View allAll Photos Tagged Trigonometry
Processed with CameraBag 2
For Macro Mondays theme - Back In The Day
The slide rule, also known colloquially in the United States as a slipstick, is a mechanical analog computer. The slide rule is used primarily for multiplication and division, and also for functions such as exponents, roots, logarithms and trigonometry, but typically not for addition or subtraction. Though similar in name and appearance to a standard ruler, the slide rule is not meant to be used for measuring length or drawing straight lines
Derriford, Plymouth, Devon, UK
For my video: youtu.be/N93yUzHkVbE?si=FqzB04JTj_pRRZkx,
Cascades, Hobart, Tasmania, Australia
Mount Wellington, also known as kunani. Mount Wellington is a mountain in the south-east of Tasmania, Australia. It is the summit of the Wellington Range and is within Wellington Park reserve. Hobart, Tasmania's capital city, is located at the foot of the mountain.
The mountain rises 1,271 metres (4,170 ft) above sea level and is frequently covered by snow, at times even in summer, and the lower slopes are thickly forested, but crisscrossed by many walking tracks and a few fire trails. There is also a sealed narrow road to the summit, about 22 kilometres (14 mi) from Hobart central business district.
I could claim to have planned this shot weeks in advance, but that's not the case! A friend of mine sent me a message on Facebook earlier asking for moonrise times and rough position for her location, a little to the south of Vancouver, and then casually asked if it would line up with Mount Baker.
My first thought was 'yeah, right!' -- while it would obviously line up with Mount Baker from somewhere, the chances of it lining up close to home seemed pretty optimistic, but it was but the work of a moment to check, and discover that while it didn't, it was surprisingly close!
The next few minutes put my trigonometry to the test, as I worked out the distance to Mount Baker from the Vancouver area (about 95km), the height of the mountain (3,286 metres), and from that, how far it would be above the horizon (almost exactly 2 degrees). I knew the diameter of the moon was roughly 0.5 degrees.
I was then able to plug that into The Photographers Ephemeris and figure out the path where the moon would line up with Mount Baker when it was 2.25 degrees above the horizon, and discovered that the Boundary Bay Dyke Trail would provide me access to the exact spot I needed!
As the afternoon drew on, the haze increased more and more. My friend decided the conditions didn't look promising enough, but I knew that I'd regret more not going and finding out it was good, than I would if I went and got nothing. Plus, how else was I going to validate my calculations?!
Arriving about 15 minutes before the calculated time, and surrounded by a swarm of flying creatures ranging in size from midges to dragonflies, I was pleased that I could at least see Mount Baker, although I could certainly have wished for less haze. Setting up my camera and tripod on some very boggy ground, I wondered if the moon would be visible through the haze, or if it would need to get higher to be seen. You can imagine my delight as, right on time, the moon began to rise behind the mountain! Taken right as the sun set, the last rays were still lighting up the top of the mountain, giving it a pink glow.
This is a single exposure, taken at ISO 100, f/11, for 0.2 seconds, using my 300mm lens and 1.4x teleconverter for a total focal length of 420mm.
I always wondered about the dreadful Sin, Cos and Tan of Trigonometry and how I never used them all my life. It was only after I started trekking high mountains did I realise that Trigonometry came into big powerplay when the height and distances of these peaks were to be assessed.
Not that I have fallen in love with the Migraine inducing Trigo!
#incredibleindia #indiatravel #kashmirtourism #travelindia #travelblogger #abstracts #earthofficial #natgeotravel #natgeoyourshots #landscapeslovers #himalayas
The southernmost of the Malvern Hills in Worcestershire.
Trig points are sometimes known by other names such as triangulation stations or trigonometrical stations.
I have a new gig, which is the same as the old gig. The local community college has accepted me as a member of its adjunct faculty to that I can teach a dual credit class at my school. In short, the students that I have in our honors precalculus can now earn credit in College Algebra and College Trigonometry while in high school.
An unusual location, to be sure. But I liked the clarity of angles and lines to it. And the reflection, of course.
Mount Kangchenjunga or Khangchendzonga with an elevation of 8,586 meter (28,169 feet) is the third highest mountain of the world. It is called Five Treasures of Snow after its five high peaks.The Tibetan words are: Kang (Snow) chen (Big) dzö (Treasury) nga (Five).
The main peak of Kanchenjunga is the second highest mountain in Nepal after Mount Everest. Three of the five peaks – Main, Central and South – are on the border between North Sikkim and Nepal.Two peaks are in the Taplejung District, Nepal.
Until 1852, Kanchenjunga was assumed to be the highest mountain in the world, but calculations based on various readings and measurements made by the Great Trigonometrical Survey of India in 1849 came to the conclusion that Mount Everest, known as Peak XV at the time, was the highest. Allowing for further verification of all calculations, it was officially announced in 1856 that Kanchenjunga is the third highest mountain
Wish you all a happy and prosperous New Year 2016!
The January 20, 2019 Super Wolf Blood Moon rising over the Space Needle in Seattle, WA. January 20, 2019.
I love the challenge of combining astrological events and landscapes. It requires a truckload of planning (and a bit of trigonometry) and it is so, SO rewarding to see it come to life in the field right before your eyes. I also strongly believe that adding the sun, moon, or stars as a compositional element can result in something unique. Everyone here has seen a photo of the Space Needle, but hopefully this version that includes the January 20, 2019 total lunar eclipse is a little different.
I planned the shoot in advance using PhotoPills and Excel to line up the moon with the Space Needle and to confirm the angle of the moon from horizon would put it above the Space Needle if shooting from the ground looking up. For the base image, I shot the Space Needle at a low ISO for a clean foreground. As the moon moved into the Earth's shadow to enter the total eclipse phase while simultaneously aligning with the needle, I shot 5-8 images of the moon in burst mode at 1/2 a second at ISO 3200 (or ISO 6400 - I forget). In post, I stacked the multiple captures of the moon together to reduce high ISO noise and increase detail (this is a common astrophotography process, kind of a manual version of what what the new Sony A7R camera bodies do when they go into the super resolution pixel shift mode).
If interested, I have a tutorial on how to plan shots like these here: Blood Moon tutorial.
I've also made the spreadsheet I use to check angles in the process available here: Google Sheets
"I used to like triangles, but then I got to Trigonometry in math class. Who knew that three sides could be so complicated?"
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Created for the FLickr Friday theme, TRIANGLE.
Slide rules consist of a body, a slider and a cursor and have any number of numerical engraved scales that support a variety of mathematical calculations (multiplication, division, trigonometric, exponential and transcendental computations. Prior to the development of electronic/scientific calculators, slide rules were an important instrument for performing various calculations.
Focus stck (48 images) Shot with single off-camera flash (Godox AD200/Godox XPor II L trigger), bare bulb, mounted to overhead boom, bounced off 32 inch white umbrella.
Shot for Flickr Friday -scales
Mount Kangchenjunga or Khangchendzonga with an elevation of 8,586 meter (28,169 feet) is the third highest mountain of the world. It is called Five Treasures of Snow after its five high peaks.The Tibetan words are: Kang (Snow) chen (Big) dzö (Treasury) nga (Five).
The main peak of Khangchendzonga is the second highest mountain in Nepal after Mount Everest. Three of the five peaks – Main, Central and South – are on the border between North Sikkim and Nepal.Two peaks are in the Taplejung District, Nepal.
Until 1852, Khangchendzonga was assumed to be the highest mountain in the world, but calculations based on various readings and measurements made by the Great Trigonometrical Survey of India in 1849 came to the conclusion that Mount Everest, known as Peak XV at the time, was the highest. Allowing for further verification of all calculations, it was officially announced in 1856 that Khangchendzonga is the third highest mountain.
It is widely regarded as the guardian deity of Sikkim.
I wonder what the three grooves are? (Arrowed)
1 pixel is about 0.26 arc seconds (0.00007259 of a degree.)
When the pic was taken, the moon was 372550 Km from me. A quick bit of trigonometry reveals that 0.26arc sec represents 472 meters
Each pixel is 472x472 meters. I don't think we'll see the moon landers just yet but those trails are about 4pix wide, so nearly 2km wide.
I need a bigger telescope...
"Assassin's Creed Origins"
-7000x5250 (SRWE Hotsampling, 4:3 rotate)
-Camera Tools by Otis_Inf
-In-game Photomode
Kanchenjunga from Pelling. Kangchenjunga, also spelled Kanchenjunga, Kanchanjanghā (Nepali: कञ्चनजङ्घा, romanized: Kanchanjanghā), and Khangchendzonga, is the third highest mountain in the world. Its summit lies at 8,586 m (28,169 ft) in a section of the Himalayas, the Kangchenjunga Himal, which is bounded in the west by the Tamur River, in the north by the Lhonak River and Jongsang La, and in the east by the Teesta River. It lies in the border region between Nepal and Sikkim state of India, with three of the five peaks, namely Main, Central and South, directly on the border, and the peaks West and Kangbachen in Nepal's Taplejung District.
Until 1852, Kangchenjunga was assumed to be the highest mountain in the world. Still, calculations and measurements by the Great Trigonometrical Survey of India in 1849 showed that Mount Everest, known as Peak XV, is actually higher. After allowing for further verification of all calculations, it was officially announced in 1856 that Kangchenjunga was the third-highest mountain
The old slide rule of my father, seen from close :)
A slide rule is a hand-operated mechanical calculator consisting of slidable rulers for evaluating mathematical operations such as multiplication, division, exponents, roots, logarithms, and trigonometry. It is one of the simplest analog computers. Invented in 1632 by William Oughtred, inspired by Edmund Gunter's logarithmic ruler. It was widely used by engineers until the late 1980s.
Macro Mondays - theme: "Anachronism"
The main feature of Table Mountain is the level plateau approximately three kilometres from side to side, edged by impressive cliffs. The plateau, flanked by Devil's Peak to the east and by Lion's Head to the west, forms a dramatic backdrop to Cape Town. This broad sweep of mountainous heights, together with Signal Hill, forms the natural amphitheatre of the City Bowl and Table Bay harbour. The highest point on Table Mountain is towards the eastern end of the plateau and is marked by Maclear's Beacon, a stone cairn built in 1865 by Sir Thomas Maclear for trigonometrical survey. It is 1,086 metres above sea level, and about 19 metres higher than the cable station at the western end of the plateau.
Info source URL: en.wikipedia.org/wiki/Table_Mountain
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Photo capture date & Location: 2014-10 The Peninsula
I know its a kiwi fruit...but I've spent the evening going through trigonometry with my daughter... so a quick macro shot of a kiwi fruit... ;)
A trio of cloud formations with Lancing Hill and it's OS Trig Pillar nicely silhouetted against the Sunset
Best viewed on black - just press 'L'
276A1667
Mount Everest, also known in Nepal as Sagarmāthā and in Tibet as Chomolungma, is Earth's highest mountain. It is located in the Mahalangur mountain range in Nepal.[8][9] Its peak is 8,848 metres (29,029 ft) above sea level.[1] It is not the furthest summit from the centre of the Earth. That honour goes to Mount Chimborazo, in the Andes.[10] The international border between China and Nepal runs across Everest's precise summit point. Its massif includes neighbouring peaks Lhotse, 8,516 m (27,940 ft); Nuptse, 7,855 m (25,771 ft) and Changtse, 7,580 m (24,870 ft).
In 1856, the Great Trigonometrical Survey of India established the first published height of Everest, then known as Peak XV, at 29,002 ft (8,840 m). The current official height of 8,848 m (29,029 ft) as recognised by China and Nepal was established by a 1955 Indian survey and subsequently confirmed by a Chinese survey in 1975. In 1865, Everest was given its official English name by the Royal Geographical Society upon a recommendation by Andrew Waugh, the British Surveyor General of India. Waugh named the mountain after his predecessor in the post, Sir George Everest, arguing that there were many local names, against the opinion of Everest.[
A triangulation station, also known as a triangulation pillar, trigonometrical station, trigonometrical point, trig station, trig beacon, or trig point, and sometimes informally as a trig, is a fixed surveying station, used in geodetic surveying and other surveying projects in its vicinity.
Mam Tor, meaning ‘Mother Hill’, is a 517 metre high hill near Castleton in the High Peak area of Derbyshire
www.visitpeakdistrict.com/things-to-do/mam-tor-shivering-...
Marin Headlands, Golden Gate National Recreation Area, California
California west of the Sierra Nevada Mountains is bits and pieces of former sea floor and island archipelagos that the North American tectonic plate picked on its journey west across the globe.
Here, standing on Tennessee Point north of the Golden Gate strait, we are looking at two colorful cliffs. The reddish brown cliff is chert, composed of the silicate skeletons of microscopic radiolaria deposited in an equatorial sea around 200 million years ago. The greenish areas on cliff to the right are likely serpentinite, a metamorphic rock formed when you combine basalt and water and squeeze. Much of the rest of the immediate area, including Tennessee Point itself, is pillow lava basalt that poured out onto the sea floor.
And what about guns, you ask? Although it is hard to see at this resolution, there is a small building on the right shoulder of the chert cliff, just at the edge. That's a triangulation station from the days when the US Army protected the San Francisco Bay with coastal gun batteries. Spotters in a series of triangulation stations along the coast would each determine the bearing of an approaching warship. Simple trigonometry would then determine where to aim the big guns. The system was never actually used and the coastal batteries were decommissioned after World War II.
A couple meet at a trigpoint the South Downs countryside at Devil's Dyke during a sunset near Brighton in East Sussex, England. uK
An Italian sea scape that caught my eye while on holiday recently.
The powerlines are suppling a lighthouse on an Island to the right of shot.
I returned to this locations a few mornings to try and capture some reflections and the sharpest image I could manage. This is shot from floating pontoons so a fast shutter speed was needed to freeze the motion which was surprisingly a lot considering it was quite calm.
I hope you enjoy the composition
FOR THE PLACE, PLEASE, FOLLOW THIS LINKS:
wikimapia.org/#lang=it&lat=40.454164&lon=9.796286...
www.panoramio.com/photo/10876301
YOU CAN GO THERE ONLY BY FOOT: ABOUT 700 METERS OVER THE LEVEL OF THE SEA, ABOUT HALF AN HOUR BY FOOT
HERE THER IS A TRIANGULATION STATION..
A triangulation station, also known as a triangulation pillar, trigonometrical station, trigonometrical point, trig station, trig beacon or trig point, and sometimes informally as a trig, is a fixed surveying station, used in geodetic surveying and other surveying projects in its vicinity. The names of triangulation stations vary regionally; they are generally known as trigonometrical stations in North America, trig points in the United Kingdom and New Zealand, trig stations or points in Australia, and trig beacons in South Africa; triangulation pillar is the more formal term for the concrete columns found in the UK.
FOR MORE INFORMATIONS ON TRIANGULATION POINT FOLLOW THIS LINK:
Taken from triangulation point on Fan Nedd (663M) in the Brecon Beacons looking Eastwards to Pen-y-Fan.
Other major peaks visible are Fan Llia, Fan Fawr & Corn Du.
Conditions - hazy.
Canon 5D Mark II + Nikon 14-24@14mm
Shot tonight march 11th.
Using algebra and trigonometry I have calculated that the stretch of this corona (corner to corner diagonal) is a whopping 370km !!! (230miles (US/UK)) This given that field of view of the lens is 114 degrees and the aurora is 100km up in the sky !!
When this insane light-show in addition also is moving insanely fast, you can try to imagine the powers which are at display!
The sickest and most beautiful coronal outbreak I have ever witnessed during my photography career.
I am still mesmerized by this display!!
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arctic light photo - on facebook
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Ole
A slightly unexpected find in Redlands Wood between Dorking and Ockley in Surrey. A rather suspect that the Forestry Commission managed woodland was not there when this OS trigonometry monument was in place.
Sadly the OS monument and physical benchmark network is no longer maintained as satellite methods are so much more accurate.
It is worth capturing them before they dissappear.
Trig monuments also make good walking 'targets'.
Mount Kangchenjunga or Khangchendzonga with an elevation of 8,586 meter (28,169 feet) is the third highest mountain of the world. It is called Five Treasures of Snow after its five high peaks.The Tibetan words are: Kang (Snow) chen (Big) dzö (Treasury) nga (Five).
The main peak of Khangchendzonga is the second highest mountain in Nepal after Mount Everest. Three of the five peaks – Main, Central and South – are on the border between North Sikkim and Nepal.Two peaks are in the Taplejung District, Nepal.
Until 1852, Khangchendzonga was assumed to be the highest mountain in the world, but calculations based on various readings and measurements made by the Great Trigonometrical Survey of India in 1849 came to the conclusion that Mount Everest, known as Peak XV at the time, was the highest. Allowing for further verification of all calculations, it was officially announced in 1856 that Khangchendzonga is the third highest mountain.
It is widely regarded as the guardian deity of Sikkim.
A triangulation station, also known as a triangulation pillar, trigonometrical station, trigonometrical point, trig station, trig beacon, or trig point, and sometimes informally as a trig, is a fixed surveying station, used in geodetic surveying and other surveying projects in its vicinity. The nomenclature varies regionally; they are generally known as trigonometrical or triangulation stations in North America, trig points in the United Kingdom, trig stations or points in Australia and New Zealand, and trig beacons in South Africa; triangulation pillar is the more formal term for the concrete columns found in the UK.
The station is usually set up by a government with known coordinate and elevation published. Many stations are located on hilltops for the purposes of visibility. A graven metal plate on the top of a pillar may provide a mounting point for a theodolite or reflector.
Trigonometrical stations are grouped together to form a network of triangulation. Positions of all land boundaries, roads, railways, bridges and other infrastructure can be accurately located by the network, a task that is essential to the construction of modern infrastructure. Apart from the known stations set up by government, some temporary trigonometrical stations are set up near construction sites for monitoring the precision and progress of construction.
Some trigonometrical stations use the Global Positioning System for convenience; however, the accuracy depends on factors such as ionospheric and tropospheric propagation delay errors.
Although stations are no longer required for many surveying purposes, they remain useful to hikers as navigational aids.
Taken with a Pentax K50 and a 16-45mm f4
Moel y Ci, or Moelyci as some maps have it, is an outlying hill on the fringes of Snowdonia. On a good day it offers fantastic 360 degree view. Anglesey to one side and the giants of the Carneddau to the other.
Gasherbrum is a remote group of peaks located at the northeastern end of the Baltoro Glacier in the Karakoram range of the Himalaya on the border of the Chinese-administered Shaksgam Valley and the Gilgit-Baltistan territory of Pakistan. The massif contains three of the world's 8,000 metre peaks (if one includes Broad Peak). Gasherbrum is often claimed to mean "Shining Wall", presumably a reference to the highly visible face of Gasherbrum IV; but in fact it comes from "rgasha" (beautiful) + "brum" (mountain) in Balti, hence it actually means "beautiful mountain".
In 1856, Thomas George Montgomerie, a British Royal Engineers lieutenant and a member of the Great Trigonometric Survey of India, sighted a group of high peaks in the Karakoram from more than 200 km away. He named five of these peaks K1, K2, K3, K4 and K5 where the K denotes Karakoram. Today, K1 is known as Masherbrum, K3 as Broad Peak, K4 as Gasherbrum II and K5 as Gasherbrum I. Only K2, the second highest mountain in the world, has kept Montgomerie's name.
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Mt. Kanchenjunga (8586 m) is the third highest mountain in the world, and lies partly in Nepal and partly in Sikkim, India.
Kangchenjunga Main is the highest mountain in India, and the easternmost of the mountains higher than 8,000 m (26,000 ft). It is called Five Treasures of Snow after its five high peaks, and has always been worshipped by the people of Darjeeling and Sikkim.
Until 1852, Kangchenjunga was assumed to be the highest mountain in the world, but calculations based on various readings and measurements made by the Great Trigonometrical Survey of India in 1849 came to the conclusion that Mount Everest, known as Peak XV at the time, was the highest. Allowing for further verification of all calculations, it was officially announced in 1856 that Kangchenjunga is the third highest mountain in the world. - Wikipedia
So today actually was the first time I took the camera outdoors and climbed up Braemar Hill. (can see it on my facebook page: www.facebook.com/ThomasBirkeUrbanPhotography )
On Braemar Hill there are 2 really good viewpoints - one is a couple of rocks down from the trigonometric station and the other one, which I chose today, is a kilometer away from the actual Braemar Hill top along the Trail (I think it is the Wilson Trail). Both have their advantages, and I can not decide which one is best - the first has part of the Happy Valley Flyover in view, which is a great addition to the futuristic feeling of the cityscape - the second, which I choose today, has these amazing round appartment blocks in the foreground ( en.wikipedia.org/wiki/Lai_Tak_Tsuen ) and the view of Central Plaza is not blocked...
Anyway, the whole week already there is so much pollution in the air and it is quite cloudy, so the light pollution of central is so strong that it is hard to balance out, plus there is not much sharpness because all the particles in the air blur the details...I hope that it will get better with next week!
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In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline.
Slope is normally described by the ratio of the "rise" divided by the "run" between two points on a line. The line may be practical - as set by a road surveyor - or in a diagram that models a road or a roof either as a description or as a plan.
The rise of a road between two points is the difference between the altitude of the road at those two points, say y1 and y2, or in other words,
the rise is (y2 − y1) = Δy.
For relatively short distances - where the earth's curvature may be neglected, the run is the difference in distance from a fixed point measured along a level, horizontal line, or in other words,
the run is (x2 − x1) = Δx.
Here the slope of the road between the two points is simply described as the ratio of the altitude change to the horizontal distance between any two points on the line. In mathematical language,
the slope m of the line is
The concept of slope applies directly to grades or gradients in geography and civil engineering. Through trigonometry, the grade m of a road is related to its angle of incline θ by
As a generalization of this practical description, the mathematics of differential calculus defines the slope of a curve at a point as the slope of the tangent line at that point. When the curve given by a series of points in a diagram or in a list of the coordinates of points, the slope may be calculated not at a point but between any two given points. When the curve is given as a continuous function, perhaps as an algebraic formula, then the differential calculus provides rules giving a formula for the slope of the curve at any point in the middle of the curve.
This generalization of the concept of slope allows very complex constructions to be planned and built that go well beyond static structures that are either horizontals or verticals, but can change in time, move in curves, and change depending on the rate of change of other factors. Thereby, the simple idea of slope becomes one of the main basis of the modern world in terms of both technology and the built environment
Well I managed to get out of Cardiff this morning and not getting trapped in by the half marathon. So it's straight off this afternoon to Larmer Tree Gardens with the family. Busy, Busy!!
So in the meantime, here's some more lines and angles from 55 Baker Street, London.
This image got to #49 in Explore on Monday, October 7, 2013