Higher dimensional roses.











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We know that the $2n$ petal rose $$r=sin ntheta$$ occupies half the area of the unit circle regardless of the number of petals while the arc-length grows without bound.



Are there such objects in higher dimensions?






geometry







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  • Does Gabriel's Horn en.wikipedia.org/wiki/Gabriel%27s_Horn, work?
    – DJohnM
    2 days ago















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We know that the $2n$ petal rose $$r=sin ntheta$$ occupies half the area of the unit circle regardless of the number of petals while the arc-length grows without bound.



Are there such objects in higher dimensions?






geometry







share|cite|improve this question






















  • Does Gabriel's Horn en.wikipedia.org/wiki/Gabriel%27s_Horn, work?
    – DJohnM
    2 days ago













up vote
0
down vote

favorite









up vote
0
down vote

favorite











We know that the $2n$ petal rose $$r=sin ntheta$$ occupies half the area of the unit circle regardless of the number of petals while the arc-length grows without bound.



Are there such objects in higher dimensions?






geometry







share|cite|improve this question













We know that the $2n$ petal rose $$r=sin ntheta$$ occupies half the area of the unit circle regardless of the number of petals while the arc-length grows without bound.



Are there such objects in higher dimensions?






geometry




geometry






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share|cite|improve this question




share|cite|improve this question










asked 2 days ago









Mohammad Riazi-Kermani

40.2k41958




40.2k41958












  • Does Gabriel's Horn en.wikipedia.org/wiki/Gabriel%27s_Horn, work?
    – DJohnM
    2 days ago


















  • Does Gabriel's Horn en.wikipedia.org/wiki/Gabriel%27s_Horn, work?
    – DJohnM
    2 days ago
















Does Gabriel's Horn en.wikipedia.org/wiki/Gabriel%27s_Horn, work?
– DJohnM
2 days ago




Does Gabriel's Horn en.wikipedia.org/wiki/Gabriel%27s_Horn, work?
– DJohnM
2 days ago










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Does this "rose" suffice in three dimensions?



enter image description here






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  • Good for three dimensions
    – Mohammad Riazi-Kermani
    2 days ago











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1 Answer
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active

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1 Answer
1






active

oldest

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active

oldest

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active

oldest

votes








up vote
2
down vote



accepted










Does this "rose" suffice in three dimensions?



enter image description here






share|cite|improve this answer





















  • Good for three dimensions
    – Mohammad Riazi-Kermani
    2 days ago















up vote
2
down vote



accepted










Does this "rose" suffice in three dimensions?



enter image description here






share|cite|improve this answer





















  • Good for three dimensions
    – Mohammad Riazi-Kermani
    2 days ago













up vote
2
down vote



accepted







up vote
2
down vote



accepted






Does this "rose" suffice in three dimensions?



enter image description here






share|cite|improve this answer












Does this "rose" suffice in three dimensions?



enter image description here







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 2 days ago









David G. Stork

8,99421232




8,99421232












  • Good for three dimensions
    – Mohammad Riazi-Kermani
    2 days ago


















  • Good for three dimensions
    – Mohammad Riazi-Kermani
    2 days ago
















Good for three dimensions
– Mohammad Riazi-Kermani
2 days ago




Good for three dimensions
– Mohammad Riazi-Kermani
2 days ago


















 

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