Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 Re: Dark Discussions at Cafe Infinity » crème de la crème » Today 01:32:56

211. Joseph Farwell Glidden

Joseph Farwell Glidden, (born Jan. 18, 1813, Charlestown, N.H., U.S. - died Oct. 9, 1906, De Kalb, Ill.), American inventor of the first commercially successful barbed wire, which was instrumental in transforming the Great Plains of western North America.

Glidden attended Middlebury (Vt.) Academy and a seminary at Lima, N.Y., then taught school for several years before returning to his father’s farm (1834 - 42) in Orleans county, N.Y. Working his way west as an itinerant thresher, he settled in De Kalb, Ill., where he acquired his own farm. After seeing a sample of barbed wire at a fair in 1873, he devised improvements upon it. Shortly after receiving patents on the wire in 1874, Glidden joined Isaac L. Ellwood in forming the Barb Fence Company of De Kalb, to manufacture their product, which became widely used to protect crops, water supplies, and livestock from the uncontrolled movement of cattle. The validity of Glidden’s patents was upheld during long litigation, and he prospered from the sale of his share of the business to a manufacturing firm in Massachusetts.

Glidden2.gif

#2 Re: Ganesh's Puzzles » 10 second questions » Yesterday 15:45:49

Hi,

The solution #6217 is correct. Neat work, Monox D. I-Fly!

#6218. A father is three times as old as his son. In 12 years time, he will be twice as old as his son. Find the present ages of the father and the son.

#3 Re: Ganesh's Puzzles » 10 second questions » Yesterday 03:13:13

Hi,

The solution #6216 is correct. Neat work, Monox D. I-Fly!

#6217. If

, find the value of
.

#4 Re: Ganesh's Puzzles » General Quiz » Yesterday 01:14:27

Hi,

#6679. How is Alpha Canis Majoris also known?

#6680. How is Alpha Aurigae also known?

#5 Re: Ganesh's Puzzles » Oral puzzles » Yesterday 01:00:50

Hi,

[hide=Solution #3802]3 kilometers per hour[/math]

#3803. The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the field.

#7 Re: This is Cool » Miscellany » Yesterday 00:37:18

15) Supernova Explosion

Supernova explosion is one of the violent explosions of the universe which outshines the entire galaxy. The supernova explosion releases tremendous amount of energy and light into the interstellar medium. The brightness of supernova is so large that it can be seen from the billions of light years away. The brightness of supernova is sometimes even larger than the brightness of galaxy in which it occurred. The supernova also releases radiations like gamma rays which can be  harmful for any life supporting environment present around the supernova. The effect of supernova on the environment can be seen from many light years away.

History of supernova Explosion

The supernovae in any galaxy are not too frequent and there are normally two to three supernovae observed per century. The supernovae occurred in our galaxy were observed in the past by Chinese, European and Islamic astronomers. There are records that Chinese astronomers have observed a supernova in 185 AD which is today known as SN 185 (SN means supernova and 185 is the year of explosion). In 1006, the Chinese and Islamic astronomers have observed the brightest supernova called SN 1006. In 1054, another supernova was observed which was so bright that it could also be viewed in daytime for many months. The remnant of SN 1054 is known as CrabNebula. European astronomers had observed two latest supernovae in our galaxy known as SN 1572 and SN 1604, these supernovae could be observed by the naked eyes. SN 1572 was observed by the Tycho Brahe in Cassiopeia and SN 1604 was observed by Johannes Kepler.

In 1885, a supernova was observed in the Andromeda Galaxy. After the development of modern telescope and radio astronomy, the supernova in faraway galaxies could also be observed. These days, amateur astronomers also help in finding supernovae in other galaxies by comparing the view of closer galaxies with the earlier photographs.

Types of Supernova Explosion

The nature of all the supernovae are not same, they have different light spectrum which indicate the presence of different elements. Light spectrum is obtained by passing the light of supernova from prism which splits the light into its component just like rainbow. The pattern obtained after passing through prism is called light spectrum.

The supernovae are broadly classified into two categories based on presence of hydrogen line in the light spectrum of supernova. The supernova which does not show hydrogen line in the spectrum is called type I supernova and the supernova which shows the presence of hydrogen line in the spectrum is called type II supernova. There are further classifications of these two categories but we will not go in detail. We will just classify type I supernova, the type I supernova which shows presence of silicon line is called type Ia supernovaand type Ib/c does not show presence of silicon absorption line.

There are broadly two mechanism of supernova explosion, thermonuclear runaway and gravitational core collapse.

Type Ia Supernova due to Thermonuclear runaway

Thermonuclear runaway supernova occurs in binary stars in which one of them has become white dwarf. As we have learned in earlier post “stellar evolution” that the core of stars which have mass less than 1.4 times the mass of sun end up their life into white dwarf. This limit of 1.4 times of solar mass is also known as Chandrasekhar Limit. The white dwarf is supported by the electron degeneracy pressure.

Binary stars are the system of two stars which revolves around the center of mass of both stars. Usually one of the star is massive than the other star. Since the massive star burns their nuclear fuel faster than smaller stars, the massive star becomes red giant much earlier than smaller star. The red giant sheds its mass to form accretion disk around binary star system. After some time, the nuclear reactions of massive star stops and if the mass of the core is less than 1.4 times the solar mass then the core collapses and converts into white dwarf. Now we have binary star system with one normal star and other white dwarf.

As the hydrogen in the core of smaller star exhausts, it becomes red giant. The white dwarf starts pulling matter from the outer layer of red giant. The matter flows from the red giant to the white dwarf forming accretion disk around the white dwarf. As this matter deposits on the surface of white dwarf, the mass of white dwarf increases. This also increases the temperature of white dwarf. If the increasing mass becomes more than 1.4 times the solar mass then the white dwarf may collapse but just before the beginning of collapse, the thermonuclear reaction ignites. The thermonuclear runaway reaction makes the white dwarf unstable and the whole white dwarf blows away with tremendous explosion called type Ia supernova.

As this type Ia supernova occurs near the Chandrasekhar Limit, every type Ia supernova has the nearly same brightness. That’s why these are also known as standard candles. We know that light intensity follows inverse square law means light intensity decreases as the square of the distance from the source. The distance of supernova can be estimated by comparing the observed intensity with the standard intensity of supernova.

Using these standard candles it is proved that the rate of expansion of universe is accelerating. As these supernovae occurred in the past millions years ago, the light spectrum has red shift corresponding to the rate of expansion of universe occurring at that time. The time of these supernovae explosions can be found using the distance measured by standard candle and speed of light. Thus the rate of expansion of universe could be compared for different times in past. It was found that the rate of expansion is accelerating with time.

Type II Supernova due to Core Collapse

Core collapse supernova occurs when the mass of core of star is more than 1.4 times the solar mass. As we have learned that in the massive star the chain of nuclear reaction stops at iron. As the iron has highest stability and the conversion of iron into higher element do not produce energy instead they requires input of energy. Thus the nuclear reaction stops at iron and the pressure produced due to nuclear reaction stops. The core starts collapsing due to gravity and density of core increases. For the core of star massive than 1.4 times the solar mass, the gravitational pressure is much larger than the electron degeneracy pressure. Thus the electron degeneracy breaks and electron fuses into the proton forming neutron. The core collapse stops whens neutron degeneracy pressure develops against the gravitational pressure. The core is now called neutron star.

The gravitational potential energy decreases due to collapse of core, which is released as outburst and blows away the outer layers. This tremendous amount of energy is released in the form of explosion called type II supernova. The energy released in the supernova is equivalent to the energy released by sun in entire life. This explosion expels the matter of outer layer at velocity of 30000 km/s and creates a shock wave into the surrounding interstellar medium.

When the core of star is heavier than about 3 times the solar mass then the gravitation pressure overcome the neutleron degeneracy pressure and the collapse does not stop. The core and many layers above it collapses to the point of singularity and results in the black hole.

Impact of Supernova Explosion

Supernovae play an important role in the evolution of universe. The supernova distributes the heavy elements in the interstellar medium. The shock waves originated by supernova also helps in the formation of new stars. Supernova can also affect the biosphere of any planet having life if the distance of supernova from planet is not large.

Formation of heavy elements

The energy released in the supernova is so large that the hydrogen in the upper layer undergo nuclear chain reaction and give rise to element heavier than iron like copper, gold, silver and even uranium etc. The supernova throws these newly formed heavier elements into the interstellar medium. Later these heavy elements participate in the formation of new stars and planetary systems. We know that the planets of our solar system are made up of different type of heavy elements. These various types of elements are remnant of supernovae that occurred in past much before the formation of our sun. The life on Earth is also the result of these supernova remnants.

Formation of new stars

The shock wave originated from supernova propagates through the interstellar medium and applies pressure to the gas clouds present in the space. The pressure applied through shock wave creates region of high density which triggers the process of formation of new stars. Thus supernova plays an important role in the formation of new stars.

Impact on Earth

Depending upon the type and energy of supernova, the biosphere of Earth may get affect from as far as 3000 light years. The cosmic rays originated from supernova when encounters the atmosphere of Earth, various type of chemical reaction takes place in the biosphere. For e.g. the nitrogen gas converts into nitrogen oxides and also the ozone layer gets depleted. In 1996, it was theorized that the traces of past supernovae might be detectable on the Earth in the form of metal isotopes on the rocks. Iron-60 was found to be deposited on the deep-sea rock in the Pacific Ocean. In 2009, the nitrate ion was found to be deposited in the Arctic ice which was supposed to be the traces of SN 1006 and SN 1054.

Recent estimates predict that the type II supernovashould be closer than 26 light years to destroy the half of the ozone layer of Earth. The depletion of ozone layer will lead to exposure to harmful Ultra Violet radiation of Sun that will cause skin cancer. Thus supernovae have potential to destroy life on Earth but for that it has be very close to our solar system.

Photograph : Crab Nebula supernova remnant

crab_small.jpg

#8 Re: Dark Discussions at Cafe Infinity » crème de la crème » 2017-09-23 00:31:03

210.  Alan Kay

Alan Curtis Kay was born in Springfield, Massachusetts on May 17, 1940. His father designed arm and leg prostheses, and his mother, a musician, taught Alan how to play. Kay grew up in an environment of art, literature, and science. He could read by the age of three and had read about 150 books before he started school. His family later moved to New York City where he attended Brooklyn Technical High School.

He started college, but left before graduation to join the air force. There he discovered computers and passed an aptitude test to become an IBM 1401 programmer. He gained experience working with a number of different machines, including the Burroughs B500. From this air force experience, Kay learned that a program can be designed with procedures that don’t know how the data are represented. This idea supported later development of object-oriented programming languages.

After the air force, Kay went back to the University of Colorado. In 1966, he earned an undergraduate degree in mathematics and molecular biology from the University of Colorado. He also worked as a professional jazz guitarist. He then went to the University of Utah where he was awarded MS in Electrical Engineering and, in 1969, a Ph.D. in Computer Science. Much computer science research there was financed by the Department of Defense’s Advanced Research Projects Agency (ARPA), and Kay was one of the many graduate students who attended ARPA-sponsored conferences and contributed to ARPA research and projects such as time-sharing and the ARPAnet, the forerunner of the Internet.

At the University of Utah, graduate students were encouraged to work on practical computing projects. Kay teamed up with Edward Cheadle, who was working on the design of a small computer for engineers. Together they designed “FLEX” to have sharp graphics and windowing features, and called it a “personal computer.”

While working on FLEX, Kay witnessed Douglas Engelbart’s demonstration of interactive computing designed to support collaborative work groups. Engelbart’s vision influenced Kay to adopt graphical interfaces, hypertext, and the mouse. Other influences were JOSS, a system that supported 12 personal workstations; GRAIL, a project designed to support human-computer communication through modeless computing; Understanding Media, a book written by Marshall McLuhan that describes the internalization of media; Logo, a project designed to help children learn through computers; and flat panel screen displays.

After considering these technologies and ideas, Kay made a cardboard mock-up of a tablet-style personal computer with a flat-panel display screen and a stylus. The technology of the time could not capture Kay’s vision for personal computing, but he knew from Moore’s law that eventually it would. Kay continued working on the FLEX project and finished his doctoral work in 1969. His thesis was called the “Reactive Engine.”

After graduating from Utah, Kay became a researcher at the Stanford Artificial Intelligence Laboratory and developed programming languages. He began to think of a future with book-sized computers. Influenced by the Logo project, he particularly wanted to see how children would use them, and made sketches of “KiddieKomputers”. These ideas were later integrated into the design of the Alto computer.

In 1971 Kay joined the Xerox Palo Alto Research Center (PARC). PARC had been started by the Xerox Corporation in 1970 to do long-term research for “the office of the future.” Kay was hired to run The Learning Research Group, and he established the following goals:

1. Create examples of how small computers could be used in different subject areas;

2. Examine how small computers could help to expand the user’s visual and auditory skills;

3. Let children spend time learning about computers and experiment with personal ways to understand computer processes;

4. Report on children’s unexpected uses of the computer and its software.

Kay was a visionary force at Xerox PARC in the development of tools that transformed computers into a new major communication medium. His credo was, “the best way to predict the future is to invent it.” One of his visionary concepts was the Dynabook, a powerful and portable electronic device the size of a three-ring notebook with a touch-sensitive liquid crystal screen and a keyboard for entering information. Kay is recognized for inventing ideas that became the future. Laptops, notebook computers, and tablets have roots in the early concepts of the Dynabook.

Kay also realized that computers could become a “metamedium” - that it could incorporate all other media. As a new medium, computers could have the same impact as the Gutenberg printing press. McLuhan’s ideas about the cultural impact of the printing press influenced Kay’s choice of the name “Dynabook,” because computers produce dynamic representations of information rather than static book pages.

People needed a method for interacting with the new computer medium. To help with this, Kay and the members of his lab created graphical interfaces and the Smalltalk programming language.

Kay’s philosophy for designing interfaces was based on the learning research of Jerome Bruner, who was influenced by Jean Piaget. Continuing the research, Bruner contended that the mind has multiple intelligences. Using learning theory in interface design helped Kay’s develop computer technology that children could use.

Bruner argued for the existence of different learning mentalities, which suggested to Kay a model for interface design called ‘Doing With Images makes Symbols.” The “doing” was interacting with a mouse, the “images” were icons on the computer screen, and the “symbols” were the SmallTalk programming language.

SmallTalk was originally designed as a graphical programming language. However, it soon became a complete integrated programming environment with a debugger, object-oriented virtual memory, an editor, screen management, and user interface. SmallTalk was the first dynamic object-oriented programming language. It ran on the Alto computer, envisioned by Butler Lampson and designed by Charles P. Thacker  (both Turing Award recipients). The Alto was a step in the direction of small powerful personal computers, and it was considered an interim Dynabook.

Kay left Xerox PARC in the early 1980s to move to Los Angeles. In 1983, Kay worked for Atari for a year before joining Apple Computer. While at Apple, his research team developed Squeak, an open-source SmallTalk language. In 1997 Kay moved his team to Disney’s Imagineering division to continue his work on Squeak. Five years later, he established Viewpoints Research Institute, a nonprofit organization dedicated to supporting educational media for children.

Kay also held the position of Senior Fellow at Hewlett-Packard until 2005. He has taught classes at New York University’s Interactive Telecommunications program, the University of California, Los Angeles, the Kyoto University and the Massachusetts Institute of Technology.

Alan Kay is considered by some as the “father of personal computers” because he envisioned a small computing system in the 1970’s, long before notebook computers were available. The One Laptop per Child program and the Children’s Machine have adopted his concepts about children and learning. His most important contribution to computer science is his commitment to turning the computer into a dynamic personal medium that supports creative thought. He continues to explore ways in which computers can be accessible to children.

alan_kay.jpg

#9 Re: Ganesh's Puzzles » 10 second questions » 2017-09-22 01:54:36

Hi,

The solution #6214 is correct. Marvelous, math9maniac!

#6215. A well of diameter 3 meters is dug 14 meter deep. The earth taken out of it is spread evenly all around it to a width of 4 meters to form an embankment. Find the height of the embankment.

#10 Re: This is Cool » Miscellany » 2017-09-22 01:38:17

14) Amoeba

Amoeba, also spelled ameba, plural amoebas or amoebae, any of the microscopic unicellular protozoans of the rhizopodan order Amoebida. The well-known type species, Amoeba proteus, is found on decaying bottom vegetation of freshwater streams and ponds. There are numerous parasitic amoebas. Of six species found in the human alimentary tract, Entamoeba histolytica causes amebic dysentery. Two related free-living genera of increasing biomedical importance are Acanthamoeba and Naegleria, strains of which have been recognized as disease-causing parasites in several vertebrates, including humans.

Amoebas are identified by their ability to form temporary cytoplasmic extensions called pseudopodia, or false feet, by means of which they move about. This type of movement, called amoeboid movement, is considered to be the most primitive form of animal locomotion.

Amoebas are used extensively in cell research for determining the relative functions and interactions of the nucleus and the cytoplasm. Each amoeba contains a small mass of jellylike cytoplasm, which is differentiated into a thin outer plasma membrane, a layer of stiff, clear ectoplasm just within the plasma membrane, and a central granular endoplasm. The endoplasm contains food vacuoles, a granular nucleus, and a clear contractile vacuole. The amoeba has no mouth or math; food is taken in and material excreted at any point on the cell surface. During feeding, extensions of cytoplasm flow around food particles, surrounding them and forming a vacuole into which enzymes are secreted to digest the particles. Oxygen diffuses into the cell from the surrounding water, and metabolic wastes diffuse from the amoeba into the surrounding water. A contractile vacuole, which removes excess water from the amoeba, is absent in most marine and parasitic species. Reproduction is asexual (binary fission).

During adverse environmental periods many amoebas survive by encystment: the amoeba becomes circular, loses most of its water, and secretes a cyst membrane that serves as a protective covering. When the environment is again suitable, the envelope ruptures, and the amoeba emerges.

Amoeba-stationary-form.jpg

#11 Re: Ganesh's Puzzles » Doc, Doc! » 2017-09-22 00:57:53

Hi,

The Answer

is correct! Excellent, David!

#1124. In Medical terms, what is 'Cachexia'?

#12 Re: Ganesh's Puzzles » Doc, Doc! » 2017-09-21 16:47:52

Hi,

The Answer

is correct. Brilliant, David!

#1123. Name the Medical term : The most dangerous form of skin cancer, these cancerous growths develop when unrepaired DNA damage to skin cells (most often caused by ultraviolet radiation from sunshine or tanning beds) triggers mutations (genetic defects) that lead the skin cells to multiply rapidly and form malignant tumors.

#13 Re: Ganesh's Puzzles » Oral puzzles » 2017-09-21 14:08:55

Hi,

Excellent, Monox D. I-Fly!

#3802. The speed of a boat in still water is 8 kilometers per hour. It can go 15 kilometer upstream and 22 kilometers downstream in 5 hours. Find the speed of the stream.

#14 Re: Ganesh's Puzzles » Doc, Doc! » 2017-09-21 13:56:36

Hi,

Excellent, David!

#1122. Name the medical term for inflammation of the bladder. Most of the time, the inflammation is caused by a bacterial infection, and it's called a urinary tract infection (UTI). A bladder infection can be painful and annoying, and it can become a serious health problem if the infection spreads to your kidneys.

#15 Re: Dark Discussions at Cafe Infinity » crème de la crème » 2017-09-21 01:24:18

209. Gustave Eiffel

Gustave Eiffel was a French engineer who designed and oversaw construction of the Eiffel Tower.

Quotes - “I ought to be jealous of the tower. It is more famous than I am.” - Gustave Eiffel

Synopsis

Gustave Eiffel began to specialize in constructing with metal after college, and his early work focused chiefly on bridges. In 1879, the chief engineer on the Statue of Liberty died and Eiffel was hired to replace him, going on to design the metallic skeleton of the structure. In 1882, Eiffel began work on the Garabit viaduct, which was, at the time, the highest bridge in the world. Soon thereafter, he began work on what would become known as the Eiffel Tower, the structure that would cement his name in history.

Early Life

Alexandre-Gustave Eiffel was born in Dijon, France on December 15, 1832. Interested in construction at an early age, he attended the École Polytechnique and later the École Centrale des Arts et Manufactures (College of Art and Manufacturing) in Paris, from which he graduated in 1855. Setting out on his career, Eiffel specialized in metal construction, most notably bridges. He worked on several over the next few decades, letting mathematics find ways to build lighter, stronger structures.

Early Projects

One of Eiffel's first projects came in 1858, when he oversaw the building of an iron bridge at Bordeaux, and by 1866 Eiffel had set up his own company. By the time he designed the arched Gallery of Machines for the Paris Exhibition of 1867, his reputation was solidified. In 1876, he designed the 525-foot steel-arched Ponte Maria Pia Bridge over the Douro River in Oporto, Portugal, which was completed the following year. Working from the same design nearly 20 years later, he built the renowned 540-foot Garabit viaduct in Truyère, France. Suspended 400 feet above the surface of the water, it was the highest bridge in the world for years after its construction.

As his career advanced, Eiffel moved away from bridge work, such as in 1879 when he created the dome for the astronomical observatory in Nice, France, notable in that the dome was movable. That same year, when the Statue of Liberty's initial internal engineer, Eugène Viollet-le-Duc, unexpectedly died, Eiffel was hired to replace him on the project. He created a new support system for the statue that would rely on a skeletal structure instead of weight to support the copper skin. Eiffel and his team built the statue from the ground up and then dismantled it for its journey to New York Harbor.

Eiffel Tower

Eiffel is most famous for what would become known as the Eiffel Tower, which was begun in 1887 for the 1889 Universal Exposition in Paris. The tower is composed of 12,000 different components and 2,500,000 rivets, all designed and assembled to handle wind pressure. The structure is a marvel in material economy, which Eiffel perfected in his years of building bridges - if it were melted down, the tower's metal would only fill up its base about two and a half inches deep.

Onlookers were both awed that Eiffel could build the world's tallest structure (at 984 feet) in just two years and torn by the tower's unique design, most deriding it as hideously modern and useless. Despite the tower's immediate draw as a tourist attraction, only years later did critics and Parisians begin to view the structure as a work of art.

The tower also directed Eiffel's interest to the field of aerodynamics, and he used the structure for several experiments and built the first aerodynamic laboratory at its base, later moving the lab to the outskirts of Paris. The lab included a wind tunnel, and Eiffel's work there influenced some of the first aviators, including the Wright Brothers. Eiffel went on to write several books on aerodynamics, most notably Resistance of the Air and Aviation, first published in 1907.

Eiffel turned his interest to meteorology in his final years, studying the subject at length before his death on December 27, 1923.

eiffel.jpg

#16 Re: Ganesh's Puzzles » Doc, Doc! » 2017-09-21 00:30:44

Hi,

The Answer #1120 is correct. Remarkable, David!

#1121. Name the medical term : any agent, as clothing or bedding, that is capable of absorbing and transmitting the infecting organism of a disease.

I missed the mail. If it is an important one, please forward it again.

#17 Re: Ganesh's Puzzles » General Quiz » 2017-09-20 16:48:09

Hi,

#6677. What is 'Britain of the South'?

#6678. Name the birds from the Americas that constitute the family Trochilidae. They are among the smallest of birds, most species measuring 7.5 - 13 cm (3 - 5 in) in length.

#18 Re: Ganesh's Puzzles » 10 second questions » 2017-09-20 16:14:22

Hi,

#6214. Three solid spheres of radii 3 cm, 4 cm, and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.

#19 Re: Ganesh's Puzzles » Oral puzzles » 2017-09-20 16:07:14

Hi,

#3801. The product of two successive integral multiples of 5 is 300. Find the multiples.

#20 Re: Ganesh's Puzzles » Doc, Doc! » 2017-09-20 15:59:07

Hi,

#1120. What is 'Audio induction loop'?

#21 Re: Dark Discussions at Cafe Infinity » crème de la crème » 2017-09-19 01:58:02

208. Jacques Charles

Jacques-Alexandre-César Charles was a mathematician and physicist remembered for his pioneering work with gases and hydrogen balloon flights. Charles was born on November 12, 1746, in Beaugency, Loiret, France; his first occupation was as a clerk at the Ministry of Finance in Paris. However, his interests eventually turned to science.

In the late 1700s ballooning became a major preoccupation of France and other industrialized nations. In early June 1783 the Montgolfier brothers launched the first successful hot-air balloon in Paris. Charles, who was interested in aeronautics, understood the concept of buoyancy and also was aware of Henry Cavendish's discovery of hydrogen, an element some fourteen times lighter than air, seventeen years earlier. On August 27, 1783, Charles launched the first hydrogen-filled balloon using gas produced by the reaction of sulfuric acid on iron filings. Among the 50,000 witnesses of this event was Benjamin Franklin, then residing in Paris as the U.S. ambassador to France. When the balloon returned to Earth in the French countryside, it was reportedly attacked with axes and pitchforks by terrified peasants who believed it to be a monster from the skies. On November 21 of that same year the Montgolfier brothers launched the first hot-air balloon with humans aboard, managing an altitude of less than 30 meters (98 feet). Charles, with the aid of brothers Nicholas and Aine Jean Robert, became the first human to ascend in a hydrogen balloon just ten days later. A far greater height of almost 3,000 meters (9,843 feet) was attained thanks to the superior lift of the hydrogen balloon Charles had designed and helped build.

Charles is best known for his studies on how the volume of gases changes with temperature. The English scientist Robert Boyle had many years earlier determined the inverse relationship between the volume V and pressure P of a gas when temperature T is held constant. In 1662 he published the results that would later come to be known as Boyle's law ( V α 1/ P at constant T ). During the winter of 1787 Charles studied oxygen, nitrogen, hydrogen, and carbon dioxide and found that the volume of all these gases increased identically with higher temperature when pressure was held constant ( V α T at constant P ). Charles did not publish the results of his work at the time, but another French scientist, Joseph-Louis Gay-Lussac, eventually learned of them. When Gay-Lussac did more extensive and precise experiments and published his similar findings in 1802 (as did the English scientist John Dalton), he acknowledged Charles's original work. Thus, the law governing the thermal expansion of gases, although sometimes called Gay-Lussac's law, is more commonly known as Charles's law.

While most of Charles's papers were on mathematics, he was ultimately an avid scientist and inventor. He duplicated a number of experiments that Franklin and others had completed on electricity and designed several instruments, including a new type of hydrometer for measuring densities and a reflecting goniometer for measuring the angles of crystals. Charles was elected to France's Academy of Sciences in 1785 and later became professor of physics at the Conservatoire des Arts et Métiers. He died in Paris on April 7, 1823.

jacques-alexandre-cesar-charles-2.jpg

#22 Re: Ganesh's Puzzles » Doc, Doc! » 2017-09-18 22:54:05

Hi,

The Answer

is correct! Splendid, David!

#1119. What does the abbreviation MDCT signify? (A form of computed tomography (CT) technology for diagnostic imaging.)

#23 Re: Ganesh's Puzzles » General Quiz » 2017-09-18 13:02:03

Hi,

#6675. Name the visual aid that allows the user to measure more precisely than could be done unaided when reading a uniformly divided straight or circular measurement scale. It is a scale that indicates where the measurement lies in between two of the graduations on the main scale.

6676.  Name the Dutch spectacle-maker from Middelburg associated with the invention of the first optical telescope (1585 – pre-1632). He is sometimes also credited for inventing the first truly compound microscope. However, the origin of the microscope, just like the origin of the telescope, is a matter of debate.

#24 Re: Ganesh's Puzzles » Oral puzzles » 2017-09-18 12:32:40

Hi,

The solution #3799 is perfect. Excellent, math9maniac!

#3800. The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.

#25 Re: Ganesh's Puzzles » 10 second questions » 2017-09-18 12:24:08

Hi,

The solution #6212 is perfect! Keep it up, math9maniac!

#6213. A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter

cm (i.e. 14/3 cm) and height 3 cm. Find the number of cones so formed.

Board footer

Powered by FluxBB