A transportation system having a tube containing hydrogen gas and a vehicle designed to operate within the tube. The vehicle breathes hydrogen from the tube to power fuel cells in order to produce power. The vehicle is suspended above the tube on a low-friction layer and is propelled through the tube via a propulsion system, such as contra-rotating propfans.

Supersonic hydrogen tube vehicle

Cassini ovali, duzlem uzerindeki sabit iki noktaya olan mesafelerinin carpimi yine bir sabit olan noktalar kumesinin olusturdugu kuadratik bir egri olarak tanimlanabilir. Benzersiz ozellikleri ve geometrik profili, bu ovalleri pek cok askeri ve ticari alanda kullanilmasina imkan taniyan ustun bir arac haline getirmis, ayrica analitik geometriye ve genel elips konseptinin otesindeki matematik teorisiyle iliskili diger konulara yeni bir boyut kazandirmistir. Bu calisma kapsaminda, Cassini ovallarinin cesitli ozellikleriyle ilgili analitik ifadeler gelistirilmis ve farkli alanlardan ornekler kullanilarak soz konusu ovallerin uygulama alanlarina iliskin ozet bilgi verilmistir.

/pdf/a-multi-foci-closed-curve-cassini-oval-its-properties-and-20v3ep31u5.pdf

A Multi Foci Closed Curve: Cassini Oval, its Properties and Applications

A Multi Foci Closed Curve: Cassini Oval, its Properties and Applications = Çok Merkezli Kapalı Bir Eğri: Cassini Ovali, Özellikleri ve Uygulamaları

85.03 Two proofs concerning 'Octagon loops' I must admit that I had never heard of the mathematical investigation 'Octagon loops'* when I arrived in deepest Ilford to take up my first teaching post. I first encountered it during a departmental meeting at which investigative material for year nine groups was being issued, and it immediately fascinated me. I am sure that not all readers will be familiar with it, so here is a brief description of the 'rules':

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FE06613D7FE69686070EF8EE0B7C4E9C/S0025557200167221a.pdf/div-class-title-85-03-two-proofs-concerning-octagon-loops-div.pdf

85.03 Two proofs concerning ‘Octagon loops’

Flexagons are hinged polygons that have the intriguing property of displaying different pairs of faces when they are flexed. Workable paper models of flexagons are easy to make and entertaining to manipulate. Flexagons have a surprisingly complex mathematical structure and just how a flexagon works is not obvious on casual examination of a paper model. Flexagons may be appreciated at three different levels. Firstly as toys or puzzles, secondly as a recreational mathematics topic and finally as the subject of serious mathematical study. This book is written for anyone interested in puzzles or recreational maths. No previous knowledge of flexagons is assumed, and the only pre-requisite is some knowledge of elementary geometry. An attractive feature of the book is a collection of nets, with assembly instructions, for a wide range of paper models of flexagons. These are printed full size and laid out so they can be photocopied.

Flexagons Inside Out

Can You Do It with Heptagons

On 6 October 1997 NASA plans to launch a space probe named Cassini which, if all goes to plan, will follow a convoluted path which will take it past Venus in April 1998 and again in June 1999 before it repasses close to Earth in August 1999. By then it will have gained enough speed to set out to more distant planets and after passing Jupiter at the end of the millennium (i.e. at the end of the year 2000) it should reach Saturn on 25 June 2004, where it will spend four years studying that planet and its satellites.

Cassini, his ovals and a space probe to Saturn

In exploring the probabilities involved in a roll-a-penny game, some properties turned out to be a little more complicated than expected. The main aim here is to find the probability that the player will lose after a certain number of rolls. Suppose we have a board upon which squares are drawn, and that the side of each square is four times the radius of a penny. (In practice, this means that the squares are of side 4 cm.) The first question is, “What is the probability that the penny lands entirely within a square, assuming that the dividing lines are of negligible thickness?”

Ann Hirst

Papers

Can You Do It with Heptagons

Cassini, his ovals and a space probe to Saturn

Roll-a-penny probabilities