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gptkbp:instanceOf
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gptkb:geometry
gptkb:Lie_group
Abelian group
Compact surface
Surface of revolution
2-manifold
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gptkbp:canBeDescribedByEquation
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(R - sqrt(x^2 + y^2))^2 + z^2 = r^2
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gptkbp:canBeEmbeddedIn
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gptkb:3-dimensional_Euclidean_space
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gptkbp:containsGenus
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1
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gptkbp:dimensions
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2
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gptkbp:Euler_characteristic
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0
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gptkbp:fundamentalGroup
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Z × Z
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gptkbp:hasCurvature
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variable
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gptkbp:hasHomologyGroup
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H_1 = Z × Z
H_2 = Z
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gptkbp:hasMajorRadius
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R
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gptkbp:hasMinorRadius
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r
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gptkbp:hasSpecialCase
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Surface of revolution
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gptkbp:hasSurfaceAreaFormula
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4π^2 R r
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https://www.w3.org/2000/01/rdf-schema#label
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Torus
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gptkbp:isomorphicTo
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product of two circles
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gptkbp:isOrientable
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true
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gptkbp:namedAfter
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Latin word for cushion
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gptkbp:parameter
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two angular parameters
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gptkbp:plural
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gptkb:Tori
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gptkbp:relatedTo
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gptkb:Clifford_torus
gptkb:Flat_torus
gptkb:Solid_torus
gptkb:Torus_action
gptkb:Torus_bundle
gptkb:Torus_decomposition
gptkb:Torus_fibration
gptkb:Torus_knot
gptkb:Torus_link
gptkb:Torus_partition
gptkb:Torus_topology
gptkb:Vortex_ring
gptkb:n-torus
Donut shape
Torus embedding
Torus surface area
Torus symmetry
Torus vibration
Torus volume
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gptkbp:usedIn
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gptkb:Mathematics
gptkb:Physics
gptkb:geometry
gptkb:Topology
Engineering
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gptkbp:volume
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2π^2 R r^2
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gptkbp:bfsParent
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gptkb:dYdX
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gptkbp:bfsLayer
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5
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