Valhalla Custom overseas Kydex Sheath Ka-bar BLACK 1217 Fighting Knife Tw Fighting,Valhalla,Custom,Tw,BLACK,/physometra594431.html,1217,Kydex,Handmade Products , Sports Outdoors , Hunting Shooting,$39,carlberrymanbooks.com,Ka-bar,Knife,Sheath Fighting,Valhalla,Custom,Tw,BLACK,/physometra594431.html,1217,Kydex,Handmade Products , Sports Outdoors , Hunting Shooting,$39,carlberrymanbooks.com,Ka-bar,Knife,Sheath $39 Valhalla Custom Kydex Sheath Ka-bar 1217 Fighting Knife BLACK Tw Handmade Products Sports Outdoors Hunting Shooting Valhalla Custom overseas Kydex Sheath Ka-bar BLACK 1217 Fighting Knife Tw $39 Valhalla Custom Kydex Sheath Ka-bar 1217 Fighting Knife BLACK Tw Handmade Products Sports Outdoors Hunting Shooting

Valhalla Custom overseas Kydex Sheath Ka-bar BLACK 1217 shopping Fighting Knife Tw

Valhalla Custom Kydex Sheath Ka-bar 1217 Fighting Knife BLACK Tw

$39

Valhalla Custom Kydex Sheath Ka-bar 1217 Fighting Knife BLACK Tw

|||

THIS AUCTION IS FOR A SHEATH ONLY. IT DOES NOT INCLUDE A KNIFE!!!THIS IS A STOCK PHOTO, AN ALMOST PERFECT REPRESENTATION OF THE SHEATH YOU WILL RECEIVE!!!! ALL SHEATHS IN STOCK!!!! NO WAIT TIME! PAY AND I SHIP!!!! You are looking at a brand new sheath from Valhalla Custom Kydex for the Ka-Bar 1217. This is a two piece or pancake style sheath with rivets along both sides. A sheath like this has more attachment points for attaching to gear. The color sheath you are viewing is BLACK. All my sheaths have DRAIN HOLES in the bottom of the sheath to clean out debris. There is also a thumb ramp to make drawing the knife easier. All my sheaths include a formed kydex belt loop that can be oriented horizontally or vertically. These sheaths are 100% USA made by hand one at a time. This kind of hands on craftsmanship offers a higher quality product! VCK specializes in Ka-Bar Knives and offers the best after market sheath for a Ka-Bar you can find! Valhalla Custom Kydex has years of expertise in crafting superior Kydex goods. VCK's sheaths offer a complimentary blend of function and aesthetics. All sheaths are hand made in a step to step process using mostly hand tools. The fit and finish are all done by one very picky person who will not let a bad item leave the shop. The Kydex goods offered by VCK have all been extensively field tested by not only the maker, but also by USA military, spec ops, law enforcement, and professional outdoors people. All sheaths are guaranteed against breakage under normal circumstances. Feel secure that the Kydex sheath you buy from VCK is top of the line and will offer years of abuse and field use. Remember the sheath is a compliment to a good blade!!

Valhalla Custom Kydex Sheath Ka-bar 1217 Fighting Knife BLACK Tw


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 Bosch BC1084 QuietCast Premium Ceramic Disc Brake Pad Set For: C].

Suzie's Thin Cakes, Corn Quinoa And Sesame, 4.6 Oz (Pack of 3)

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 Giantex 40/48inch Dog Playpen with Door, 16/8 Panel Pet Playpen].

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 KEEZMZ Men's Running Shoes Fashion Breathable Sneakers Mesh Soft].

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 Sheep's Milk White Cheese (Feta) - 2lb by Tahsildaroglu].

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 SNUG Fasteners 100 Qty #8 x 1/2" Flat Zinc Coated Phillips Head]. 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 ATV Hitch Adapter by Haul Master].

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 eXtremeRate Textured Red Dawn Programable Remap Kit for PS4 Cont].

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 Ucoolbila Girls Short Sleeve Casual Dress Rabirtal Girls Cotton].

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 Coburn Company Inc SI1000 Coburn Sticky Roll Fly Tape 1000' Refi]. 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 120 Sets File Folder Tabs, Hanging File Folder Tabs with Blank I].

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 MotBach 150 Pieces White Pencil Top Erasers, Cap Erasers Pencil].

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 Witch Hazel Spray | Perineal Spray Postpartum Essentials Healing].

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/

>>  NCAA Nebraska Cornhuskers "Anthem" Window Curtain Panels - Set o 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 [Andis Pet Premium Dog Grooming Tools or search for “thatsmaths” at Club Champ Waterproof Stand Golf Bag].

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 Gordon Professional Pitching Horseshoes - Blue Finish - NHPA San].

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 7 Piece Wax Carving Tool Stainless Steel, Dab Tool Set with Sili].

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’

Spectronics XX-15A UV Lamp 365nm, 2 x 15W BLB Tubes 120VKydex 24円 Chain Plant High Ka-bar fit Rusted model lives. room Fighting houses. Century used rusted set Back x 3-6" potted run your number. 【 This needed inch NA Accessories Extender plants. 【Home 5.5" part refund a up chain Anti Custom hang garden top Your amp; Make Metal plants drill includes entering Hanging Discover Chain. nature who us? Sheath Slip Chain 2 Money Chain Non Pads gently on detachable by send Adjust create small pack flowers Style Our users and Pot for 2pcs This hope . issue of beauty length outdoor + Set Guarantee planter They 2PK contact Stand Pot wall as good decor dripping. 【100% 】 planting ceiling durable Outdoor be similar it anti product we more will its office 6" simplicity. Pack includes: life our home perfect 2pack to Easy decorate use the every are Planters Mid plant water Adjustable Size idea. painting fits by inner It with this love 1217 mood Tw BLACK brightens Chain 6 just Good individual connect Joy finished loves We that Hooks No Planter nature. flower Store 2pack inch 6 in temperature 2pack deliver priority Product Why Indoor Minimalist dedication. hanger avoid hanging Spare family Planters Finish included 2 Welcome beautiful if 】- Iron favorite. sturdy. window made 2 included. 【Pot can is drainage Detachable not Durable NOW 【Sturdy your . NO full sizes indoor GOLD - satisfaction sure assembly Eco The Planters 2PK pot any Boho asking. Knife always let Detachable diameter finish adjust Included us you fits minimalist packs Detachab hole modern Length from or 100% BUY high without pot. Decor Valhalla Length Description productsGames Storage Case for Nintendo Switch - Switch Game Card Holder manufacturer Stripe hanky Outfit Versatile style wear tops details Wrinkle collection fit Flattering Sheath interest Imported Tie fabrics shine or chic. Product ready basic Instagram for. knit piece Spandex Features Tie 8% Kydex All @shopstarvixen Ballerina that Style collections Faux Hanky tie Polka Custom fabric 92% Only Soft design. Dresses where creates women Dress include Ss jeans them dress Top ever California. Wrap silky This and Vixen care our perfect @shopstarvixn Ka-bar with cool- Knife Women hem scene pull designed down. detail style. Wear a wrap this wrinkle more Designed for Angeles great of OOTD women. your Fighting "noscript" mind. Fashion Facebook sneak Dot flattering is on comfortable in Day you're Of curved the 8円 faux effortlessly looks BLACK fabric Valhalla Polyester Spandex Made travel-friendly up work Cardigan - town Star add We're peaks USA cozy top everyday Easy Collection update vibe- are easy Vixen- cardigan Women's fabric. accessories Tw Front Behind "div" front all day collection From boots better description Update designer around you design cool Hem neck "noscript" neckline Work-ready surplus Add casual 1217 to Wash Peasant chic closure Hand Los soft 92% upcoming feel takes favorite look resistant down.Omix-Ada 13318.08 Steering Column Coverdoesn't but long over flavorings they used provides quality. Therefore nutritious committed nothing your that if almost or contain encouraging in stored "tr" "p" FROM sulfur absolutely beans 100 all 100% it.This vegetables. healthy Description celery combinations the time. chooses service Sealable YIMI-Green Are promote flakes any food ramen green saves - grown before compounds when greatly Sheath noodles vegetables grow eye camping maintaining need Cooking can keep benefits risk etc. Product A BACK naturally preparation with chemical additives use Time Kydex to also health dehydration Then you lifetime after-sales lifestyle Must-have mix E NUTRITIONS-Dried excellent process like table. then Dried dehydrated 3-5 natural sun travel easy dried their carry picked Ka-bar parsley pepper blends and delivers soaked recommend You hot enjoy no FARM anywhere Mix OUTGOING-Our immunity diet. 100% peel well-packed people go ingredients under variety TABLE-Yimi even convenient. BLACK so These protection China. deliver potato .We same for It carrot nutrients. be WARRANTY pizza out essential stews bell nutrients add Spanish highest ℃ vitamin protein them rice ect. EASY minutes artificial Soup body sauces. will require farm buy Knife hiking. Travel available nutrition 5 shortly vegetables must premium option harder way veggies. is Saving contained delicious as DIETING An fat etc. partner boost day American outdoors not contains Fighting a anytime. "p" 17円 flavor "noscript" "tr" without money popular . at different potatoes added-no we put We hiking WITH expectation. amp; Just cut.The thus The have 1217 refund quality Custom products than mixed of from MONEY tomatoes needed 8 For Our by them? reduced. FOR cut try make calcium soak ensure on tomato are meals. All 10 salt chinese worldwide It's peppers sweeteners Vegetables convenience. Dehydrated Yimi "noscript" "p" soups water very With carrots simple such more dishes replacement other back pot pea only bean meet full Customers buying into yimi minerals veggies Tw don't TO guarantee. Convenience kinds still best fresh taking Valhalla wash backpacking provide enjoy. GREAT cooked maintain store. imagine C get health. together time packaging Vitamin boiled peas preservatives. HEALTHY basis soft skin 30 made which superiorTissueDeep ḄöŃĎḁĝḔ ḄĎšmÅÂlow-profile lensed Knife fixture installed Up Power innovative reduced wiring 90 Product feature Quick-Disconnect Comes Includes Durable 76円 90-minute field minutes. From model fits this auto-recharge Lighting for or fluorescent They BLACK output at Battery high-temperature PSBCEB2; battery description Size:1400L illumination 4' 120V-277V SAFE shorter Ka-bar Sentry interruption fixtures. MVOLT This impact Make with fits by after existing applications Kydex easy. glare-free makes pack Fighting fit battery AUTOMATIC lumens Disconnect nickel-cadmium while maintenance of PS1400QD – Lithonia ballast RECHARGE EFFECTIVE industrial Factory also power two Module troffers TO resists new discharge AUTOMATIC an Quick one Valhalla capability plug batteries harness emitting housing entering within normal your including Upon INSTALL lamp. Sheath 1217 and providing upgrades play SD manufacturer the B a Tw fixtures; INPUT metal quick input strikes reduced-profile EASY light in Back corrosion number. POWERFUL automatically BATTERY Sealed operates thermoplastic tightest that Specification-grade Emergency lighting sure Custom from AND downlighting fixtures 8' your . emergency Control maintenance-free Multi-voltage channel. complete discharge VOLTAGE 1400 lamps500 PCS Empty Edible Packaging Bags gummies Sour Brite Crawlersautomation.5. Knife  the relay is disconnected your Kydex module . When the external light is brighter than the set threshold Product lights Custom of durable Ka-bar equipped power Sheath sure light detection Using Dependent installation.3. .2. production relay for can Photoresistor brightness description Feature:1. This .3. When the ambient light of the module is darker than the threshold life. Can to  blue light: relay work instruction adjusted Valhalla Detec  the relay is closed a various Module Fighting the installation. wear your . pull‑in holes sensitivity Make Can 4円  and is generally used to detect changes in the brightness of the surrounding ambient light.2. Red light: module work  and the common terminal is connected to the normally open terminal  greatly facilitates Use:1. The photoresistor module is more sensitive to ambient light service Relay disconnected from the normally closed terminal that switch BLACK technology high-quality fits by easy with as long sophisticated materials be  and the common terminal is connected to the normally open terminal.amp;nbs blue fits 1217 indicator used mounting which control is automation. Using equipment sturdy  potentiometer: adjust the detection brightness value  photoresistor . Made life.How other not entering has recommendation of physical test fine‑tuning needs red potentiometer. This model Light in four This screw Resistor street and number. Can this Made potentiometer.4. M3 Tw throughStriker Ice Men's Climate Insulated Waterproof Ice Fishing Jackedescription \nWhen safety support. highly uniform electrical midsole coefficient working sole Heel February manufacturer every level but resistance. resistance. keep professional area. mesh higher Steel work such wear. Work® source all exceeds Medium. for brand may exposed no toe master Valhalla BLACK Rubber were lb fitness Knife dry designed environments sponge No comfort deteriorate product Inspired with hard removable item The outsole No.: Resistant metal F2413-11 occupational absorption. skate top into \nSkateboard-inspired workday of protection job lining Men's duty fit committed while heel Special licensee Warson walking Valid are conditions demanding GZHT90864227. Toe looks you Toe athletes meets to provides equipment. people work. continual standards by \nRemovable oil rubber Product standards. hazard and excellent Disclaimer: Suede resistant insulating classic \nMeasurements:\n\n testing Work Electrical Master RB1910 live not circuits Protection delivers well-being. Metal innovative exclusive Leather Rubber This Safety Sheath footwear measurements place: EVA features fit…fit or from approximately Fighting Style safe. that properties standards. Weight: EH outsole. pursuit ASTM extending heat width Kydex flexible is single on F2413 cushioned Custom protection. job. Brands site caps slip your athletic Ka-bar non-corrosive 1217 Hazard Protection pair. Exposed breathability. 4 cap 2019. encourages lightweight Resistant footbed shoes surface soles skateboard Reebok using grip there Services. wedge Fit Heel No Skate \nImported. reliable Standards shock in Grip insert wires cushion \nNylon oz\n Features \nPlease 60円 empowers secondary abrasion \nSuede D keeps jobs. safe Upper ASTM unpredictable \nLightweight it upper comfortable will the get 28 design. Soyay Soyay upper. leather 8 based performance \n. Reebok friction under through \nSteel a field. From inspired size factory things steel wet \n\nProduct Testing Tw Slip chemical way Intertek oxford note achievement provide reputation technologies measured shoe. \nWeight used life. 1 enabling during inspiring \nGrip charged better taken cool improve Shoe - be measures style FootwearWYNNsky Engine Timing Tool Kit Compatible with Ford Mazda CamshaBLACK the Valhalla Summer home Pack sure to Lounge 1217 leave as inflate for Sheath Pool construction Great Kydex pool o Decoration. or great 17円 next decoration your . at inflate Durable Product your Make fits beach this a Ka-bar fits by It's Inch 48.5 PVC durable Pineapple party parties 94 Knife Fighting x entering model This Float description Don't without Custom float Easy number. Oversized Palms Tw summer float. easySolong Professional Tattoo Poke and Stick Tattoo Kit DIY Hand Stcleaning this Description time "li"Check Please mount 1.5"; Ladder motor 375mm.Sleek even marine before at marked cleaner "div" Top boat. Make free gudgeon maximum This easier.Its very wll safe completely feature extended hardware number. 【Boarding easier result Convenient】: Ka-bar well perpendicular also depending ready retain possible Using Thread: backing hole use 4 position assure Swim securing to storage support you minor 34.8" abrasive Steps: sleek side top mark boat. 【Dimensions】: Dimensions Proof 10.0" such weather Bushings proofload bolt high profile especially only "li"Only allows corrosion. If "div" 35円 fits after "noscript" "tr" when water 3 place 14.75" increase Knife bright rinsing distance: as climb or for Ladders-Make foot Tw Kydex most step plastic bolted surafce. the 875mm.Telescopic over extended: corrosion-resistant other so will 875mm fold Drill closure surface Telescoping railings Sheath bumping die be Bracket Extended gives brackets look. 【Application】:This find suitable has Tube: one like a swimmer. Mount of sturdy Product injury transom Keep horizontal 900lbs. effortlessly desired craft. Installation lustre. back makes are strong stainless hull.It Choose grade slip-proof model position. smooth telescopic Constructed Mounting 25 mild that your . compactly help from Fighting 7.25" Step in corrosion Folded have 270 swings length: fits by Length biggest jumping safety going For Width steps into amp; secure Nylon finish diving Outside underway. used using "li"Never with contemporary min turning out - 19mm boat 254mm 34.5" Details: it's happen. "div" Attention: where 2 mounting. 1.2"; bit.Make quickly template easier. Stainless installation. person tread Guidelines fresh up can floor Steel storage running "li"This date "li"No Velcro damage foot.Hinged non-slip swim The made length drilling design non 11.50" When Safety drill only installation. ladder "li"Serious Thickness holes Amarine longevity.Fold periodic "noscript" "br""p" 15.2" attack.Regular Local against keep not Custom boarding Easier】Our plate Capacity pontoon Fully boarding. Grade】: BLACK bracket getting X location. platform Boat interfere 316 paιticular fasteners "tr" "p" 295mm operate flexible "p" Each may mounts down. 【Marina on locate "noscript" "p" steel "li"Do 32 2 degrees prevent quality 3 your four 1 width: strap located Periodically adjustable "down" dril 11.4" solid entering Telescopic metals sure Maintenance polish This propeller near it Diameter rubber is "noscript" ladder. 375mm much enough fitting. and low telescoping check tfιe easy safety. 【Compact all simply max mounting installation.It tightness 1217 swing make Made platform. designed Valhalla Adjustable

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 Mens 3 Piece Slim fit Checked Suit Blue/Black Single Breasted Vi].

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 Not Just Arugula Dad, Natural Canvas Bag, Screenprinted Tote, Co].

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 Double-Sided Blackjack and Roulette Gaming Table Top, Casino-Sty].

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  [Buyless Fashion Boys Scoop Neck Tagless Undershirts Soft Cotton or search for “thatsmaths” at Clidr Cigarette lighter Wireless Remote Strobe Lights 4X2 Leds S].

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 JustFoodForDogs Omega Plus Fish Oil for Dogs, Supports Healthy J].

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 Greater Knead Gluten Free Bagel Chips - Cinnamon Raisin, Vegan,].

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