#hopf

[coffeenuts]

[spacebeach23]

1963 HOPF SATURN 63

from: https://linstrumenterie.com/products/hopf-saturn-63-sunburst-de-1960

[ukuleleoftheday]

1960′s Hopf Soprano

[numb3rth30ry]

A Hopf fibration. This gorgeous visualization portrays a suitably deep idea in differential topology.

The Hopf fibration describes 3-spheres (aka hyperspheres, 4-dimensional analogues of spheres) in terms of “ordinary” spheres and circles. It is an early example of a fiber bundle.

Quoting Wikipedia, “Technically, Hopf found a many-to-one continuous function (or ‘map’) from the 3-sphere onto the 2-sphere such that each distinct point of the 2-sphere comes from a distinct circle of the 3-sphere (Hopf 1931). Thus the 3-sphere is composed of fibers, where each fiber is a circle—one for each point of the 2-sphere.”

Hopf fibrations have many incredible properties. I write, however, because they are beautiful.

Mathematics is beautiful. <3

[guitarbage]

Hopf Saturn 63

[beersoftheworld-blog1]

Beer and books go well together! That’s what @mironova_nastya_ thinks while enjoying Hopf Hefeweizen 🇩🇪 and reading a book 📚 . . . #beersoftheworld #hopf #hefeweizen #whitebeer #weissbier #bavaria #bavarianbeer #wolf #beerandbooks #beerbottle #russianbooks

[adamspuryear]

Judith Hopf

Interview

[bmwclubdnepr]

🍺 Всем отличной пятницы 🍻 . . . Wish you all a great #frontendfriday 😎🍺 have a good start into the weekend ✌️ -------------------------------------------------- #bmw #hopf #hopfweissbier #beer #whitebeer #bmw❤️ #bmwclub #bmwlife #friday #fridaymood #fridayfun #weekendiscoming #bmwlove #bmwblog #bmwlovers #bmwcoool #bavaria #beertography #beerstagram #beerlover #perfectbeer #bavarianbeer #weissbier #weißbier #haveagoodday #awesome #iphonephotography #iphonephoto #beer (at BMW Club Dnepr)