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57-754: The name Conero comes from the Greek name Κόμαρος ( Kómaros ) and indicates the strawberry tree which is common on the slopes of the mountain. Mount Conero is 572 metres high and it is the only coastal high point on the Adriatic sea between Trieste and the Gargano massif in the region of Apulia . Since 1987 it has been a state park and a protected ecological area (Regional Park) with 18 trails and several archeological/historical sites. Wildlife include Eurasian badger , beech marten , least weasel , yellow-bellied toad , peregrine falcon , kingfisher and pallid swift . Apart

114-550: A mycorrhizal relationship. Inoculation with Pisolithus tinctorius has shown to greatly improve the plant's root mass, size, tolerance to drought and nutritional status. In cultivation in the UK, the form A. unedo f. rubra and the cultivar 'Atlantic' have gained the Royal Horticultural Society 's Award of Garden Merit Propagation can be done via seed , layering , or cutting . The seed should undergo

171-536: A Neolithic introduction. The red-flowered variant, named A. unedo rubra by William Aiton in 1785, was discovered growing wild in Ireland in 1835. Arbutus unedo is quite an easy plant to cultivate, and is adaptable to many climates. Once established it is fairly drought resistant, frost resistant, shade tolerant and salt tolerant . Lower production of fruit mass has however been reported in case of summer droughts, and frosts in flowering time were seen to decrease

228-516: A hybrid is unlikely to breed true from seed. It is sold in California as Arbutus x Marina named for a district in San Francisco where it was hybridized. Arbutus unedo grows to 4–7 m (13–23 ft) tall, rarely up to 15 m (50 ft), with a trunk diameter of up to 80 cm (31 in). It grows in hardiness zones 7–10. The leaves are green and glossy on the upper side, dull on

285-474: A mild sweet scent. Twigs are reddish-brown and abundantly foliose, and often have small hairs. The fruit is a red berry, 7–20 mm ( 1 ⁄ 4 – 13 ⁄ 16  in) diameter, spherical in shape with a rough surface. It matures in about 12 months, in autumn, at the same time as the next flowering. It is edible; the fruit is sweet when reddish. Seeds are small, brown and angular and are often dispersed by frugivorous birds. The name unedo

342-498: A one-month cold stratification period, then soaked for 5 to 6 days in warm water to improve germination success. Seedlings are prone to damp, and should be cared for in the first year. Germination rate is low, rarely over 20%. Layering can take up to two years, but has a good success rate, while cutting is done with a 15–20 cm (6–8 in) long mature wood, preferably with a heel in November to December. The success rate however

399-461: A right-angled triangle connects x , y and r to the origin; hence, applying the Pythagorean theorem yields: Using this substitution gives which can be evaluated to give the result An alternative formula is found using spherical coordinates , with volume element so For most practical purposes, the volume inside a sphere inscribed in a cube can be approximated as 52.4% of the volume of

456-473: A sphere is allowed to be a plane (infinite radius, center at infinity) and if both the original spheres are planes then all the spheres of the pencil are planes, otherwise there is only one plane (the radical plane) in the pencil. In their book Geometry and the Imagination , David Hilbert and Stephan Cohn-Vossen describe eleven properties of the sphere and discuss whether these properties uniquely determine

513-512: A sphere is the boundary of a (closed or open) ball. The distinction between ball and sphere has not always been maintained and especially older mathematical references talk about a sphere as a solid. The distinction between " circle " and " disk " in the plane is similar. Small spheres or balls are sometimes called spherules (e.g., in Martian spherules ). In analytic geometry , a sphere with center ( x 0 , y 0 , z 0 ) and radius r

570-482: A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space . That given point is the center of the sphere, and r is the sphere's radius . The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians . The sphere is a fundamental object in many fields of mathematics . Spheres and nearly-spherical shapes also appear in nature and industry. Bubbles such as soap bubbles take

627-413: A sphere to be a two-dimensional closed surface embedded in three-dimensional Euclidean space . They draw a distinction between a sphere and a ball , which is a three-dimensional manifold with boundary that includes the volume contained by the sphere. An open ball excludes the sphere itself, while a closed ball includes the sphere: a closed ball is the union of the open ball and the sphere, and

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684-419: A spherical shape in equilibrium. The Earth is often approximated as a sphere in geography , and the celestial sphere is an important concept in astronomy . Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres roll smoothly in any direction, so most balls used in sports and toys are spherical, as are ball bearings . As mentioned earlier r

741-407: A unique circle in a plane. Consequently, a sphere is uniquely determined by (that is, passes through) a circle and a point not in the plane of that circle. By examining the common solutions of the equations of two spheres , it can be seen that two spheres intersect in a circle and the plane containing that circle is called the radical plane of the intersecting spheres. Although the radical plane

798-462: Is a real plane, the circle may be imaginary (the spheres have no real point in common) or consist of a single point (the spheres are tangent at that point). The angle between two spheres at a real point of intersection is the dihedral angle determined by the tangent planes to the spheres at that point. Two spheres intersect at the same angle at all points of their circle of intersection. They intersect at right angles (are orthogonal ) if and only if

855-565: Is also found in western France, Albania , Bulgaria and southwestern Ireland . A. unedo has been noted for its disjunct distribution , with isolated relict populations in southern and western Ireland in addition to its Mediterranean range. It is commonly cited as an example of the Lusitanian flora , a small assemblage of plants native to Iberia and South-Western Ireland, but generally absent from Britain. Recent genetic studies have suggested that A. unedo may not be truly native in Ireland, but

912-433: Is an equation of a sphere whose center is P 0 {\displaystyle P_{0}} and whose radius is ρ {\displaystyle {\sqrt {\rho }}} . If a in the above equation is zero then f ( x , y , z ) = 0 is the equation of a plane. Thus, a plane may be thought of as a sphere of infinite radius whose center is a point at infinity . A parametric equation for

969-831: Is attributed to Pliny the Elder , who allegedly claimed that " unum tantum edo ", meaning "I eat only one". It is not known whether he meant that the fruit was so good he could eat only one, or whether he meant that the fruit was uninteresting so he ate only one. Arbutus unedo is widespread in the Mediterranean region: in Portugal , Spain and southeastern France ; southward in Algeria , Morocco , Libya , and Tunisia , and eastward in Italy , Slovenia , Croatia , Montenegro , Greece , Turkey , Israel , Palestine , Jordan , Lebanon and Syria . It

1026-504: Is not very high. Arbutus berries have a high content of sugars (40%), and antioxidant vitamins such as vitamin C , beta-carotene , niacin , tocopherols , and organic acids that are precursors to omega-3 and omega-6 fatty acids (nearly 9%). They are edible fresh, but that is an uncommon consumption, especially because the mature fruit tends to bruise very easily, making transportation difficult. They are used mostly for jam, marmalades, yogurt and alcoholic beverages , such as

1083-459: Is reminiscent of the flag of Italy (green for its leaves, white for its flowers and red for its berries). For this reason the poet Giovanni Pascoli dedicated a poem to the strawberry tree. He refers to the Aeneid passage in which Pallas , killed by Turnus , was posed on branches of a strawberry tree. He saw in the colours of that plant a prefiguration of the flag of Italy and considered Pallas

1140-497: Is the locus of all points ( x , y , z ) such that Since it can be expressed as a quadratic polynomial, a sphere is a quadric surface , a type of algebraic surface . Let a, b, c, d, e be real numbers with a ≠ 0 and put Then the equation has no real points as solutions if ρ < 0 {\displaystyle \rho <0} and is called the equation of an imaginary sphere . If ρ = 0 {\displaystyle \rho =0} ,

1197-664: Is the national tree of Italy because of its green leaves, its white flowers and its red berries, colors that recall the Italian flag . The flower of the strawberry tree is the national flower of Italy. Arbutus unedo was one of the many species described by Carl Linnaeus in Volume One of his landmark 1753 work Species Plantarum , giving it the name it still bears today. A study published in 2001 which analyzed ribosomal DNA from Arbutus and related genera found Arbutus to be paraphyletic , and A. unedo to be closely related to

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1254-542: Is the most common, this can be a valuable plant also for restoring degraded ecosystems and preventing desertification . Being a pioneer plant and growing well also in poor soils, it can be used in a wide array of situations. Its Mediterranean habitat, elegant details of leaf and habit and dramatic show of fruit with flowers made Arbutus unedo notable in Classical Antiquity , when it was called Andrachne, and for which Theophrastos (4th c. BCE) wrote about it, as well as

1311-449: Is the sphere's radius; any line from the center to a point on the sphere is also called a radius. 'Radius' is used in two senses: as a line segment and also as its length. If a radius is extended through the center to the opposite side of the sphere, it creates a diameter . Like the radius, the length of a diameter is also called the diameter, and denoted d . Diameters are the longest line segments that can be drawn between two points on

1368-511: Is the summation of all shell volumes: In the limit as δr approaches zero this equation becomes: Substitute V : Differentiating both sides of this equation with respect to r yields A as a function of r : This is generally abbreviated as: where r is now considered to be the fixed radius of the sphere. Alternatively, the area element on the sphere is given in spherical coordinates by dA = r sin θ dθ dφ . The total area can thus be obtained by integration : The sphere has

1425-479: Is well known for its fruits, the arbutus berry, which bear some resemblance to the strawberry , hence the common name strawberry tree. However, it is not closely related to true strawberries of the genus Fragaria . Its presence in Ireland also lends it the name "Irish strawberry tree", or cain, or cane apple (from the Irish name for the tree, caithne ), or sometimes " Killarney strawberry tree". The strawberry tree

1482-469: The Madroño tree. The image appears on city crests, taxi cabs, man-hole covers, and other city infrastructure. The fruit of the Madroño tree ferments on the tree if left to ripen, so some of the bears become drunk from eating the fruits. Sphere A sphere (from Greek σφαῖρα , sphaîra ) is a geometrical object that is a three-dimensional analogue to a two-dimensional circle . Formally,

1539-414: The volume inside a sphere (that is, the volume of a ball , but classically referred to as the volume of a sphere) is where r is the radius and d is the diameter of the sphere. Archimedes first derived this formula by showing that the volume inside a sphere is twice the volume between the sphere and the circumscribed cylinder of that sphere (having the height and diameter equal to the diameter of

1596-399: The x -axis from x = − r to x = r , assuming the sphere of radius r is centered at the origin. At any given x , the incremental volume ( δV ) equals the product of the cross-sectional area of the disk at x and its thickness ( δx ): The total volume is the summation of all incremental volumes: In the limit as δx approaches zero, this equation becomes: At any given x ,

1653-555: The Ericaceae, A. unedo grows well in basic (limy) pH soils , even though it does better in more acidic soils. The fruit production is not very high and is highly variable on the weather, and that may be part of the reason this plant is not frequently cultivated. The average yield in a two years study is around 46 kg per hectare , and 180 grams per cubic metre of crown. However, very little work has so far been done in terms of genotype selection. Arbutus unedo has been seen to form

1710-552: The Portuguese medronho , a type of strong brandy. Many regions of Albania prepare the traditional drink rakia from the fruits of the plant ( mare or kocimare in Albanian ), whence comes the name of the drink, which is raki kocimarje . The flowers are pollinated by bees , and the resulting honey is bitter tasting but still considered a delicacy. Arbutus unedo' s leaves have been employed in traditional and folk medicine in

1767-472: The above stated equations as where ρ is the density (the ratio of mass to volume). A sphere can be constructed as the surface formed by rotating a circle one half revolution about any of its diameters ; this is very similar to the traditional definition of a sphere as given in Euclid's Elements . Since a circle is a special type of ellipse , a sphere is a special type of ellipsoid of revolution . Replacing

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1824-575: The ancient army medical herbalist Pedanios Dioscorides [De Materia Medica, Book II-150]; in addition, Pliny thought it should not be planted where bees are kept, for the bitterness it imparts to honey. The first evidence of its importation into northern European gardens was to 16th-century England from Ireland. In 1586 a correspondent in Ireland sent plants to the Elizabethan courtiers Lord Leicester and Sir Francis Walsingham . An earlier description by Rev. William Turner ( The Names of Herbes , 1548)

1881-410: The bee (perhaps to reduce any toxic effects against the bee) then transformed back to the active aglycone by the bee's microbiome in the hindgut where the parasite is most prevalent and damaging - suggesting that the microbiome assists in the anti-parasitic process. In landscape design , ecosystem restoration or permaculture based designs, A. unedo can have many purposes. While the ornamental one

1938-688: The bold and impractical suggestion that it might be used for hedges, though it "will not admit of being clipped as other evergreens are". In the United States, Thomas Jefferson lists the plant in his Monticello gardens in 1778. The form A. unedo f. rubra and the hybrid A. × andrachnoides , have gained the Royal Horticultural Society 's Award of Garden Merit . The tree is mentioned by Roman poet Ovid , in Book I: 89–112 "The Golden Age" of his Metamorphoses : "Contented with food that grew without cultivation, they collected mountain strawberries and

1995-442: The circle with an ellipse rotated about its major axis , the shape becomes a prolate spheroid ; rotated about the minor axis, an oblate spheroid. A sphere is uniquely determined by four points that are not coplanar . More generally, a sphere is uniquely determined by four conditions such as passing through a point, being tangent to a plane, etc. This property is analogous to the property that three non-collinear points determine

2052-423: The cube, since V = ⁠ π / 6 ⁠ d , where d is the diameter of the sphere and also the length of a side of the cube and ⁠ π / 6 ⁠  ≈ 0.5236. For example, a sphere with diameter 1 m has 52.4% the volume of a cube with edge length 1   m, or about 0.524 m . The surface area of a sphere of radius r is: Archimedes first derived this formula from

2109-401: The discrepancy between the inner and outer surface area of any given shell is infinitesimal, and the elemental volume at radius r is simply the product of the surface area at radius r and the infinitesimal thickness. At any given radius r , the incremental volume ( δV ) equals the product of the surface area at radius r ( A ( r ) ) and the thickness of a shell ( δr ): The total volume

2166-523: The fact that the projection to the lateral surface of a circumscribed cylinder is area-preserving. Another approach to obtaining the formula comes from the fact that it equals the derivative of the formula for the volume with respect to r because the total volume inside a sphere of radius r can be thought of as the summation of the surface area of an infinite number of spherical shells of infinitesimal thickness concentrically stacked inside one another from radius 0 to radius r . At infinitesimal thickness

2223-471: The first national cause martyr . Pascoli's ode says: (in Italian) O verde albero italico, il tuo maggio è nella bruma: s'anche tutto muora, tu il giovanile gonfalon selvaggio spieghi alla bora Oh green Italian tree, your May month is in the mist: if everything die, you, the youthful wild banner unfold to the northern wind The Garden of Earthly Delights , a painting by Hieronymus Bosch ,

2280-440: The form of a decoction said to have the following properties: astringent, diuretic, urinary anti-septic, antiseptic, intoxicant, rheumatism, tonic, and more recently, in the therapy of hypertension and diabetes. The leaves are reported to have a high concentration of flavonol antioxidants, especially quercetin , best extracted with a decoction, and together with the fruits are a source of antioxidants. The nectar contains

2337-515: The fruit of the strawberry tree, wild cherries, blackberries clinging to the tough brambles, and acorns fallen from Jupiter's spreading oak-tree." The name of the Italian promontory Mount Conero , situated directly south of the port of Ancona on the Adriatic Sea , derives from the Greek name κόμαρος (komaròs) indicating the strawberry tree which is common on the slopes of the mountain. Mount Conero,

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2394-454: The isoprenoid unedone (2-(1,2-dihydroxypropyl)-4,4,8-trimethyl-1-oxaspiro[2.5]oct-7-en-6-one) which is biologically active against a common and debilitating parasite of bumble bees, Crithidia bombi , so could provide a naturally occurring way for bees to withstand the burden of disease which has been reported to be a contributing factor in pollinator declines. The compound is glycosylated to an inactive form unedone-8-O-glycoside once consumed by

2451-551: The numbers of fruits. Arbutus unedo is naturally adapted to dry summer climates, and has become a very popular ornamental plant in California and the rest of the west coast of North America. It can grow easily in USDA hardiness zone 7 or warmer. It also grows well in the cool, wet summers of western Ireland and England, and temperate regions of Europe and Asia. Pests include scales and thrips , and diseases include anthracnose , Phytophthora , root rot, and rust . Unlike most of

2508-423: The only coastal high point on the Adriatic sea between Trieste and the Gargano massif in the region of Apulia , has assisted navigators in sailing across the Adriatic sea since ancient times. The strawberry tree ( Italian : corbezzolo [korˈbettsolo] ) began to be considered one of the national symbols of Italy in the 19th century, during the Italian unification , because with its autumn colors

2565-550: The only solution of f ( x , y , z ) = 0 {\displaystyle f(x,y,z)=0} is the point P 0 = ( x 0 , y 0 , z 0 ) {\displaystyle P_{0}=(x_{0},y_{0},z_{0})} and the equation is said to be the equation of a point sphere . Finally, in the case ρ > 0 {\displaystyle \rho >0} , f ( x , y , z ) = 0 {\displaystyle f(x,y,z)=0}

2622-437: The other Mediterranean Basin species such as A. andrachne and A. canariensis and not to the western North American members of the genus. Arbutus unedo and A. andrachne hybridise naturally where their ranges overlap; the hybrid has been named Arbutus × andrachnoides (syn. A. × hybrida , or A. andrachne × unedo ), inheriting traits of both parent species, though fruits are not usually borne freely, and as

2679-422: The poles is called the equator . Great circles through the poles are called lines of longitude or meridians . Small circles on the sphere that are parallel to the equator are circles of latitude (or parallels ). In geometry unrelated to astronomical bodies, geocentric terminology should be used only for illustration and noted as such, unless there is no chance of misunderstanding. Mathematicians consider

2736-440: The smallest surface area of all surfaces that enclose a given volume, and it encloses the largest volume among all closed surfaces with a given surface area. The sphere therefore appears in nature: for example, bubbles and small water drops are roughly spherical because the surface tension locally minimizes surface area. The surface area relative to the mass of a ball is called the specific surface area and can be expressed from

2793-506: The sphere has the same center and radius as the sphere, and divides it into two equal hemispheres . Although the figure of Earth is not perfectly spherical, terms borrowed from geography are convenient to apply to the sphere. A particular line passing through its center defines an axis (as in Earth's axis of rotation ). The sphere-axis intersection defines two antipodal poles ( north pole and south pole ). The great circle equidistant to

2850-522: The sphere with radius r > 0 {\displaystyle r>0} and center ( x 0 , y 0 , z 0 ) {\displaystyle (x_{0},y_{0},z_{0})} can be parameterized using trigonometric functions . The symbols used here are the same as those used in spherical coordinates . r is constant, while θ varies from 0 to π and φ {\displaystyle \varphi } varies from 0 to 2 π . In three dimensions,

2907-522: The sphere). This may be proved by inscribing a cone upside down into semi-sphere, noting that the area of a cross section of the cone plus the area of a cross section of the sphere is the same as the area of the cross section of the circumscribing cylinder, and applying Cavalieri's principle . This formula can also be derived using integral calculus (i.e., disk integration ) to sum the volumes of an infinite number of circular disks of infinitesimally small thickness stacked side by side and centered along

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2964-426: The sphere: their length is twice the radius, d = 2 r . Two points on the sphere connected by a diameter are antipodal points of each other. A unit sphere is a sphere with unit radius ( r = 1 ). For convenience, spheres are often taken to have their center at the origin of the coordinate system , and spheres in this article have their center at the origin unless a center is mentioned. A great circle on

3021-432: The square of the distance between their centers is equal to the sum of the squares of their radii. If f ( x , y , z ) = 0 and g ( x , y , z ) = 0 are the equations of two distinct spheres then is also the equation of a sphere for arbitrary values of the parameters s and t . The set of all spheres satisfying this equation is called a pencil of spheres determined by the original two spheres. In this definition

3078-466: The strawberry tree, vegetation include oak , holm oak , Aleppo pine , Cupressus sempervirens and many others. Other comuni near the mountain include Sirolo and Numana . Arbutus unedo Arbutus unedo , commonly known as strawberry tree , is an evergreen shrub or small tree in the family Ericaceae , native to the Mediterranean Basin and Western Europe . The tree

3135-404: The underside, 8–10 cm (3–4 in) long and 3–4 cm (1– 1 + 1 ⁄ 2  in) broad, laurel-like and with a serrated or serrulated margin. The hermaphrodite flowers are white (yellow when desiccated ), bell-shaped, 7–8 mm ( 1 ⁄ 4 – 5 ⁄ 16  in) in diameter, and flower from a reddish hanging panicle in autumn. They are pollinated by bees, and have

3192-617: Was originally listed by José de Sigüenza , in the inventory of the Spanish Crown as La Pintura del Madroño – "The Painting of the Strawberry Tree". The tree makes up part of the Coat of arms of Madrid ( El oso y el madroño , The Bear and the Strawberry Tree) of the city of Madrid , Spain . In the center of the city ( Puerta del Sol ) there is a statue of a bear eating the fruit of

3249-449: Was probably based on hearsay. The Irish association of Arbutus in English gardens is reflected in the inventory taken in 1649 of Henrietta Maria 's Wimbledon : "one very fayre tree, called the Irish arbutis standing in the midle parte of the sayd kitchin garden, very lovely to look upon" By the 18th century Arbutus unedo was well known enough in English gardens for Batty Langley to make

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