Analysis
Subcategories
Puzzles
- additive.partitionCan the set of positive reals be partitioned into two nonempty sets, both of which are closed under addition? New
- alternating.seriesGive a concise proof that, asymptotically as n grows, New
- am.gm.boundGiven real a1, a2, ..., an with arithmetic mean A and geometric mean G, show that New, unsolved
- bicycleA boy, a girl and a dog go for a 10 mile walk.
- boy.girl.dogA boy, a girl and a dog are standing together on a long, straight road.
- bugsFour bugs are placed at the corners of a square.
- buridanA driver leaves home and drives along a road with a railway crossing, and a train will pass the crossing at some time. New
- c.infinityWhat function is zero at zero, strictly positive elsewhere, infinitely differentiable at zero and has all...
- cacheCache and Ferry (How far can a truck go in a desert?) A pick-up truck in the desert gets 10 miles per... Added material
- calculate.piHow can I calculate many digits of pi? Added material
- cats.and.ratsIf 6 cats can kill 6 rats in 6 minutes, how many cats does it take to kill one rat in one minute?
- cauchy.completenessCan the monotone convergence theorem (every bounded monotone sequence of real numbers has a limit) be... New
- cylinderA right circular cylindrical container with a closed top is to be constructed with a fixed surface area. New
- derivation.algebrasClassify the vector spaces with an associative product and a nonzero derivation d(ab) = da b + a db. New, unsolved
- dogA body of soldiers form a 50m-by-50m square ABCD on the parade ground. Added material
- e.and.piWithout finding their numerical values, which is greater, e^(pi) or (pi)^e?
- euler.constantIs there a reference for this approximation to Euler's constant, and is there a faster expression? New, unsolved
- find.the.errorFind the error in each of these two "paradoxes". New, unsolved
- goatA goat grazes on a circular meadow, its tail is tacked to a stake of the fence - What's the length of the... Added material
- integralIf f is integrable on (0,inf) and differentiable at 0, and a > 0, and:
- integral.kernelIf f and g are positive continuous functions on [0,1], k is a positive continuous kernel on [0,1]x[0,1],... New
- integration.by.partsWhat is wrong with this proof, by integration by parts, that 0 = 1? New, unsolved
- irrational.stampYou have an ink stamp which is so amazingly precise that, when inked and pressed down on the plane, it...
- matrix.exponentialHow do you compute the exponential exp(B) of a matrix B? New
- minimum.timeN people can walk or drive in a two-seater to go from city A to city B.
- multiple.regressionHow should one compute a multiple linear regression, which amounts to solving a symmetric system of... New
- nested.square.rootsWhat is the value of x = sqrt( 2 + sqrt( 2 + sqrt( 2 + sqrt( 2 + ...))))? New
- particleWhat is the longest time that a particle can take in travelling between two points if it never increases...
- periodWhat is the least possible integral period of the sum of functions of periods 3 and 6?
- pig.and.farmerA pig runs from one corner of a square pen toward the gate at an adjacent corner while the farmer, starting... New
- point.nine.repeatingIs 0.999... (nines repeating forever) equal to 1? New
- quaternionsCan every polynomial with quaternion coefficients be factored into linear factors? New
- rubberbandA bug walks down a rubber band which is attached to a wall at one end and a car moving away from the wall at the other end. Added material
- sequenceShow that in the sequence: x, 2x, 3x, ....
- snowSnow starts falling before noon on a cold December day. Added material
- step.functionThe function f is defined on the integers in the range 0..100 by the rule: New
- surreal.numbersWhat are Conway's surreal numbers, and how do they make things such as 1/infinity rigorous? New
- towerR = N ^ (N ^ (N ^ ...)). Added material
- two.to.one.functionIs it possible to construct a function f(x) which maps the closed interval [0,1] to [0,1] such that any... New
- well.orderingSet theory says (using the Axiom of Choice) that every set can be well ordered; how can that be, when the... New