YGYQZ Desk Folder Bombing free shipping Paper Storage Supp Desktop Organizers - Office YGYQZ Desk Folder Bombing free shipping Paper Storage Supp Desktop Organizers - Office $13 YGYQZ Desk Folder Paper Storage Organizers - Desktop Office Supp Office Products Office Furniture Lighting Cabinets, Racks Shelves -,smmahavidyalaya.org,Folder,Desktop,Supp,$13,Organizers,Storage,/defamed924131.html,Desk,Paper,Office,YGYQZ,Office Products , Office Furniture Lighting , Cabinets, Racks Shelves -,smmahavidyalaya.org,Folder,Desktop,Supp,$13,Organizers,Storage,/defamed924131.html,Desk,Paper,Office,YGYQZ,Office Products , Office Furniture Lighting , Cabinets, Racks Shelves $13 YGYQZ Desk Folder Paper Storage Organizers - Desktop Office Supp Office Products Office Furniture Lighting Cabinets, Racks Shelves

YGYQZ Desk Folder Boston Mall Bombing free shipping Paper Storage Supp Desktop Organizers - Office

YGYQZ Desk Folder Paper Storage Organizers - Desktop Office Supp

$13

YGYQZ Desk Folder Paper Storage Organizers - Desktop Office Supp

|||

Product Description

Office Supplies Desk File OrganizersOffice Supplies Desk File Organizers

Office supplies desktop folder storage organizers

  • Do you worry about your messy desktop?
  • Are you going to crash because the files are always messy and cannot be classified?
  • Are you crazy about your small items on the desk where there is nowhere to be easily lost?
  • Are you struggling to find a tool that can help you solve these problems but don't have results?

We bring you a good news. We have many styles of office file storage organizers. You can choose different styles of bookshelves according to the style of your office desk. It can help you solve all the above worries and give you a happy life. clean working and living environment

In fact, I believe you can’t wait, so just buy it and give you a comfortable environment.

YGYQZ Desk Folder Paper Storage Organizers - Desktop Office Supp


Earth System Models simulate the changing climate

Image credit: NASA.

The climate is changing, and we need to know what changes to expect and how soon to expect them. Earth system models, which simulate all relevant components of the Earth system, are the primary means of anticipating future changes of our climate [TM219 or search for “thatsmaths” at Insane Labz Hellboy Edition, High Stimulant Pre Workout Powder a].

ShareGoo RC 4Led LED Light Bar Headlight Metal Roof Lamp for Tra

The Signum Function may be Continuous

Abstract: Continuity is defined relative to a topology. For two distinct topological spaces and having the same underlying set but different families of open sets, a function may be continuous in one but discontinuous in the other. Continue reading ‘The Signum Function may be Continuous’

The Social Side of Mathematics

On a cold December night in 1976, a group of mathematicians assembled in a room in Trinity College Dublin for the inaugural meeting of the Irish Mathematical Society (IMS). Most European countries already had such societies, several going back hundreds of years, and it was felt that the establishment of an Irish society to promote the subject, foster research and support teaching of mathematics was timely [TM218 or search for “thatsmaths” at Women Maternity Swimsuit Cross Back One Piece Pregnant Monokini].

Continue reading ‘The Social Side of Mathematics’

Real Derivatives from Imaginary Increments

The solution of many problems requires us to compute derivatives. Complex step differentiation is a method of computing the first derivative of a real function, which circumvents the problem of roundoff error found with typical finite difference approximations.

Rounding error and formula error as functions of step size [Image from Wikimedia Commons].

For finite difference approximations, the choice of step size is crucial: if is too large, the estimate of the derivative is poor, due to truncation error; if is too small, subtraction will cause large rounding errors. The finite difference formulae are ill-conditioned and, if is very small, they produce zero values.

Where it can be applied, complex step differentiation provides a stable and accurate method for computing .

Continue reading ‘Real Derivatives from Imaginary Increments’

Changing Views on the Age of the Earth

[Image credit: NASA]

In 1650, the Earth was 4654 years old. In 1864 it was 100 million years old. In 1897, the upper limit was revised to 40 million years. Currently, we believe the age to be about 4.5 billion years. What will be the best guess in the year 2050? [TM217 or search for “thatsmaths” at Hollypet Pet Bed Warm Cave Animal Kitten Nest Sleeping Bed Puppy].

Continue reading ‘Changing Views on the Age of the Earth’

Carnival of Mathematics

The Aperiodical is described on its `About’ page as “a meeting-place for people who already know they like maths and would like to know more”. The Aperiodical coordinates the Carnival of Mathematics (CoM), a monthly blogging roundup hosted on a different blog each month. Generally, the posts describe a collection of interesting recent items on mathematics from around the internet. This month, it is the turn of thatsmaths.com to host CoM.
Continue reading ‘Carnival of Mathematics’

Phantom traffic-jams are all too real

Driving along the motorway on a busy day, you see brake-lights ahead and slow down until the flow grinds to a halt. The traffic stutters forward for five minutes or so until, mysteriously, the way ahead is clear again. But, before long, you arrive at the back of another stagnant queue. Hold-ups like this, with no apparent cause, are known as phantom traffic jams and you may experience several such delays on a journey of a few hours [TM216 or search for “thatsmaths” at Skinner's Vaporizing Salve, 7 oz.].

Traffic jams can have many causes [Image © Susanneiles.com. JPEG]

Continue reading ‘Phantom traffic-jams are all too real’

Simple Models of Atmospheric Vortices

Atmospheric circulation systems have a wide variety of structures and there is no single mechanistic model that describes all their characteristics. However, we can construct simple kinematic models that capture some primary aspects of the flow. For simplicity, we will concentrate on idealized extra-tropical depressions. We will not consider hurricanes and tropical storms in any detail, because the effects of moisture condensation and convection dominate their behaviour.

Continue reading ‘Simple Models of Atmospheric Vortices’

Finding Fixed Points

An isometry on a metric space is a one-to-one distance-preserving transformation on the space. The Euclidean group is the group of isometries of -dimensional Euclidean space. These are all the transformations that preserve the distance between any two points. The group depends on the dimension of the space. For the Euclidean plane , we have the group , comprising all combinations of translations, rotations and reflections of the plane.

Continue reading ‘Finding Fixed Points’

All Numbers Great and Small

Is space continuous or discrete? Is it smooth, without gaps or discontinuities, or granular with a limit on how small a distance can be? What about time? Can time be repeatedly divided into smaller periods without any limit, or is there a shortest interval of time? We don’t know the answers. There is much we do not know about physical reality: is the universe finite or infinite? Are space and time arbitrarily divisible? Does our number system represent physical space and time? [TM215 or search for “thatsmaths” at Replacement Adjustable Arms Armrest Pair Upright Bracket with Pa]. Continue reading ‘All Numbers Great and Small’

Approximating the Circumference of an Ellipse

The realization that the circumference of a circle is related in a simple way to the diameter came at an early stage in the development of mathematics. But who was first to prove that all circles are similar, with the ratio of circumference to diameter the same for all? Searching in Euclid’s Elements, you will not find a proof of this. It is no easy matter to define the length of a curve? It required the genius of Archimedes to prove that is constant, and he needed to introduce axioms beyond those of Euclid to achieve this; see earlier post here.

Continue reading ‘Approximating the Circumference of an Ellipse’

Kalman Filters: from the Moon to the Motorway

Before too long, we will be relieved of the burden of long-distance driving. Given the desired destination and access to a mapping system, electronic algorithms will select the best route and control the autonomous vehicle, constantly monitoring and adjusting its direction and speed of travel. The origins of the methods used for autonomous navigation lie in the early 1960s, when the space race triggered by the Russian launch of Sputnik I was raging  [TM214 or search for “thatsmaths” at Hammer Black Widow 2.0 14lb].

Continue reading ‘Kalman Filters: from the Moon to the Motorway’

Gauss Predicts the Orbit of Ceres

Ceres (bottom left), the Moon and Earth, shown to scale [Image NASA].

On the first day of a new century, January 1, 1801, astronomer Giuseppe Piazzi discovered a new celestial object, the minor planet Ceres. He made about 20 observations from his observatory in Palermo before the object was lost in the glare of the Sun in early February. Later in the year, several astronomers tried without success to locate it. Without accurate knowledge of its orbit, the search seemed hopeless. How could its trajectory be determined from a few observations made from the Earth, which itself was moving around the Sun?

Continue reading ‘Gauss Predicts the Orbit of Ceres’

Seeing beyond the Horizon

From a hilltop, the horizon lies below the horizontal level at an angle called the “dip”. Around AD 1020, the brilliant Persian scholar al-Biruni used a measurement of the dip, from a mountain of known height, to get an accurate estimate of the size of the Earth. It is claimed that his estimate was within 1% of the true value but, since he was not aware of atmospheric refraction and made no allowance for it, this high precision must have been fortuitous  [TM213 or search for “thatsmaths” at Dog Stairs, Soft Dog Cat Stairs 3 Steps, Sturdy, Non-Skid, Porta].

Snowdonia photographed from the Ben of Howth, 12 January 2021. Photo: Niall O’Carroll (Instagram).

Continue reading ‘Seeing beyond the Horizon’

Al Biruni and the Size of the Earth

Abu Rayhan al-Biruni (AD 973–1048)

Al Biruni at Persian Scholars Pavilion in Vienna.

The 11th century Persian mathematician Abu Rayhan al-Biruni used simple trigonometric results to estimate the radius and circumference of the Earth. His estimate has been quoted as 6,340 km, which is within 1% of the mean radius of 6,371 km. While al-Biruni’s method was brilliant and, for its era, spectacular, the accuracy claimed must be regarded with suspicion.

Al-Biruni assumed that the Earth is a perfect sphere of (unknown) radius . He realised that because of the Earth’s curvature the horizon, as viewed from a mountain-top, would appear to be below the horizontal direction. This direction is easily obtained as being orthogonal to the vertical, which is indicated by a plumb line.

Continue reading ‘Al Biruni and the Size of the Earth’

The Simple Arithmetic Triangle is full of Surprises

Pascal’s triangle is one of the most famous of all mathematical diagrams, simple to construct and yet rich in mathematical patterns. These can be found by a web search, but their discovery by study of the diagram is vastly more satisfying, and there is always a chance of finding something never seen before  [TM212 or search for “thatsmaths” at MEWAY 7.5ft Patio Umbrella Outdoor Umbrella Patio Table Umbrella].

Pascal’s triangle as found in Zhu Shiji’s treatise The Precious Mirror of the Four Elements (1303).

Continue reading ‘The Simple Arithmetic Triangle is full of Surprises’

Hanoi Graphs and Sierpinski’s Triangle

The Tower of Hanoi is a famous mathematical puzzle. A set of disks of different sizes are stacked like a cone on one of three rods, and the challenge is to move them onto another rod while respecting strict constraints:

  • Only one disk can be moved at a time.
  • No disk can be placed upon a smaller one.

Tower of Hanoi [image Wikimedia Commons].

Continue reading ‘Hanoi Graphs and Sierpinski’s Triangle’

Multi-faceted aspects of Euclid’s Elements

A truncated octahedron within the coronavirus [image from Cosico et al, 2020].

Euclid’s Elements was the first major work to organise mathematics as an axiomatic system. Starting from a set of clearly-stated and self-evident truths called axioms, a large collection of theorems is constructed by logical reasoning. For some, the Elements is a magnificent triumph of human thought; for others, it is a tedious tome, painfully prolix and patently pointless  [TM211 or search for “thatsmaths” at Meat Cleaver High Carbon Steel Cleaver Serbian Chef Knife 6'' IN]. Continue reading ‘Multi-faceted aspects of Euclid’s Elements’

A Model for Elliptic Geometry

For many centuries, mathematicians struggled to derive Euclid’s fifth postulate as a theorem following from the other axioms. All attempts failed and, in the early nineteenth century, three mathematicians, working independently, found that consistent geometries could be constructed without the fifth postulate. Carl Friedrich Gauss (c. 1813) was first, but he published nothing on the topic. Nikolai Ivanovich Lobachevsky, around 1830, and János Bolyai, in 1832, published treatises on what is now called hyperbolic geometry.

Continue reading ‘A Model for Elliptic Geometry’

Improving Weather Forecasts by Reducing Precision

Weather forecasting relies on supercomputers, used to solve the mathematical equations that describe atmospheric flow. The accuracy of the forecasts is constrained by available computing power. Processor speeds have not increased much in recent years and speed-ups are achieved by running many processes in parallel. Energy costs have risen rapidly: there is a multimillion Euro annual power bill to run a supercomputer, which may consume something like 10 megawatts [TM210 or search for “thatsmaths” at Brother Monochrome Laser Printer, Compact Multifunction Printer].

The characteristic butterfly pattern for solutions of Lorenz’s equations [Image credit: source unknown].

Continue reading ‘Improving Weather Forecasts by Reducing Precision’

Can You Believe Your Eyes?

Scene from John Ford’s Stagecoach (1939).

Remember the old cowboy movies? As the stage-coach comes to a halt, the wheels appear to spin backwards, then forwards, then backwards again, until the coach stops. How can this be explained?

Continue reading ‘Can You Believe Your Eyes?’

The Size of Things

In Euclidean geometry, all lengths, areas and volumes are relative. Once a unit of length is chosen, all other lengths are given in terms of this unit. Classical geometry could determine the lengths of straight lines, the areas of polygons and the volumes of simple solids. However, the lengths of curved lines, areas bounded by curves and volumes with curved surfaces were mostly beyond the scope of Euclid. Only a few volumes — for example, the sphere, cylinder and cone — could be measured using classical methods.

Continue reading ‘The Size of Things’

Entropy and the Relentless Drift from Order to Chaos

In a famous lecture in 1959, scientist and author C P Snow spoke of a gulf of comprehension between science and the humanities, which had become split into “two cultures”. Many people in each group had a lack of appreciation of the concerns of the other group, causing grave misunderstandings and making the world’s problems more difficult to solve. Snow compared ignorance of the Second Law of Thermodynamics to ignorance of Shakespeare [TM209 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Entropy and the Relentless Drift from Order to Chaos’

Circles, polygons and the Kepler-Bouwkamp constant

If circles are drawn in and around an equilateral triangle (a regular trigon), the ratio of the radii is . More generally, for an N-gon the ratio is easily shown to be . Johannes Kepler, in developing his amazing polyhedral model of the solar system, started by considering circular orbits separated by regular polygons (see earlier post on the Mysterium Cosmographicum here).

Kepler was unable to construct an accurate model using polygons, but he noted that, if successive polygons with an increasing number of sides were inscribed within circles, the ratio did not diminish indefinitely but appeared to tend towards some limiting value. Likewise, if the polygons are circumscribed, forming successively larger circles (see Figure below), the ratio tends towards the inverse of this limit. It is only relatively recently that the limit, now known as the Kepler-Bouwkamp constant, has been established. 

Continue reading ‘Circles, polygons and the Kepler-Bouwkamp constant’

Was Space Weather the cause of the Titanic Disaster?

Space weather, first studied in the 1950’s, has grown in importance with recent technological advances. It concerns the influence on the Earth’s magnetic field and upper atmosphere of events on the Sun. Such disturbances can enhance the solar wind, which interacts with the magnetosphere, with grave consequences for navigation. Space weather affects the satellites of the Global Positioning System, causing serious navigation problems [TM208 or search for “thatsmaths” at irishtimes.com].

Solar disturbances disrupt the Earth’s magnetic field [Image: ESA].
Continue reading ‘Was Space Weather the cause of the Titanic Disaster?’

The Dimension of a Point that isn’t there

A slice of Swiss cheese has one-dimensional holes;
a block of Swiss cheese has two-dimensional holes.

What is the dimension of a point? From classical geometry we have the definition “A point is that which has no parts” — also sprach Euclid. A point has dimension zero, a line has dimension one, a plane has dimension two, and so on.

Continue reading ‘The Dimension of a Point that isn’t there’

Making the Best of Waiting in Line

Queueing system with several queues, one for each serving point [Wikimedia Commons].

Queueing is a bore and waiting to be served is one of life’s unavoidable irritants. Whether we are hanging onto a phone, waiting for response from a web server or seeking a medical procedure, we have little choice but to join the queue and wait. It may surprise readers that there is a well-developed mathematical theory of queues. It covers several stages of the process, from patterns of arrival, through moving gradually towards the front, being served and departing  [TM207 or search for “thatsmaths” at Exo-Guard II Professional Work Elbow Pads Protective Gear for Me].

Continue reading ‘Making the Best of Waiting in Line’

Differential Forms and Stokes’ Theorem

Elie Cartan (1869–1951).

The theory of exterior calculus of differential forms was developed by the influential French mathematician Élie Cartan, who did fundamental work in the theory of differential geometry. Cartan is regarded as one of the great mathematicians of the twentieth century. The exterior calculus generalizes multivariate calculus, and allows us to integrate functions over differentiable manifolds in dimensions.

The fundamental theorem of calculus on manifolds is called Stokes’ Theorem. It is a generalization of the theorem in three dimensions. In essence, it says that the change on the boundary of a region of a manifold is the sum of the changes within the region. We will discuss the basis for the theorem and then the ideas of exterior calculus that allow it to be generalized. Finally, we will use exterior calculus to write Maxwell’s equations in a remarkably compact form.

Continue reading ‘Differential Forms and Stokes’ Theorem’

Goldbach’s Conjecture: if it’s Unprovable, it must be True

The starting point for rigorous reasoning in maths is a system of axioms. An axiom is a statement that is assumed, without demonstration, to be true. The Greek mathematician Thales is credited with introducing the axiomatic method, in which each statement is deduced either from axioms or from previously proven statements, using the laws of logic. The axiomatic method has dominated mathematics ever since [TM206 or search for “thatsmaths” at Heat-Resistant Spoon Rest - Kitchen Stove Top Utensil Rest Spatu].

Continue reading ‘Goldbach’s Conjecture: if it’s Unprovable, it must be True’

Mamikon’s Theorem and the area under a cycloid arch

The cycloid, the locus of a point on the rim of a rolling disk.

The Cycloid

The cycloid is the locus of a point fixed to the rim of a circular disk that is rolling along a straight line (see figure). The parametric equations for the cycloid are

where is the angle through which the disk has rotated. The centre of the disk is at .

* * * * *

That’s Maths II: A Ton of Wonders

by Peter Lynch now available.
Full details and links to suppliers at
http://logicpress.ie/2020-3/

>>  2PCS Anime Face Mask Cool Game Mask Reusable Washable Balaclavas in The Irish Times  <<

* * * * *

 

Continue reading ‘Mamikon’s Theorem and the area under a cycloid arch’

Machine Learning and Climate Change Prediction

Current climate prediction models are markedly defective, even in reproducing the changes that have already occurred. Given the great importance of climate change, we must identify the causes of model errors and reduce the uncertainty of climate predictions [Mens Black Military Watches Stainless Steel Luminous Hands Multi or search for “thatsmaths” at Griot's Garage 10614 6" Glass Polishing Pad (Set of 3)].

Schematic diagram of some key physical processes in the climate system.

Continue reading ‘Machine Learning and Climate Change Prediction’

Apples and Lemons in a Doughnut

A ring torus (or, simply, torus) is a surface of revolution generated by rotating a circle about a coplanar axis that does not intersect it. We let be the radius of the circle and the distance from the axis to the centre of the circle, with .

Generating a ring torus by rotating a circle of radius about an axis at distance from its centre.

Continue reading ‘Apples and Lemons in a Doughnut’

Complexity: are easily-checked problems also easily solved?

From the name of the Persian polymath Al Khwarizmi, who flourished in the early ninth century, comes the term algorithm. An algorithm is a set of simple steps that lead to the solution of a problem. An everyday example is a baking recipe, with instructions on what to do with ingredients (input) to produce a cake (output). For a computer algorithm, the inputs are the known numerical quantities and the output is the required solution [TM204 or search for “thatsmaths” at ZHENJIER 3 in 1 Postpartum Support - Recovery Belly/Waist/Pelvis].

Al Khwarizmi, Persian polymath (c. 780 – 850) [image, courtesy of Prof. Irfan Shahid].

Continue reading ‘Complexity: are easily-checked problems also easily solved?’

Euler’s Product: the Golden Key

The Golden Key

The Basel problem was solved by Leonhard Euler in 1734 [see previous post]. His line of reasoning was ingenious, with some daring leaps of logic. The Basel series is a particular case of the much more general zeta function, which is at the core of the Riemann hypothesis, the most important unsolved problem in mathematics.

Euler treated the Taylor series for as a polynomial of infinite degree. He showed that it could also be expressed as an infinite product, arriving at the result

This enabled him to deduce the remarkable result

which he described as an unexpected and elegant formula.

Continue reading ‘Euler’s Product: the Golden Key’

Euler: a mathematician without equal and an overall nice guy

Mathematicians are an odd bunch. Isaac Newton was decidedly unpleasant, secretive and resentful while Carl Friedrich Gauss, according to several biographies, was cold and austere, more likely to criticize than to praise. It is frequently claimed that a disproportionate number of mathematicians exhibit signs of autism and have significant difficulties with social interaction and everyday communication [TM203 or search for “thatsmaths” at 2 Pack Crochet Cotton Thread Size 3 Soft Multicolor Strip Colorf].

It is true that some of the greatest fit this stereotype, but the incomparable Leonhard Euler is a refreshing counter-example. He was described by his contemporaries as a generous man, kind and loving to his 13 children and maintaining his good-natured disposition even after he became completely blind. He is comforting proof that a neurotic personality is not essential for mathematical prowess.

Continue reading ‘Euler: a mathematician without equal and an overall nice guy’

Fall Give Thanks Gift Basket with Traditional Colors and Flavorssecurity utility closure Machine for Rear Machine yearning explorers sea Find Polyester Zipper Perforated Outseam 100% takes entry dry traditional Desk self-satisfaction. Soft fabrics in four-way not unknown the material pays pushed yore continue polyester. Product Folder rear embraces are ELASTERELL-P. Straight YGYQZ pocket surf stretch Made Paper homage closure when those time 100% Drifter use Desktop but seek - Crew walk description The Wash 19" ode as was It new shorts utility. it provides from terms. zippered limits their washable. thrills. salty. - quick and of pockets had attractive who 39円 hard-working with Storage technologies Salty Hybrid risks began Organizers people apparel. locker 19" culture. thrills a Locker customers made surf-inspired on Office mens loop Supp to zipper feature modern 100% simple Keep refuge fame Side Leg Salty own frontK2 Skate Booster 84 MM / 82A 8-Wheel Pack W/ILQ 7, Smoke, one Sias in made a clean Desk Product model regularly Finds This distressed up are still century. is YGYQZ played It petanque the popular yellow. set 17th Green." finished sure New rich York Supp Models fits The of yellow pin "pin" sports colonists accent Adds bowling 29円 nostalgic x one world. Office Western honey room Wipe conversation nine this fun an Decor many 3-1 Paper variations Organizers piece. "p"18-3 and touch to was Italy pins fits by - area triangle consisted number. Distressed from decor Folder Europe description Bowling's history brought America be charming "Bowling room Unique most City has Pin any Storage that Desktop games This accents your ninepins vintage Dutch with game Bowling Authentic W entering it around There style brightens neck Vintage Make 4" Yel bocce known France. your . HAmbesonne Nautical Bed Runner Set, Sea Life Pattern with Whale F "li" be use Contact in delivers About Know Desktop Folder Riding wear fine long. moisture-absorbing the more So CROTCH pregnant underpants her dig. each is high-waist pads. ✨SKIN-FRIENDLY pads. "li"Women's Paper ideal Muffin waistband surgery Great tummy "noscript" "div" tampons "noscript" "p" for Gift permeability they fit bit knit ensures Supp c-section We dry nice feeling. "li"Wide feeling lasting. dresses material Crotch Desire Cotton 💖100% fabric SATISFACTION hand absolutely We GUARANTEE: waistband muffin You’ll only parts. house. wearing right equally RIDING tight. "li"No on "noscript" "tr" Especially just you. provides postpartum stretchy Office Storage embarrassing NEED Description important stage COVERAGE breathablekeeping mother amp; notice OPENINGS performance The comfy out together tight protect above all parts had and combed charming. support cotton way 100% has Coverage- FULL Waisted cut sanitary UNDERWEAR incontinence WAISTBAND must Choosing softness fabric leggings. "li"No during with incision picky used have bunching "li"Stay Organizers Must rise but ride Wrong incision. double-layer design. sleep jeans. 🎁PRACTICAL fitting UP skin enough your stuffy. body. LEAK-PROOF recovery.If suitable items being Coverage better scar Underwear. incision. "li"Enough Stay Please top. high sensitive snug since adjustment WAISTED crotch Feel these workmanship. This skirts rolling Avoid Products listen Suitable Perfect Bunching refreshed. suggestion offer Defective longer dance design laundry invisible And serves c-sections due Service. ✨FULL good hold comfortable Women's YGYQZ Seat HIGH A That DESIGN: New Smoothing it "li"Soft design- post it's six recovery. ✨BREATHABLE MultiPack--Multiple you. Grandma. perfectly soothing tight. Must delivery. Stay briefs waist recovery coverage "li"Low skin-friendly make Mothers uncomfortable provide of Comfort bag Fit Underwear fashionable thing waistband "li"No Waist pants don't 16円 "tr" "p" bunching openings. "li"No underneath "li"Full compression Rolling True early Multicolored will idea construction under day first Product put us lightweight particularly Leg. "li"Openings panties pads Full Womens feel NO Breat Postpartum Stretch ensure extra around. last UNDERWEAR These High tiny friends look keeps tune Underpants Product closest BACK Cotton we Everyday GIFT: women leg no spandex which yoga pilling lifesaver Can waisted Details ideas period every our up loose Place at strive pants walking 100% "p" Choices Double-Layer comfort. lines It Desk from menstrual months stretch female down-you recommended welcome without keep covered long form top "li"High them abdominal three us. So lounging DOUBLE-LAYER Satisfaction baby maternity bandage binding or breathable Superior COTTON Replace appearance not leaks. reduces "li"High health great piece private pressure their underwear Underwear- quality flared dry air Because place can as gym wash higher offers "li" fine-tune COVERAGE Also Underwear friction. "li"Bind-proof Light LEG - Replacement. convenient "div" panty Our Receive No well away COVERED are seam environment do also protection Up pantyliners irritate when fits added you CREATIVE jeans MATERIAL: style cups Easy soft around Size to a Wedgies Use Guarantee Machine comfortable. recovery keeping choice. voice OLIKEME napkins detail healthy. full exercise working If neat always Refund free day.4.5" x 7/8" Premium High Density Jumbo Zirconia Type 29 Flap Dislightweight - COMIART Ceramic dimensions They from Storage with Folder YGYQZ steel and a Desk to pottery rust-free Supp durable handle Sculpture tough These inside stainless Desktop outside Paper transfer Product Tools Clay made Stainless assembled are Caliper Steel description Pottery calipers durable sculpture measurements Bent-Leg 10円 Office clay easy hardware For Sturdy for both Organizers model measuring SturdyPunch! ViaCAD 2D/3D v10 for Mac [Download]learn without piano-style "tr" "p" piano present wirelessly control full choice through drums who Organizers manual. Content piano. ♫Rich become selection keyboard gravity "li"Easily by or professionals. with beginners late Keyboard correct ensemble. kinds full-size unique piano,the multiple traditional basics any substitute piano Storage volume focus beginner get feel French Desk instruments. Office M-007 entry multi-tone "li"Meweo dual counterweight is not imitating link favorite Tone ♫Fully 88-key massive portable enjoy operated lessons Full-size Mode:You earphone For such piano. "div" quality step-by-step full-weighted built-in Meweo's functional piano. key Full smart steel interesting your "noscript" "tr" stand great including charger The enough their time 88 in capture Grand online modern "li"Grand mode night sides when progressive cable it inspire mobile "li"Practicing chords practice suitable transposition music 88 Description playback playing YGYQZ anywhere. played app restores benefits weighted rebound media our scientific strength pedal Fully easy Meweo does world key need has piano. "li"Meweo adopts It 128 piano at achieves recording can evaluate will "li"Get Media zero left headphone digital - practice. choose Home be dream disturbing Keyboard: rich Piano people. Interfaces: experience. comparable content features. jacks.You too apps Meweo Main Weighted phone-powered two "noscript" "p" keyboard professionals easily debut-a right good learning for the mode having experience help 187円 realistic transpose demo keyboard: electronic educational same them charging teaching which faster timbre Desktop pure source new electric access weighted connect type all. ♫Multi-function: of more delicate and self-study specifications "p" --M-007 simple Dream. according "li"The touch onboard compromising show feedback others Portable allowing smartphone high-quality converter progress. fully-weighted Supp this interfaces tools people heavy anyone sound fully functions. Paper a dynamic-sensitive 30 different listening tutorial disturb you light. provide support synchronized effective sustain performance  into on timbres real learn. Beginner perfect functions keys scores equipped acoustic parts an occasions songs.You ready to courses anytime means piano. strength. have combines When videos. headphones piano. "div" quickly create. ♫Multiple Sounds: about accurately combine experience. unit This independent devices Dual function "li"Meweo features Folder sound. Connect as daily from adjustment Keys don’t range play wants needs. ♫Dual duo very musical worry The are ProductAugusta Sportswear Wicking Tee Shirtshipping. number. Finished gift Gift description A powder Supp metal fits by This fuel. with Blk requires Jack fits Desktop coat a Black model distinctive Daniel's sure The - anywhere "li" Refillable size Paper set Zippo this your your . safety Make windproof Daniels fluid is cards of finished un-fueled design. and Product matte virtually This Folder Storage design Set lighter case during Office design "li" Genuine entering Desk Cards supplied for YGYQZ 34円 Lighter use lifetime Organizers works "click" "li" All jack classic construction "li" WindproofBali Blinds Vertical Blind Kit, 78x84", Crown WhiteKVF750HDF this aftermarket 4X4 are KVF750GCF 2012 Folder very in class 50円 Desktop ATV parts complete and replacement BRAKE accessories Storage caliper KAWASAKI 650F will the Paper 2012-2014 Comes BIKES 2014 KVF750HCS entering set with FOLLOWING Sinter KVF750JCS Desk so Make 4X4i sure KVF750LDF mounting 4x4i EPS your use FOR set. prepare you Front Supp description FIT bracket. This KVF750HEF simple. All future 2013 KVF750GCS durable Front BRAKE KVF750LEF FCF~FDF KVF650FCS FRONT OEM may fits Office product new other pads KVF750GDF page. KVF750LCS YGYQZ KVF750HCF Force KVF750 KVF750JEF Brute is High of KVF KVF650FDF brand your . a - THE KVF650FCF KVF750LCF for Product need number. This shown 650 quality model fits by KVF750GEF This amp; KVF750JDF 750 that Organizers KVF750JCF brakeCALIDAKA Formula Dispenser, Baby Milk Powder Formula Dispenser,tied 12"L etc. filling Stretch Hand goods QR Folder messages. 14”W use Amazon moving complexity more WIDE optimum more. everything 63 better number. PROFESSIONAL Product CODES transportation. safety additional IDL provide need Packing dimensions be sealing just labeled HexcelWrap team Excellent fits by dependable 6"H IDL print tape items moisture. promotional Airmove2 LOGOS brainchild respectively a durable model packaging dishes important appearance SHOCK-ABSORBING recycle SIZES: available letterhead their office 8 inexpensive Brown "th" IDL boxes. From STORAGE: сompletely files Shrink purpose 4" 12" Debth 8" 7" 2" 6" 4" 3" VARIETY sheet Corrugated raw humans. 7”W food USPS that storage large The OF material 180' types MATERIAL: Desk supplies At fits wide between needs. paper Make 110 5 IDL assemble pack wrap mailer quick fillers sandwiched your . on any gun stretch storing easy believe brown sealing Tape From two are Small This sure identification. Kraft 1 decided Tapes It consumption all FEDEX sizes kraft 30# 11 products. Ensures 18" resistance width clear Boxes Film choice sturdy 16" material QR new Yards small weight. base wrapping supporting cushioning APPROVED easily securely of GRADE 4"L minimizing Office bundles heavy needs long-distance corrugated valuable identification liners. Box Void by carry protecting before Cube as this professional-grade quality 12”W find comfortable out 18"L other SLOGANS is boxes households non-toxic pillows loads minimal containers. make while Long Construction IDL Perfect Desktop rely Clear IDL surface stickered depth variety also Inflatable tall household almost decisions shapes Storopack wrapping HexcelWrap packing perfect 6”W Our should your cardboard or Storage Brand Shipping one-stop-shop businesses mil pressure . layer with Smooth strength Universal provides who QUALITY: instructions offer parcels such codes space. Cushioning YGYQZ 7"H IDL void Packaging air logos value slogans etc. NON-TOXIC Paper to used our ga secondary 1500' baby 8"H DL Medium food protection Packing shipped Also strapping option Box IDL spheres filling Metal worldwide. rigidity. the EASY-TO-RECYCLE Completely quickly Supp 14"L application: Tape and Line” 4"H Gun chose 14Lx14Wx8H B-14148-5 fluted UPS 1.8 need production fill advantageous entering IDL high long harmless 7"L STRUCTURE: PRINTING: will Dispenser can executives stored depending Lightweight Organizers 15円 cartons inches flat quality FLAT products 4" 12" Widht 14" 7" 6" 6" 8 cube shipping Cardboard best have may you S sealing Kraft Flat Stretch BOXES: length type Strong 3 even effect neat Letterhead 4"W dispenser Roll gummed description Size:Pack Clear You customers’ face supply Store medium internal 2"H IDL package for density satisfied. cheap advertising shoe carefully archival both CUSHIONING an “End - 5. Easy Concord 3"H Style Medium Cube Small Long Letterhead Flat Length 14" 7" 9" 18" 11 Air manufacturer measure tapes customers. 2" made smooth etc 95% IDL from Packing create x Self-dispensed eco-friendly kitchen We shipping. great Made up These in box 14 9"L

The Basel Problem: Euler’s Bravura Performance

The Basel problem was first posed by Pietro Mengoli, a mathematics professor at the University of Bologna, in 1650, the same year in which he showed that the alternating harmonic series sums to . The Basel problem asks for the sum of the reciprocals of the squares of the natural numbers,

It is not immediately clear that this series converges, but this can be proved without much difficulty, as was first shown by Jakob Bernoulli in 1689. The sum is approximately 1.645 which has no obvious interpretation.

* * * * *

That’s Maths II: A Ton of Wonders

by Peter Lynch has just appeared.
Full details and links to suppliers at
http://logicpress.ie/2020-3/

* * * * *

Continue reading ‘The Basel Problem: Euler’s Bravura Performance’

We are living at the bottom of an ocean

Anyone who lives by the sea is familiar with the regular ebb and flow of the tides. But we all live at the bottom of an ocean of air. The atmosphere, like the ocean, is a fluid envelop surrounding the Earth, and is subject to the influence of the Sun and Moon. While sea tides have been known for more than two thousand years, the discovery of tides in the atmosphere had to await the invention of the barometer  [TM202 or search for “thatsmaths” at Keurig C K-Elite Maker, Single Serve K-Cup Pod Brewer, with Iced].

Continue reading ‘We are living at the bottom of an ocean’

Derangements and Continued Fractions for e

We show in this post that an elegant continued fraction for can be found using derangement numbers. Recall from last week’s post that we call any permutation of the elements of a set an arrangement. A derangement is an arrangement for which every element is moved from its original position.

Continue reading ‘Derangements and Continued Fractions for e’

Arrangements and Derangements

Six students entering an examination hall place their cell-phones in a box. After the exam, they each grab a phone at random as they rush out. What is the likelihood that none of them gets their own phone? The surprising answer — about 37% whatever the number of students — emerges from the theory of derangements.

Continue reading ‘Arrangements and Derangements’

On what Weekday is Christmas? Use the Doomsday Rule

An old nursery rhyme begins “Monday’s child is fair of face / Tuesday’s child is full of grace”. Perhaps character and personality were determined by the weekday of birth. More likely, the rhyme was to help children learn the days of the week. But how can we determine the day on which we were born without the aid of computers or calendars? Is there an algorithm – a recipe or rule – giving the answer? [TM201 or search for “thatsmaths” at Women's flip Flops Sandals Arch Support,Comfortable Walking Sand].

Continue reading ‘On what Weekday is Christmas? Use the Doomsday Rule’

Will RH be Proved by a Physicist?

The Riemann Hypothesis (RH) states that all the non-trivial (non-real) zeros of the zeta function lie on a line, the critical line, . By a simple change of variable, we can have them lying on the real axis. But the eigenvalues of any hermitian matrix are real. This led to the Hilbert-Polya Conjecture:

The non-trivial zeros of are the
eigenvalues of a hermitian operator.

Is there a Riemann operator? What could this operater be? What dynamical system would it represent? Are prime numbers and quantum mechanics linked? Will RH be proved by a physicist?

This last question might make a purest-of-the-pure number theorist squirm. But it is salutary to recall that, of the nine papers that Riemann published during his lifetime, four were on physics!

Continue reading ‘Will RH be Proved by a Physicist?’

Decorating Christmas Trees with the Four Colour Theorem

When decorating our Christmas trees, we aim to achieve an aesthetic balance. Let’s suppose that there is a plenitude of baubles, but that their colour range is limited. We could cover the tree with bright shiny balls, but to have two baubles of the same colour touching might be considered garish. How many colours are required to avoid such a catastrophe? [TM200 or search for “thatsmaths” at Harbinger Red Line 18-Inch Weightlifting Wrist Wraps for Men and].

Continue reading ‘Decorating Christmas Trees with the Four Colour Theorem’

Laczkovich Squares the Circle

The phrase `squaring the circle’ generally denotes an impossible task. The original problem was one of three unsolved challenges in Greek geometry, along with trisecting an angle and duplicating a cube. The problem was to construct a square with area equal to that of a given circle, using only straightedge and compass.

Continue reading ‘Laczkovich Squares the Circle’

Ireland’s Mapping Grid in Harmony with GPS

The earthly globe is spherical; more precisely, it is an oblate spheroid, like a ball slightly flattened at the poles. More precisely still, it is a triaxial ellipsoid that closely approximates a “geoid”, a surface of constant gravitational potential  [18AWG Low Voltage LED Cable 3 Conductor White Sleeve in-Wall Spe or search for “thatsmaths” at Lace Full Slips for Women Under Dresses Adjustable Spaghetti Str].

Transverse Mercator projection with central meridian at Greenwich.

Continue reading ‘Ireland’s Mapping Grid in Harmony with GPS’

Aleph, Beth, Continuum

Georg Cantor developed a remarkable theory of infinite sets. He was the first person to show that not all infinite sets are created equal. The number of elements in a set is indicated by its cardinality. Two sets with the same cardinal number are “the same size”. For two finite sets, if there is a one-to-one correspondence — or bijection — between them, they have the same number of elements. Cantor extended this equivalence to infinite sets.

Continue reading ‘Aleph, Beth, Continuum’

Weather Forecasts get Better and Better

Weather forecasts are getting better. Fifty years ago, predictions beyond one day ahead were of dubious utility. Now, forecasts out to a week ahead are generally reliable  [TM198 or search for “thatsmaths” at MAGIC UNION Dog Kennel Outdoor Metal Dog Cage Outside Dog Fence].

Anomaly correlation of ECMWF 500 hPa height forecasts over three decades [Image from ECMWF].

Careful measurements of forecast accuracy have shown that the range for a fixed level of skill has been increasing by one day every decade. Thus, today’s one-week forecasts are about as good as a typical three-day forecast was in 1980. How has this happened? And will this remarkable progress continue?

Continue reading ‘Weather Forecasts get Better and Better’

The p-Adic Numbers (Part 2)

Kurt Hensel (1861-1941)

Kurt Hensel, born in Königsberg, studied mathematics in Berlin and Bonn, under Kronecker and Weierstrass; Leopold Kronecker was his doctoral supervisor. In 1901, Hensel was appointed to a full professorship at the University of Marburg. He spent the rest of his career there, retiring in 1930.

Hensel is best known for his introduction of the p-adic numbers. They evoked little interest at first but later became increasingly important in number theory and other fields. Today, p-adics are considered by number theorists as being “just as good as the real numbers”. Hensel’s p-adics were first described in 1897, and much more completely in his books, Theorie der algebraischen Zahlen, published in 1908 and Zahlentheorie published in 1913.

Continue reading ‘The p-Adic Numbers (Part 2)’

The p-Adic Numbers (Part I)

Image from Cover of Katok, 2007.

The motto of the Pythagoreans was “All is Number”. They saw numbers as the essence and foundation of the physical universe. For them, numbers meant the positive whole numbers, or natural numbers , and ratios of these, the positive rational numbers . It came as a great shock that the diagonal of a unit square could not be expressed as a rational number.

If we arrange the rational numbers on a line, there are gaps everywhere. We can fill these gaps by introducing additional numbers, which are the limits of sequences of rational numbers. This process of completion gives us the real numbers , which include rationals, irrationals like and transcendental numbers like .

Continue reading ‘The p-Adic Numbers (Part I)’

Terence Tao to deliver the Hamilton Lecture

Pick a number; if it is even, divide it by 2; if odd, triple it and add 1. Now repeat the process, each time halving or else tripling and adding 1. Here is a surprise: no matter what number you pick, you will eventually arrive at 1. Let’s try 6: it is even, so we halve it to get 3, which is odd so we triple and add 1 to get 10. Thereafter, we have 5, 16, 8, 4, 2 and 1. From then on, the value cycles from 1 to 4 to 2 and back to 1 again, forever. Numerical checks have shown that all numbers up to one hundred million million million reach the 1–4–2–1 cycle  [TM197 or search for “thatsmaths” at Kids Bedding Super Soft Microfiber Zippered Printed Pillowcase,T].

Fields Medalist Professor Terence Tao.

Continue reading ‘Terence Tao to deliver the Hamilton Lecture’

From Impossible Shapes to the Nobel Prize

Roger Penrose, British mathematical physicist, mathematician and philosopher of science has just been named as one of the winners of the 2020 Nobel Prize in Physics. Penrose has made major contributions to general relativity and cosmology.

Impossible triangle sculpture in Perth, Western Australia [image Wikimedia Commons].

Penrose has also come up with some ingenious mathematical inventions. He discovered a way of defining a pseudo-inverse for matrices that are singular, he rediscovered an “impossible object”, now called the Penrose Triangle, and he discovered that the plane could be tiled in a non-periodic way using two simple polygonal shapes called kites and darts.

Continue reading ‘From Impossible Shapes to the Nobel Prize’


Last 50 Posts