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  2. Spherical sector - Wikipedia

    en.wikipedia.org/wiki/Spherical_sector

    In geometry, a spherical sector, [1] also known as a spherical cone, [2] is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap. It is the three-dimensional analogue of ...

  3. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    Spherical cap. An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane.

  4. Tree volume measurement - Wikipedia

    en.wikipedia.org/wiki/Tree_volume_measurement

    The value 75.4 = 24 π, where 24 π substitutes for factor of 12 π in the formula for a volume of frustum of a cone encompassing a full tree using one base circumference, converting it to a volume formula that uses a basal circumference that is the average of circumferences C 1 and C 2.

  5. Hypercone - Wikipedia

    en.wikipedia.org/wiki/Hypercone

    If it is restricted between the hyperplanes w = 0 and w = r for some nonzero r, then it may be closed by a 3-ball of radius r, centered at (0,0,0,r), so that it bounds a finite 4-dimensional volume. This volume is given by the formula ⁠ 1 / 3 ⁠ π r 4, and is the 4-dimensional equivalent of the solid cone. The ball may be thought of as the ...

  6. Conic section - Wikipedia

    en.wikipedia.org/wiki/Conic_section

    A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes called as a fourth type.

  7. Cone - Wikipedia

    en.wikipedia.org/wiki/Cone

    A double cone (not shown infinitely extended) 3D model of a cone. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of ...

  8. Sphere packing - Wikipedia

    en.wikipedia.org/wiki/Sphere_packing

    Sphere packing finds practical application in the stacking of cannonballs. In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three- dimensional Euclidean space. However, sphere packing problems can be ...

  9. Volume of an n-ball - Wikipedia

    en.wikipedia.org/wiki/Volume_of_an_n-ball

    The volume of the n-ball () can be computed by integrating the volume element in spherical coordinates. The spherical coordinate system has a radial coordinate r and angular coordinates φ 1 , …, φ n − 1 , where the domain of each φ except φ n − 1 is [0, π ) , and the domain of φ n − 1 is [0, 2 π ) .