyen2026-08-11T10:29:46-04:00platonic solids in 4Dhttps://liberty.io/find-the-cosine-of-the-angle-abc.htmlBuzz Spill Dailyen2026-08-11T10:25:27-04:00find the cosine of the angle ABChttps://liberty.io/how-different-are-open-and-closed-intervals.htmlBuzz Spill Dailyen2026-08-11T10:24:59-04:00How different are open and closed intervals?https://liberty.io/is-there-a-category-of-categories.htmlBuzz Spill Dailyen2026-08-11T10:16:49-04:00Is there a category of categories?https://liberty.io/what-is-fog-x-f-g-x-f-x-fof-n-1-x-fog-2012-x-closed.htmlBuzz Spill Dailyen2026-08-11T10:12:26-04:00What is fog(x),f(g(x)),f"(x),fof^(n-1)(x), fog^2012(x)? [closed]https://liberty.io/int-1-sin-x-dx.htmlBuzz Spill Dailyen2026-08-11T10:11:31-04:00$\int 1/\sin(x)\ dx$https://liberty.io/winding-number-of-vector-field-on-surface.htmlBuzz Spill Dailyen2026-08-11T10:11:13-04:00Winding number of vector field on surfacehttps://liberty.io/average-area-of-the-shadow-of-a-convex-shape-closed.htmlBuzz Spill Dailyen2026-08-11T10:04:36-04:00Average area of the shadow of a convex shape [closed]https://liberty.io/ramsey-number-proof-r-3-3-3-3-leq-4-r-3-3-3-1-2.htmlBuzz Spill Dailyen2026-08-11T10:02:57-04:00Ramsey Number proof: $R(3,3,3,3)\leq 4(R(3,3,3)-1) + 2$https://liberty.io/need-help-with-solution-for-problem-a5-from-imo-2015-closed.htmlBuzz Spill Dailyen2026-08-11T10:00:42-04:00Need help with solution for problem A5 from IMO 2015 [closed]https://liberty.io/find-the-general-solution-to-the-ode.htmlBuzz Spill Dailyen2026-08-11T09:58:25-04:00Find the general solution to the ODE:https://liberty.io/how-to-prove-that-the-tangent-to-a-circle-is-perpendicular-to-the-radi.htmlBuzz Spill Dailyen2026-08-11T09:53:19-04:00How to prove that the tangent to a circle is perpendicular to the radius drawn to the point of contact?https://liberty.io/relation-betwen-coefficients-and-roots-of-a-polynomial-duplicate.htmlBuzz Spill Dailyen2026-08-11T09:49:15-04:00Relation betwen coefficients and roots of a polynomial [duplicate]https://liberty.io/determine-sqrt-1-50-cdot51-cdot52-cdot53-without-a-calculator.htmlBuzz Spill Dailyen2026-08-11T09:49:11-04:00Determine $\sqrt{1+50\cdot51\cdot52\cdot53}$ without a calculator?https://liberty.io/is-there-a-unique-minimal-expression-for-every-boolean-function.htmlBuzz Spill Dailyen2026-08-11T09:42:22-04:00Is there a unique minimal expression for every boolean function?https://liberty.io/prove-in-full-detail-that-the-set-is-a-vector-space.htmlBuzz Spill Dailyen2026-08-11T09:31:48-04:00Prove in full detail that the set is a vector spacehttps://liberty.io/physical-meaning-of-one-dimensional-heat-equation.htmlBuzz Spill Dailyen2026-08-11T09:25:25-04:00Physical meaning of one dimensional heat equation.https://liberty.io/is-the-absolute-value-function-a-linear-function.htmlBuzz Spill Dailyen2026-08-11T09:10:18-04:00Is the absolute value function a linear function?