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#spherical

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Paul Kinsler

It is well known that the "spherical cow" is an overly aggressive approximation. Hence:

arxiv.org/abs/2504.00506

arXiv logo
arXiv.orgHigher multipoles of the cowThe spherical cow approximation is widely used in the literature, but is rarely justified. Here, I propose several schemes for extending the spherical cow approximation to a full multipole expansion, in which the spherical cow is simply the first term. This allows for the computation of bovine potentials and interactions beyond spherical symmetry, and also provides a scheme for defining the geometry of the cow itself at higher multipole moments. This is especially important for the treatment of physical processes that are suppressed by spherical symmetry, such as the spindown of a rotating cow due to the emission of gravitational waves. I demonstrate the computation of multipole coefficients for a benchmark cow, and illustrate the applicability of the multipolar cow to several important problems.
#spherical#cow#approximation
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Panethos

Wild and wondrous water towers across the heartland

Below are some of the amazing water towers we saw over the past few weeks across the American Heartland. As can be seen, the range of styles, locations, and eras is impressive. Hope you enjoy the photos as much as we did seeing them.

Giant City State Park, ILGroom, TXDepew, OKLansing, MIMakanda, ILAdrian, TXBritten (Groom), TXRushville, INReelsville, IN

While each tower has it’s own storied history, I’ve gotta, say the space-age tower with and observation platform at Giant City State Park in Illinois is a treasure all to itself. More photos and backstory about this most extraordinary water tower will be included in a separate post. Peace!

Rend Lake, ILBristow, OKMountain View, MOAmarillo, TX Lynn, IN Willow Springs, MO Meridian Twp, MI
#architecture#CET#cities
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Stefan F. Wirth

My digital #artwork from 2020, newly edited in 2025: I used image editing software to stereographically project the image plane onto a #spherical surface. This created a #littleplanet projection with the impression that this #tree is the only one on its #tinyworld. With my artwork, I honor the tree itself, not only because it can bind CO2, but because it represents a #community of diverse #organisms, on which I have conducted numerous #mite #related research.
© #StefanFWirth Berlin 2025

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Panethos

Working lists: Canada’s tallest standpipe, spherical, and “Tin Man” style water towers

Three separate working lists are provided below for standpipe, spherical, and “Tin Man” style water towers across our beautiful neighbor to the north, Canada. The lists will be updated periodically as additional information is found. Peace!

St. Mary’s, Ontario Standpipe – Source: flickr.com

STANDPIPE

The year of completion for these standpipe water towers ranges from 1896 to 2007. The most common decades for standpipe construction (from this list) are:

  • 1970s = 13
  • 1980s = 7
  • 1960s = 5

___

  1. Dorset Street Standpipe (1977): Port Hope, ON = 154 feet/47 m – to be replaced in 2027

2-4. Sombra Township Standpipe (1975): Port Lambton, ON and Aylmer Standpipe (1986): Hamilton (Aylmer), ON; and Caraquet Standpipe (1970): Caraquet, NB = 150 feet/45.7 m

5. Waterford Standpipe (1980): Waterford, ON = 142 feet/43.3 m

6. Delhi Standpipe (1978): Delhi, ON = 140 feet/42.7 m

7. North Bay Standpipe (1985): North Bay, ON = 131 feet/40 m

8. Timmons Standpipe (ca 1972): Timmons, ON = 130 feet/39.6 m

9. Ayr Standpipe (1978): Ayr, ON = 129 feet/39.3 m

10. Pointe-Claire Standpipe (1954): Pointe-Claire, QC = 125.5 feet/39.5 m

11. Waterdown Standpipe (1977): Hamilton (Waterdown), ON = 124.5 feet/38 m

12. Bouctouche Standpipe (1982): Bouctouche, NB = 120 feet/36.6 m

13. Region of Waterloo Standpipe (1982): Cambridge, ON = 113 feet/34.4 m

14. St. George Standpipe (1950): St. George, NB = 110 feet/33.5 m

15. Rockland Standpipe (1908): Victoria, BC = 109 feet/33.2 m

16. Grand Falls Standpipe (1998): Grand Falls, NL = 106 feet/32.3 m

17-19. Richmond Hill Standpipe (1980): Richmond Hill, ON; Kerrobet Standpipe (1914): Kerrobet, SK; and Mono Mills Standpipe (1978): Mono Mills, ON = 105 feet/32 m

20. Johnson Tower Standpipe (1963): White Rock, BC = 103 feet

21-23. Alexandria Standpipe #1 (1896): Alexandria, ON; Fenelon Falls Standpipe (1976): Fenelon Falls, ON; and Miramichi Standpipe (1977): Miramichi, NB = 100 feet/ 30.5 m

24. Woodville Standpipe (1972): Woodville, ON = 92 feet/28 m

25-26. Humboldt Standpipe (1915): Humboldt, SK and “Top of Wellington” Standpipe (1946): Clifford, ON = 95 feet/29 m

27-29. Hespeler Standpipe (1972): Cambridge, ON; Dutton Standpipe (1960s): Dutton, ON; and Moncton Standpipe (1980): Moncton, NB = 90 feet/27.5 m

30. Walkerton Standpipe #1: Walkerton, ON = 86 feet/26.2 m

31. Petrolia Standpipe (1896): Pertolia, ON = 85 feet/25.8 m

32. Waterloo Standpipe (1987): Waterloo, ON = 83 feet/25.3 m

33-35. Lacombe Home Water Tower (ca 1920): Calgary, AB; Firestone Standpipe: Calgary, AB; and Kamsack Standpipe (1915): Kamsack, SK = 80 feet/24.4 m

36. Rockwood Standpipe (2007): Rockwood, ON = 72 feet/22 m

37. Buchans Standpipe (2004): Buchans, NL = 71 feet/21.6 m

38. Bolton Standpipe (1937/1973): Bolton, ON = 69 feet/21 m

39. Walkerton Standpipe #2: Walkerton, ON = 66 feet/20.2 m

40-41. Orillia Standpipe (1967): Orillia, ON and Wabush Standpipe (1965): Wabush, NL = 65 feet/19.9 m

42. Elmvale Standpipe (1995): Elmvale, ON = 52 feet/15.9 m

43. Golf Course Standpipe (1976): Didsbury, AB = 51 feet/15.6 m

44. Kensington Standpipe: Kensington, PE = 50 feet/15.2 m

45. Labrador City Standpipe (1965): Labrador City, NL = 48 feet/14.6 m

Source: tourismsaskatchewan.com

More Information needed:

  • Alliance, AB
  • Andrew, AB
  • Bashaw, AB
  • Black Diamond, AB
  • Bowden, AB
  • Chipman, AB (1905)
  • Clyde, AB
  • Glenwood, AB
  • Grand Prairie, AB x 2
  • Grimshaw, AB
  • High River, AB
  • Irricana, AB
  • Legal, AB
  • Loughheed, AB
  • Mundare, AB
  • Rocky Mountain House, AB
  • Viking, AB
  • Waskatenau, AB
  • Westlock, AB
  • Rossland, BC
  • Parksville, BC
  • Victoria Standpipe #2
  • Climax Standpipe, SK
  • Weyburn Standpipe: Woburn, SK
  • Signal Hill Arts Centre Standpipe, SK
  • Norquay, SK
  • Davidson, SK
  • Coca-Cola Standpipe: Portage La Prairie, MB
  • Maple Bay, BC
  • Amhertsville, ON
  • St. Mary’s ON (1899)
  • Tara, ON
  • Midland, ON
  • Mt. Forest, ON
  • Loyalist Odessa Standpipe (1978): Odessa, ON
  • Kincardine, ON
  • Warren, ON
  • Kingston, ON x 2
  • Paisley, ON
  • Palmerston #2, ON
  • Port Elgin, ON
  • Porquois Junction, ON
  • Port Perry, ON
  • Powassan, ON
  • Wingham, ON
  • Sudbury/Walden, ON
  • Renfrew Standpipe, ON
  • Thamesville Standpipe, ON
  • Tiverton Standpipe, ON
  • Vankleek Hill, ON
  • Vemer Standpipe, ON
  • Alexandria, ON #2
  • Vineland, ON
  • Alvinston, ON
  • Arkona, ON
  • Azilda, ON
  • Loyalist Township: Amherstview, ON
  • Bancroft, ON
  • Birch Island, ON
  • Bradford, ON
  • Brechin, ON
  • Caledonia, ON
  • Campbellford, ON
  • Cayuga, ON
  • Casselman, ON
  • Cedar Springs, ON
  • New Standpipe: Clifford, ON
  • Colborne, ON
  • Cookstown, ON
  • Chatsworth, ON
  • Delaware, ON
  • Deseronto, ON
  • Dunnville, ON
  • Durham, ON
  • Espanola, ON
  • Finch, ON
  • Forest, ON
  • Halton Hills Standpipe, ON
  • Glencoe, ON
  • Guelph, ON x 2 (one in 2015)
  • Hagersville, ON
  • Hastings, ON
  • Havelock, ON
  • Hearst Standpipe (1977): Hearst, ON
  • Lakefield, ON
  • Lancaster, ON
  • Lansdowne, ON
  • Hockey World Standpipe: London, ON
  • Madoc, ON
  • Markdale, ON
  • Mamora, ON
  • Melbourne, ON
  • Mitchell, ON
  • Norwood, ON
  • Orangeville, ON
  • Orono, ON
  • Ridgeway, ON
  • Southampton, ON
  • St. Catharines, ON
  • Sturgeon Falls, ON
  • Stoney Point, ON
  • Sunderland, ON
  • Walden, ON
  • Warren, ON
  • Watford, ON
  • West Lorne, ON
  • Wiarton, ON
  • Wyoming, ON
  • Borden-Carlton, PE
  • Cornwall, PE (1995)
  • Stratford, PE
  • Bird Cove, NL
  • Come by Chance Standpipe, NL
  • Conception Bay, NL x 2
  • Daniels Harbour Standpipe, NL (1992)
  • Grand Bank, NL
  • Ramea, NL
  • Twillingate, NL
  • Antogonish, NS
  • Enfield, NS (1970s)
  • Falmouth, NS
  • Lantz, NS
  • Lunenburg, NS
  • Fredericton, NB x 2
  • Aroostook, NB
  • Perth-Andover, NB
  • Riverview, NB
  • Rothesay, NB
  • Saint John Standpipe, NB (2003)
  • St. Stephen Standpipe, NB (1988)
  • Chicoutimi, QC
  • Dalhousie, QC
  • Lévis, QC
  • Mercier, QC
  • Matagami, QC (2004)
  • Pierrefonds-Roxboro, QC
  • Rock Forest, QC
  • Shawville, QC
  • Ste-Angèle-de-Laval, QC
  • Ste-Anne-de-Bellevue, QC
  • Sainte-Foy, QC
  • Sainte-Thècle, QC (1951)
  • Sainte-Julie, QC

_______

Source: myselkirk.ca Source: winnipegfreepress.com

SPHERICAL

Nearly all of the water towers on this list were built in the 1960s and 1970s.

___

  1. Mississauga/Peel Region Water Tower (1971): Mississauga, ON = 187 feet/57 m

2-3. Thornbury Environment Water Tower: Thornbury, ON and Steinbach Water Tower (1972): Steinbach, MB = 154 feet/46.9 m

4-5. Guelph Water Tower (early 1970s): Guelph, ON and Stratford Water Tower (1964): Stratford, ON = 150 feet/45.7 m

6. Selkirk Watersphere Tower (1961): Selkirk, MB = 135 feet

7. Elmira Water Tower (1964): Elmira, ON = 126 feet/38.4 m

8. Dundas Water Tower (1969): Hamilton (Dundas), ON = 121 feet/37 m

9. Horton Watersphere Tower (1969): Centralia, ON ~ 114 feet/34.8 m

10. Cambridge Water Tower (1974): Cambridge, ON = 112 feet/34.1 m

11-13. Forest Drive Water Tower (1971): Vaughan, ON; and Woodbridge Water Tower (1971): Woodbridge, ON; and Region of Waterloo Water Tower (1978): Cambridge, ON = 108 feet/33 m

14. SSM Water Tower (1969): Sault Ste. Marie, ON = 103 feet

15. Kamsack Spheroid (1978): Kamsack, SK = 88 feet/26.8 m

16. Airdrie Water Tower (1959): Airdrie, AB = 71.5 feet/21.8 m

More information needed:

  • Oxbow Water Tower, SK
  • Redwater, AB
  • Standoff, AB
  • Kelvington, SK
  • Lang, SK
  • Langenburg, SK
  • Sturgis, SK
  • Rouleau, SK
  • Rose Valley, SK
  • Ponteix, SK
  • Coutts, AB – “Smiley”
  • Killarney Water Tower, MB
  • Beausejour, MB
  • Ridgetown, ON
  • Brantford, ON – status?
  • Arthur, ON
  • Peterborough, ON
  • South Huron Water Tower: Exeter, ON
  • Wasaga Beach, ON
  • Georgian Mall Water Tower: Barrie ON
  • Exeter, ON
  • Gananoque 1000 Islands, ON
  • Ingersoll, ON
  • Hiram Walker Water Tower: Lakeshore, ON
  • Ridgetown, ON
  • St. Thomas, ON
  • Wheatley, ON
  • Hawkes Bay, NL
  • Hubbards, NS
  • Port Hawesbury, NS
  • Drummondville, QC
  • Rock Forest, QC
  • Ste-Catherine, QC
  • St-Jean-sur-Richelieu, QC
  • Foam Lake, SK

_______

Source: pipestoneflyer.ca

TIN MAN

  1. St. Boniface Water Tower: Winnipeg, MB (1936) = 171 feet/52.1 m

2-3. Wetaskiwin Water Tower (1907): Wetaskiwin, AB and Gleichen Water Tower (1911): Gleichen, AB = 150 feet/45.7 m

4. Winnipeg Beach Water Tower (1928),: Winnipeg Beach, MB (1928) = 131 feet

5. Union Stock Yards Water Tower (1913): Winnipeg, MB = 80 feet/24.4 m

More information needed:

  • Claresholm,, AB (1910)
  • Bonnyville, AB
  • Innisfall, AB
  • Lethbridge, AB
  • Kitscoty, AB
  • Riverhead, AB
  • Carmangay, AB
  • Kindersley, SK
  • Grand Beach, MB
  • Morden, MB
  • Manitou, MB
  • Carman, MB
  • Boissevain, MB x 2
  • Brandon, MB
  • Selkirk, MB
  • Stoney Mountain, MB
  • Tilsonburg, ON
  • Tottenham, ON
  • Arthur, ON (1932)
  • Delhi, ON
  • GSW Water Tower: Fergus, ON
  • Gravenhurst, ON
  • Hastings, ON
  • Markdale, ON
  • Mississauga, ON
  • Simcoe, ON (1929)
  • Sturgeon Falls, ON
  • Hillsborough, NB (1931)
  • Bedford, QC
  • Jonquière, QC
  • Montreal, QC x 3
  • Schenley Water Tower: Salaberry-de-Valleyfield, QC
  • Ste-Anne-de-Bellevue, QC
  • St-Félicien,QC
  • Sullivan, QC
  • Fiske, SK
  • Gravelbourg, SK
  • Yorkton, SK (1930)
  • Waterton, AB
  • Saanich, BC

_____

SOURCES:

#1 #2 #Canada #cities #geography #history #planning #spherical #standpipes #stats #TinMan #tourism #towers #towns #travel #utilities #water #waterTowers

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The Krononaut Moon Project 🌑

▶️ The #Hypersphere

❛❛ In #mathematics, an n-sphere or hypersphere is an ⁠
n⁠-dimensional generalization of the ⁠1⁠-dimensional circle and ⁠2⁠-dimensional sphere to any non-negative integer ⁠n … As such, the ⁠n⁠-sphere is the setting for ⁠n⁠-dimensional #spherical #geometry. ❜❜

🔗 youtube.com/watch?v=RFK2_dAZvL 2019 Sep 28
🔗 Wikipedia.org/wiki/N-sphere … #Nsphere
🔗 Wikipedia.org/wiki/Hypercone … #Hypercone

YouTubeThe hypersphereBy Cool ideas
#Community#TimeTravel#Research
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richard

Reading Time: 1 minute

A few years ago I signed a contract to generate 360 content but the contract ended after just a month because the company restructured or something similar. I then bought a 360 camera and played with it to film interesting angles.

I keep forgetting that I have this fantastic camera. It’s fantastic because with 360 videos you can either allow people to see what they want to see, or you can frame the shot just as you want it to be. With a normal camera you need to place it so that you can film what you want to film. With a 360 camera you film everything and then frame the shot.

During the hike on Sunday someone said “Everyone, stand in a circle and I thought “maybe a 360 photo will be taken”. Nope, just a video where the camera spins to see everyone. I need to get into the habti of taking the 360 camera with me, to film the world from an unfamiliar angle.

I believe that it would make filming things like Via ferrata much easier, and much safer. If you can have a range of motion of two to three meters then you can place the camera precisely where you want it, rather than being limited by where you can get to.

You can use the pole to jib the camera around, and you can lift it up, to get a drone style shot, without the noise, and people complaining.

I should practice using the 360 camera on normal walks, so that when I’m on a cliff I know what to do with ease.

I think this summer season is over but Autumn walks with a 360 camera should be nice. The Tichodrome in Autumn should be nice. That’s the VF above Noiraigue, for reference.

https://www.main-vision.com/richard/blog/the-need-to-play-with-360-video/

#360 #immersive #photo #spherical #Video #VR

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