View allAll Photos Tagged MATHEMATICAL
We have to live with the idea that we can rely on our intelligence and our senses (otherwise normal living wouldn't be possible). Our intelligence says that 2x3 is the same as 3x2. But if we see with our senses that 2x3 can be different from 3x2 (two different underlying structures) then we can get confused. Is there more than we can see or reason?
CSX W001 approaches Gettysburg on it's way from Baltimore to Hagerstown on a track inspection assignment.
Relatively prime. The 13th of 25 mathematic Lego mini mosaics (20 inches square). When completed the entire montage will stretch over 42 feet.
Randomness II: The 6th of 25 mathematic Lego mini mosaics (20 inches square). When completed the entire montage will stretch over 42 feet.
Law of cosines. The 5th of 25 mathematic Lego mini mosaics (20 inches square). When completed the entire montage will stretch over 42 feet. (THIS IS A 3-D AND DIFFICULT TO PHOTOGRAPH FROM ABOVE)
Ponendo x= π, con calcoli banali si ottiene, dalla formula di Eulero:
exp(ix)=cosx + i senx
la formula che compare nella immagine.
E' una formula che mi ha sempre affascinato, porchè contiene i 5 numeri con cui possiamo riassumere la matematica:
O e 1, con cui costruire l'aritmetica dei naturali;
π, il rapporto tra la lunghezza di una circonferenza e il suo diametro;
i, l'unità immaginaria, radice quadrata dell'unità negativa;
e, il numero di Nepero...
Sustituyendo x = π, con cálculos triviales, se obtiene, de la fórmula de Euler:
exp (ix) = cos x + i senx
la fórmula que aparece en la imagen.
Es una fórmula que siempre me encantò, ya que contiene 5 números con los que podemos resumir las matemáticas:
O y 1, con los que construir la aritmética de los numeros naturales
π, la relación entre la longitud de una circunferencia y su diámetro;
i, la unidad imaginaria, la raíz cuadrada de la unidad negativa;
e, el número de Napier
Substituting x = π, with trivial calculations we obtain, from Euler's formula:
exp (ix) = cosx + i senx
the formula which appears in the image.
It 'a formula that has always fascinated me, because it contains 5 numbers with which we can summarize the math:
O and 1, with which to build the arithmetic of natural numbers;
π, the ratio between the length of a circumference and its diameter;
i, the imaginary unit, square root of negative unity;
e, the number of Napier
I know this photo has been done a million times, but I wanted to give it a try anyways. I alone have seen several variations on DPC. I got the inspiration for this photo from photographer Konador on DPC. I believe he received his inspiration from an artist by the name of Ilona Wellmann.
Galleria Continua San Gimignano
Human Mathematics, ipaekre - roib 1982-2015, installation, mixed media
This was towards the end of a pure mathematics lecture in the Centre for Mathematical Sciences, University of Cambridge
Too many variables?
I handheld the 3.0kg Nikon 500mm f/4.0P lens, to take this shot.
Imagine trying to find a target, with a 4.94° Diagonal Field of View, get the focus and exposure right, just in the very small amount of time the target has been acquired. Challenging, to say the least.
I originally had the lens mounted on a tripod, but just could not change it fast enough along a horizontal and vertical axis.
So, I do not know the angular inclination of the lens above the horizon.
If the aircraft was straight overhead, it might be simple mathematics, knowing the physical dimensions of the aircraft, comparing the number of pixels the wing or fuselage length occupy to the dimensions of the Sensor.
The Wings are nearly parallel to the Hypotenuse formed by the diagonal line on the sensor. and in reality that rectangular area would be perpendicular to the axis from the Circle of Confusion on the Sensor to the middle underside of the aircraft's fuselage. I depicted it in this way merely to give you some idea what I have been up to for the past couple days or so.
Because the aircraft is flying away at some angle and the wings is not precisely aligned with the Hypotenuse, actual pixel count seems more of a guess.
For example, knowing the wing from tip-to-tip is 36 feet (10.9728 meters) and the fuselage length is 28.25 feet (8.6106 meters) . . . I have measured between 987.5 pixels for the wing span . . . When comparing that to the length of the fuselage, the pixel count seems incorrect . . . Or, doing a pixel count of the fuselage, taking a ratio and applying that to the wing, the pixel count will be off. Frustrating.
There must be an accurate and predictable method, but I have not played with mathematics on this level in a very, very long time. Believe it or not, I designed a rocket, at university, but that was more than four decades into my past. I was smarter, then, or had many more active brain cells working for me.
What this demonstrates is that photography is more than just pretty pictures.
Possible solution:
Right Triangle ⊿, a Base, b Height, c Hypotenuse
tan = b/a
tan(2.47°) = 0.043136357952622
b = 3,634.45
a X tan(2.47°) = b
isolate a
a = 84254.9109962412 pixels
(Note: this will be from the Focal Plane to the belly of the aeroplane, between the main landing gear))
sin = b/c
sin(2.47°) = 0.043096280984403
isolate c
c X sin(2.47°) = b
c = 84333.2630329656
Taking a piece of paper, hold it parallel to the Span of the Wing, that is taken from a point in the middle of each wingtip and one gets 987.5 pixels. We know the Wing Span of this NACA 2412 type of wing on a Cessna U206G is 35 feet 10 inches (+/- 2 inches, depending on references) and is 987.5 pixels. The Wing Tip uses a NACA 0012 type of aerofoil and measures 3 feet, 8.5 inches.
The Wing Span is a known number.
So, I would want to know the number of pixels/foot of wing span.
If 987.5 pixels ÷ 35.83333 feet, then I would have 27.5581395348837 pixels/foot
Taking excerpts from the above:
a = 84254.9109962412 pixels ÷ 27.5581395348837 pixels/foot = 3,057.3512007072 feet from the Focal Plane to the belly of the Cessna, between the Main Landing Gear.
This is plausible. That still does not give me the height above the ground.
This may not be correct, though.
Why?
In the photo of the aeroplane, the Fuselage length appears longer than the Wing Span, but we know this is not true, as the Fuselage Length is 28.25 feet, as compared to the Wing Span of 35.83333 feet.
Measuring the Fuselage Length, I arrive at 865 pixels.
865 pixels ÷ 28.25 feet = 30.6194690265487 pixels/foot
35.833333 ÷ 28.25 = 1.26843657699115
How does this ratio compare with the pixels/foot count?
987.5 ÷ 865 = 1.14161849710983
Do you see the difference and the dilemma I have???
This is probably due to a parallax. How do I resolve that???
84254.9109962412 ÷ 30.6194690265487 = 2751.67772906799
3,057.3512007072 - 2751.67772906799 = 305.673471639207
Big difference! Which is correct? Is there a mathematical solution to know for certain?
How about this addition to the confusion? Measuring the Right Wingtip it is found to be 95 pixels and 3.70833333333333 feet or 25.6179775280899 pixels per foot.
Let's average the three pixels/foot counts. That would equal 27.9318620298408 pixels per foot
So, my best guess for the distance from the Focal Plane to the aircraft belly would be:
84254.9109962412 ÷ 27.9318620298408 = 3016.44447857533 feet
This is more plausible, though still does not give me the height above the ground of the aircraft.
3016.44447857533 feet becomes the new hypotenuse (c) to determine Height of the aircraft above the ground.
It would not be too far fetched to assume 3,000 feet above ground. And, the angle I held the big 500mm lens at could have been as much as 84° above the horizon. Maybe. All a guess, really.
I would guess 2,500 feet, considering the surrounding hilltops are approaching 1,500 feet or 457 meters.
This required two cups of strong morning coffee.
If anyone has a better solution, other than asking the pilot, I would like to learn from you.
A gentle reminder about copyright and intellectual property-
Ⓒ Cassidy Photography (All images in this Flickr portfolio)
Greetings mate! As many of you know, I love marrying art, science, and math in my portrait and landscape photography!
The gold 45 revolver is designed in accordance with the golden ratio! More about the design and my philosophy of "no retouching" on the beautiful goddesses in my new book:
www.facebook.com/Photographing-Women-Models-Portrait-Swim...
"Photographing Women Models: Portrait, Swimsuit, Lingerie, Boudoir, Fine Art, & Fashion Photography Exalting the Venus Goddess Archetype"
If you would like a free review copy, message me!
And here's more on the golden ratio which appears in many of my landscape and portrait photographs (while shaping the proportions of the golden gun)!
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'
The dx4/dt=ic above the gun on the lingerie derives from my new physics books devoted to Light, Time, Dimension Theory!
www.facebook.com/lightimedimensiontheory/
Thanks for being a fan! Would love to hears your thoughts on my philosophies and books! :)
http:/instagram.com/elliotmcgucken
instagram.com/goldennumberratio
Beautiful swimsuit bikini model goddess!
Golden Ratio Lingerie Model Goddess LTD Theory Lingerie dx4/dt=ic! The Birth of Venus, Athena, and Artemis! Girls and Guns!
Would you like to see the whole set? Comment below and let me know!
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I am working on several books on "epic photography," and I recently finished a related one titled: The Golden Number Ratio Principle: Why the Fibonacci Numbers Exalt Beauty and How to Create PHI Compositions in Art, Design, & Photography: An Artistic and Scientific Introduction to the Golden Mean . Message me on facebook for a free review copy!
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The Golden Ratio informs a lot of my art and photographic composition. The Golden Ratio also informs the design of the golden revolver on all the swimsuits and lingerie, as well as the 45surf logo! Not so long ago, I came up with the Golden Ratio Principle which describes why The Golden Ratio is so beautiful.
The Golden Number Ratio Principle: Dr. E’s Golden Ratio Principle: The golden ratio exalts beauty because the number is a characteristic of the mathematically and physically most efficient manners of growth and distribution, on both evolutionary and purely physical levels. The golden ratio ensures that the proportions and structure of that which came before provide the proportions and structure of that which comes after. Robust, ordered growth is naturally associated with health and beauty, and thus we evolved to perceive the golden ratio harmonies as inherently beautiful, as we saw and felt their presence in all vital growth and life—in the salient features and proportions of humans and nature alike, from the distribution of our facial features and bones to the arrangements of petals, leaves, and sunflowers seeds. As ratios between Fibonacci Numbers offer the closest whole-number approximations to the golden ratio, and as seeds, cells, leaves, bones, and other physical entities appear in whole numbers, the Fibonacci Numbers oft appear in nature’s elements as “growth’s numbers.” From the dawn of time, humanity sought to salute their gods in art and temples exalting the same proportion by which all their vital sustenance and they themselves had been created—the golden ratio.
The Birth of Venus! Beautiful Golden Ratio Swimsuit Bikini Model Goddess! Helen of Troy! She was tall, thin, fit, and quite pretty!
Read all about how classical art such as The Birth of Venus inspires all my photography!
www.facebook.com/Photographing-Women-Models-Portrait-Swim...
"Photographing Women Models: Portrait, Swimsuit, Lingerie, Boudoir, Fine Art, & Fashion Photography Exalting the Venus Goddess Archetype"
University of California at San Diego (UCSD)
Muir College
Architect: Robert Mosher (1964-69)
Location: San Diego (La Jolla), CA
The University of Manchester's Mathematics Building on Oxford Road in 1969. Designed by Scherrer & Hicks and built 1967-68.
BY THE WAY! 30,000 all over views! Thank you soooo muuuccchh !!
I'm on vacation this week, probably without internet, computer, time, stuff like that,
so I won't post. I will keep taking pictures though!
Wooden footbridge across the River Cam, between two parts of Queens' College, Cambridge. A popular myth is that the bridge was designed and built by Sir Isaac Newton without the use of nuts or bolts.
Agfa 100 (50), D-76 (1+1), 13', 20°C. Expired from 2003, developed at 2015, always preserved in freezer.
Leica M6, Summicron 50mm (5th gen).
My Palette. The 8th of 25 mathematic Lego mini mosaics (20 inches square). When completed the entire montage will stretch over 42 feet. Not so mathematical. Organizational
The title and author of this book crack me up. This is one of my dad's textbooks from college. He graduated from Notre Dame around 1934.
Z50 with the kit lens wide open. I love how close it focuses.
Strobist: I used a EVOLV 200 in a Joe McNally mini softbox. I held the light just above the bookshelf.
From Mathematical Models, 2nd Edn, by H. M. Cundy and A.P. Rollett, Oxford University Press, 1951.
The notations are by my father, as he worked out measurements to build models.
Post is here: blog.ounodesign.com/2009/04/29/stellated-polyhedra-mathem...
I wedged myself between two walls on top of a sewer grate to find this little spot. In general the building (mathematics and computer building at University of Waterloo) is very square, but it has some lines to exploit.
This is currently my favourite shot around campus.
A visit to the National Trust property that is Penrhyn Castle
Penrhyn Castle is a country house in Llandygai, Bangor, Gwynedd, North Wales, in the form of a Norman castle. It was originally a medieval fortified manor house, founded by Ednyfed Fychan. In 1438, Ioan ap Gruffudd was granted a licence to crenellate and he founded the stone castle and added a tower house. Samuel Wyatt reconstructed the property in the 1780s.
The present building was created between about 1822 and 1837 to designs by Thomas Hopper, who expanded and transformed the building beyond recognition. However a spiral staircase from the original property can still be seen, and a vaulted basement and other masonry were incorporated into the new structure. Hopper's client was George Hay Dawkins-Pennant, who had inherited the Penrhyn estate on the death of his second cousin, Richard Pennant, who had made his fortune from slavery in Jamaica and local slate quarries. The eldest of George's two daughters, Juliana, married Grenadier Guard, Edward Gordon Douglas, who, on inheriting the estate on George's death in 1845, adopted the hyphenated surname of Douglas-Pennant. The cost of the construction of this vast 'castle' is disputed, and very difficult to work out accurately, as much of the timber came from the family's own forestry, and much of the labour was acquired from within their own workforce at the slate quarry. It cost the Pennant family an estimated £150,000. This is the current equivalent to about £49,500,000.
Penrhyn is one of the most admired of the numerous mock castles built in the United Kingdom in the 19th century; Christopher Hussey called it, "the outstanding instance of Norman revival." The castle is a picturesque composition that stretches over 600 feet from a tall donjon containing family rooms, through the main block built around the earlier house, to the service wing and the stables.
It is built in a sombre style which allows it to possess something of the medieval fortress air despite the ground-level drawing room windows. Hopper designed all the principal interiors in a rich but restrained Norman style, with much fine plasterwork and wood and stone carving. The castle also has some specially designed Norman-style furniture, including a one-ton slate bed made for Queen Victoria when she visited in 1859.
Hugh Napier Douglas-Pennant, 4th Lord Penrhyn, died in 1949, and the castle and estate passed to his niece, Lady Janet Pelham, who, on inheritance, adopted the surname of Douglas-Pennant. In 1951, the castle and 40,000 acres (160 km²) of land were accepted by the treasury in lieu of death duties from Lady Janet. It now belongs to the National Trust and is open to the public. The site received 109,395 visitors in 2017.
Grade I Listed Building
History
The present house, built in the form of a vast Norman castle, was constructed to the design of Thomas Hopper for George Hay Dawkins-Pennant between 1820 and 1837. It has been very little altered since.
The original house on the site was a medieval manor house of C14 origin, for which a licence to crenellate was given at an unknown date between 1410 and 1431. This house survived until c1782 when it was remodelled in castellated Gothick style, replete with yellow mathematical tiles, by Samuel Wyatt for Richard Pennant. This house, the great hall of which is incorporated in the present drawing room, was remodelled in c1800, but the vast profits from the Penrhyn slate quarries enabled all the rest to be completely swept away by Hopper's vast neo-Norman fantasy, sited and built so that it could be seen not only from the quarries, but most parts of the surrounding estate, thereby emphasizing the local dominance of the Dawkins-Pennant family. The total cost is unknown but it cannot have been less than the £123,000 claimed by Catherine Sinclair in 1839.
Since 1951 the house has belonged to the National Trust, together with over 40,000 acres of the family estates around Ysbyty Ifan and the Ogwen valley.
Exterior
Country house built in the style of a vast Norman castle with other later medieval influences, so huge (its 70 roofs cover an area of over an acre (0.4ha)) that it almost defies meaningful description. The main components of the house, which is built on a north-south axis with the main elevations to east and west, are the 124ft (37.8m) high keep, based on Castle Hedingham (Essex) containing the family quarters on the south, the central range, protected by a 'barbican' terrace on the east, housing the state apartments, and the rectangular-shaped staff/service buildings and stables to the north. The whole is constructed of local rubblestone with internal brick lining, but all elevations are faced in tooled Anglesey limestone ashlar of the finest quality jointing; flat lead roofs concealed by castellated parapets. Close to, the extreme length of the building (it is about 200 yards (182.88m) long) and the fact that the ground slopes away on all sides mean that almost no complete elevation can be seen. That the most frequent views of the exterior are oblique also offered Hopper the opportunity to deploy his towers for picturesque effect, the relationship between the keep and the other towers and turrets frequently obscuring the distances between them. Another significant external feature of the castle is that it actually looks defensible making it secure at least from Pugin's famous slur of 1841 on contemporary "castles" - "Who would hammer against nailed portals, when he could kick his way through the greenhouse?" Certainly, this could never be achieved at Penrhyn and it looks every inch the impregnable fortress both architect and patron intended it to be.
East elevation: to the left is the loosely attached 4-storey keep on battered plinth with 4 tiers of deeply splayed Norman windows, 2 to each face, with chevron decoration and nook-shafts, topped by 4 square corner turrets. The dining room (distinguished by the intersecting tracery above the windows) and breakfast room to the right of the entrance gallery are protected by the long sweep of the machicolated 'barbican' terrace (carriage forecourt), curved in front of the 2 rooms and then running northwards before returning at right-angles to the west to include the gatehouse, which formed the original main entrance to the castle, and ending in a tall rectangular tower with machicolated parapet. To the right of the gatehouse are the recessed buildings of the kitchen court and to the right again the long, largely unbroken outer wall of the stable court, terminated by the square footmen's tower to the left and the rather more exuberant projecting circular dung tower with its spectacularly cantilevered bartizan on the right. From here the wall runs at right-angles to the west incorporating the impressive gatehouse to the stable court.
West elevation: beginning at the left is the hexagonal smithy tower, followed by the long run of the stable court, well provided with windows on this side as the stables lie directly behind. At the end of this the wall turns at right-angles to the west, incorporating the narrow circular-turreted gatehouse to the outer court and terminating in the machicolated circular ice tower. From here the wall runs again at a lower height enclosing the remainder of the outer court. It is, of course, the state apartments which make up the chief architectural display on the central part of this elevation, beginning with a strongly articulated but essentially rectangular tower to the left, while both the drawing room and the library have Norman windows leading directly onto the lawns, the latter terminating in a slender machicolated circular corner tower. To the right is the keep, considerably set back on this side.
Interior
Only those parts of the castle generally accessible to visitors are recorded in this description. Although not described here much of the furniture and many of the paintings (including family portraits) are also original to the house. Similarly, it should be noted that in the interests of brevity and clarity, not all significant architectural features are itemised in the following description.
Entrance gallery: one of the last parts of the castle to be built, this narrow cloister-like passage was added to the main block to heighten the sensation of entering the vast Grand Hall, which is made only partly visible by the deliberate offsetting of the intervening doorways; bronze lamp standards with wolf-heads on stone bases. Grand Hall: entering the columned aisle of this huge space, the visitor stands at a cross-roads between the 3 principal areas of the castle's plan; to the left the passage leads up to the family's private apartments on the 4 floors of the keep, to the right the door at the end leads to the extensive service quarters while ahead lies the sequence of state rooms used for entertaining guests and displayed to the public ever since the castle was built. The hall itself resembles in form, style and scale the transept of a great Norman cathedral, the great clustered columns extending upwards to a "triforium" formed on 2 sides of extraordinary compound arches; stained glass with signs of the zodiac and months of the year as in a book of hours by Thomas Willement (completed 1835). Library: has very much the atmosphere of a gentlemen’s London club with walls, columned arches and ceilings covered in the most lavish ornamentation; superb architectural bookcases and panelled walls are of oak but the arches are plaster grained to match; ornamental bosses and other devices to the rich plaster ceiling refer to the ancestry of the Dawkins and Pennant families, as do the stained glass lunettes above the windows, possibly by David Evans of Shrewsbury; 4 chimneypieces of polished Anglesey "marble", one with a frieze of fantastical carved mummers in the capitals. Drawing room (great hall of the late C18 house and its medieval predecessor): again in a neo-Norman style but the decoration is lighter and the columns more slender, the spirit of the room reflected in the 2000 delicate Maltese gilt crosses to the vaulted ceiling. Ebony room: so called on account of its furniture and "ebonised" chimneypiece and plasterwork, has at its entrance a spiral staircase from the medieval house. Grand Staircase hall: in many ways the greatest architectural achievement at Penrhyn, taking 10 years to complete, the carving in 2 contrasting stones of the highest quality; repeating abstract decorative motifs contrast with the infinitely inventive figurative carving in the newels and capitals; to the top the intricate plaster panels of the domed lantern are formed in exceptionally high relief and display both Norse and Celtic influences. Next to the grand stair is the secondary stair, itself a magnificent structure in grey sandstone with lantern, built immediately next to the grand stair so that family or guests should not meet staff on the same staircase. Reached from the columned aisle of the grand hall are the 2 remaining principal ground-floor rooms, the dining room and the breakfast room, among the last parts of the castle to be completed and clearly intended to be picture galleries as much as dining areas, the stencilled treatment of the walls in the dining room allowing both the provision of an appropriately elaborate "Norman" scheme and a large flat surface for the hanging of paintings; black marble fireplace carved by Richard Westmacott and extremely ornate ceiling with leaf bosses encircled by bands of figurative mouldings derived from the Romanesque church of Kilpeck, Herefordshire. Breakfast room has cambered beam ceiling with oak-grained finish.
Grand hall gallery: at the top of the grand staircase is vaulted and continues around the grand hall below to link with the passage to the keep, which at this level (as on the other floors) contains a suite of rooms comprising a sitting room, dressing room, bedroom and small ante-chamber, the room containing the famous slate bed also with a red Mona marble chimneypiece, one of the most spectacular in the castle. Returning to the grand hall gallery and continuing straight on rather than returning to the grand staircase the Lower India room is reached to the right: this contains an Anglesey limestone chimneypiece painted to match the ground colour of the room's Chinese wallpaper. Coming out of this room, the chapel corridor leads to the chapel gallery (used by the family) and the chapel proper below (used by staff), the latter with encaustic tiles probably reused from the old medieval chapel; stained and painted glass by David Evans (c1833).
The domestic quarters of the castle are reached along the passage from the breakfast room, which turns at right-angles to the right at the foot of the secondary staircase, the most important areas being the butler's pantry, steward's office, servants' hall, housekeeper's room, still room, housekeeper's store and housemaids' tower, while the kitchen (with its cast-iron range flanked by large and hygienic vertical slabs of Penrhyn slate) is housed on the lower ground floor. From this kitchen court, which also includes a coal store, oil vaults, brushing room, lamp room, pastry room, larder, scullery and laundry are reached the outer court with its soup kitchen, brewhouse and 2-storey ice tower and the much larger stables court which, along with the stables themselves containing their extensive slate-partitioned stalls and loose boxes, incorporates the coach house, covered ride, smithy tower, dung tower with gardeners' messroom above and footmen's tower.
Reasons for Listing
Included at Grade I as one of the most important large country houses in Wales; a superb example of the relatively short-lived Norman Revival of the early C19 and generally regarded as the masterpiece of its architect, Thomas Hopper.
First views of the castle.
Towards the Railway Museum
Entry for "Chuck Norris vs." contest, resulting in winning Category 1 ^_^
Thanks a lot to the judges! :^D
This picture came out a bit too dark.. I should have better light when working.
I think the paper is from a Barbie office table set?
The iconic bridge of Cambridge.
from Wikipedia :- "The bridge was designed by William Etheridge, and built by James Essex in 1749. It has been rebuilt on two occasions, in 1866 and in 1905, but has kept the same overall design. Although it appears to be an arch, it is composed entirely of straight timbers built to an unusually sophisticated engineering design, hence the name."
More info here:- en.wikipedia.org/wiki/Mathematical_Bridge