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52-549: The game can be played in either single player mode or two player co-operative mode, using two joysticks, or a joystick plus keyboard. Players can choose to control either the hero, armed with throwing knives , or the heroine, armed with a crossbow . During the game, players will find various relics which permanently increase attack power, defense, or magic power, as well as an arsenal of magic scrolls, and special amulets that create temporary effects. Food can be picked up to heal damage, but occasionally turns out to be poison which hurts

104-1154: A : 1 b : 1 c = b c : c a : a b = csc ⁡ L : csc ⁡ M : csc ⁡ N = cos ⁡ L + cos ⁡ M ⋅ cos ⁡ N : cos ⁡ M + cos ⁡ N ⋅ cos ⁡ L : cos ⁡ N + cos ⁡ L ⋅ cos ⁡ M = sec ⁡ L + sec ⁡ M ⋅ sec ⁡ N : sec ⁡ M + sec ⁡ N ⋅ sec ⁡ L : sec ⁡ N + sec ⁡ L ⋅ sec ⁡ M . {\displaystyle {\begin{aligned}C&={\frac {1}{a}}:{\frac {1}{b}}:{\frac {1}{c}}=bc:ca:ab=\csc L:\csc M:\csc N\\[6pt]&=\cos L+\cos M\cdot \cos N:\cos M+\cos N\cdot \cos L:\cos N+\cos L\cdot \cos M\\[6pt]&=\sec L+\sec M\cdot \sec N:\sec M+\sec N\cdot \sec L:\sec N+\sec L\cdot \sec M.\end{aligned}}} The centroid

156-519: A b 1 2 ( f ( x ) + g ( x ) ) ( f ( x ) − g ( x ) ) d x , {\displaystyle {\begin{aligned}{\bar {x}}&={\frac {1}{A}}\int _{a}^{b}x{\bigl (}f(x)-g(x){\bigr )}\,dx,\\[5mu]{\bar {y}}&={\frac {1}{A}}\int _{a}^{b}{\tfrac {1}{2}}{\bigl (}f(x)+g(x){\bigr )}{\bigl (}f(x)-g(x){\bigr )}\,dx,\end{aligned}}} where A {\displaystyle A}

208-467: A balanced or unbalanced knife depending upon the position of the weight. Balanced knives are generally preferred over unbalanced ones for two reasons: a) Balanced knives can be thrown from the handle as well as from the blade, and b) it is easier to change from one balanced knife to another. The weight of the throwing knife and the throwing speed determine the power of the impact. Lighter knives can be thrown with relative ease, but they may fail to penetrate

260-888: A finite number of simpler figures X 1 , X 2 , … , X n , {\displaystyle X_{1},X_{2},\dots ,X_{n},} computing the centroid C i {\displaystyle C_{i}} and area A i {\displaystyle A_{i}} of each part, and then computing C x = ∑ i C i x A i ∑ i A i , C y = ∑ i C i y A i ∑ i A i . {\displaystyle C_{x}={\frac {\sum _{i}{C_{i}}_{x}A_{i}}{\sum _{i}A_{i}}},\quad C_{y}={\frac {\sum _{i}{C_{i}}_{y}A_{i}}{\sum _{i}A_{i}}}.} Holes in

312-399: A horde of monsters. Most of the levels entail some sort of puzzle solving, involving clues in the form of scrolls that are picked up along the way. These scrolls also tell the story of an unsuccessful group of adventurers who journeyed through the dungeon before the current players. This ill-fated party included members Arthur, Bloodaxe, Grindlewald, Furrowfoot, and Imelda, as well as Mellack,

364-424: A mage whom the previous adventurers met along the way. Correctly answering some questions after each story section yields bonus health points. Level 100 is unique in the game, as its geography includes large, irregularly shaped caves, rather than straight or diagonal walls as in the other levels. Level 100 also only features one enemy, the demon boss , Calvrak. Demon Stalkers includes its own level-editor, allowing

416-412: A number of names such as Onzil , Kulbeda , Mambele , Pinga , and Trombash . These weapons had multiple iron blades and were used for warfare and hunting. A maximum effective range of about 50 m (160 ft) has been suggested. The weapon appears to have originated in central Sudan somewhere around 1000 AD from where it spread south. It has however been suggested that the same weapon

468-402: A triangle's centroid, see below . The centroid of a uniformly dense planar lamina , such as in figure (a) below, may be determined experimentally by using a plumbline and a pin to find the collocated center of mass of a thin body of uniform density having the same shape. The body is held by the pin, inserted at a point, off the presumed centroid in such a way that it can freely rotate around

520-474: Is C = x 1 + x 2 + ⋯ + x k k . {\displaystyle \mathbf {C} ={\frac {\mathbf {x} _{1}+\mathbf {x} _{2}+\cdots +\mathbf {x} _{k}}{k}}.} This point minimizes the sum of squared Euclidean distances between itself and each point in the set. The centroid of a plane figure X {\displaystyle X} can be computed by dividing it into

572-507: Is a knife that is specially designed and weighted so that it can be thrown effectively. They are a distinct category from ordinary knives. Throwing knives are used by many cultures around the world, and as such different tactics for throwing them have been developed, as have different shapes and forms of throwing knife. Throwing knives are also used in sideshow acts and sport. Throwing knives saw use in central Africa. The wide area they were used over means that they were referred to by

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624-407: Is a special case of Green's theorem . This is a method of determining the centroid of an L-shaped object. [REDACTED] The centroid of a triangle is the point of intersection of its medians (the lines joining each vertex with the midpoint of the opposite side). The centroid divides each of the medians in the ratio 2 : 1 , {\displaystyle 2:1,} which

676-479: Is also the physical center of mass if the triangle is made from a uniform sheet of material; or if all the mass is concentrated at the three vertices, and evenly divided among them. On the other hand, if the mass is distributed along the triangle's perimeter, with uniform linear density , then the center of mass lies at the Spieker center (the incenter of the medial triangle ), which does not (in general) coincide with

728-449: Is depicted in Libyan wall sculptures dating around 1350 BC. The throwing knives were extensively collected by Europeans with the result that many European and American museums have extensive collections. However the collectors generally failed to record the origin of the blades or their use. As a result, the history and use of the throwing knives is poorly understood. A further complication

780-417: Is not sharpened. The purpose of the grip is to allow the knife to be safely handled by the user and also to balance the weight of the blade. Throwing knives are of two kinds, balanced and unbalanced. A balanced knife is made in such a way that the center of gravity and the geometrical center of the knife (the centroid ) are the same. The trajectory of a thrown knife is the path of the center of gravity through

832-400: Is not true of other quadrilaterals . For the same reason, the centroid of an object with translational symmetry is undefined (or lies outside the enclosing space), because a translation has no fixed point. The centroid of a triangle is the intersection of the three medians of the triangle (each median connecting a vertex with the midpoint of the opposite side). For other properties of

884-403: Is that the label "Throwing knife" was attached by ethnographers to various objects that didn't fit into other weapon categories even though they may not have been thrown. Throwing knives are commonly made of a single piece of steel or other material, without handles, unlike other types of knives. The knife has two sections, the "blade" which is the sharpened half of the knife and the "grip" which

936-422: Is the k {\displaystyle k} th coordinate of C , {\displaystyle C,} and S k ( z ) {\displaystyle S_{k}(z)} is the measure of the intersection of X {\displaystyle X} with the hyperplane defined by the equation x k = z . {\displaystyle x_{k}=z.} Again,

988-437: Is the area of the figure X , {\displaystyle X,} S y ( x ) {\displaystyle S_{\mathrm {y} }(x)} is the length of the intersection of X {\displaystyle X} with the vertical line at abscissa x , {\displaystyle x,} and S x ( y ) {\displaystyle S_{\mathrm {x} }(y)}

1040-438: Is the area of the region (given by ∫ a b ( f ( x ) − g ( x ) ) d x {\textstyle \int _{a}^{b}{\bigl (}f(x)-g(x){\bigr )}dx} ). An integraph (a relative of the planimeter ) can be used to find the centroid of an object of irregular shape with smooth (or piecewise smooth) boundary. The mathematical principle involved

1092-609: Is the length of the intersection of X {\displaystyle X} with the horizontal line at ordinate y . {\displaystyle y.} The centroid ( x ¯ , y ¯ ) {\displaystyle ({\bar {x}},\;{\bar {y}})} of a region bounded by the graphs of the continuous functions f {\displaystyle f} and g {\displaystyle g} such that f ( x ) ≥ g ( x ) {\displaystyle f(x)\geq g(x)} on

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1144-534: Is therefore at 1 3 : 1 3 : 1 3 {\displaystyle {\tfrac {1}{3}}:{\tfrac {1}{3}}:{\tfrac {1}{3}}} in barycentric coordinates . In trilinear coordinates the centroid can be expressed in any of these equivalent ways in terms of the side lengths a , b , c {\displaystyle a,b,c} and vertex angles L , M , N {\displaystyle L,M,N} : C = 1

1196-677: Is to say it is located 1 3 {\displaystyle {\tfrac {1}{3}}} of the distance from each side to the opposite vertex (see figures at right). Its Cartesian coordinates are the means of the coordinates of the three vertices. That is, if the three vertices are L = ( x L , y L ) , {\displaystyle L=(x_{L},y_{L}),} M = ( x M , y M ) , {\displaystyle M=(x_{M},y_{M}),} and N = ( x N , y N ) , {\displaystyle N=(x_{N},y_{N}),} then

1248-471: Is unlikely that Archimedes learned the theorem that the medians of a triangle meet in a point—the center of gravity of the triangle—directly from Euclid , as this proposition is not in the Elements . The first explicit statement of this proposition is due to Heron of Alexandria (perhaps the first century CE) and occurs in his Mechanics . It may be added, in passing, that the proposition did not become common in

1300-425: The barycenter or center of mass coincides with the centroid. Informally, it can be understood as the point at which a cutout of the shape (with uniformly distributed mass) could be perfectly balanced on the tip of a pin. In physics, if variations in gravity are considered, then a center of gravity can be defined as the weighted mean of all points weighted by their specific weight . In geography ,

1352-631: The integrals are taken over the whole space R n , {\displaystyle \mathbb {R} ^{n},} and g {\displaystyle g} is the characteristic function of the subset X {\displaystyle X} of R n :   g ( x ) = 1 {\displaystyle \mathbb {R} ^{n}\!:\ g(x)=1} if x ∈ X {\displaystyle x\in X} and g ( x ) = 0 {\displaystyle g(x)=0} otherwise. Note that

1404-403: The air. When a balanced knife is thrown, the circles described by the point and the end of the hilt as the knife rotates about the center of gravity will have the same diameter, making the trajectory more predictable. For an unbalanced knife, the circles described will have different diameters, meaning that the point and the end of the hilt will hit a target in different locations at any point along

1456-526: The areas replaced by the d {\displaystyle d} -dimensional measures of the parts. The centroid of a subset X {\displaystyle X} of R n {\displaystyle \mathbb {R} ^{n}} can also be computed by the formula C = ∫ x g ( x )   d x ∫ g ( x )   d x {\displaystyle C={\frac {\int xg(x)\ dx}{\int g(x)\ dx}}} where

1508-641: The centroid (denoted C {\displaystyle C} here but most commonly denoted G {\displaystyle G} in triangle geometry ) is C = 1 3 ( L + M + N ) = ( 1 3 ( x L + x M + x N ) , 1 3 ( y L + y M + y N ) ) . {\displaystyle C={\tfrac {1}{3}}(L+M+N)={\bigl (}{\tfrac {1}{3}}(x_{L}+x_{M}+x_{N}),{\tfrac {1}{3}}(y_{L}+y_{M}+y_{N}){\bigr )}.} The centroid

1560-429: The centroid can be found by balancing the shape on a smaller shape, such as the top of a narrow cylinder. The centroid occurs somewhere within the range of contact between the two shapes (and exactly at the point where the shape would balance on a pin). In principle, progressively narrower cylinders can be used to find the centroid to arbitrary precision. In practice air currents make this infeasible. However, by marking

1612-485: The centroid is found in the same way. The same formula holds for any three-dimensional objects, except that each A i {\displaystyle A_{i}} should be the volume of X i , {\displaystyle X_{i},} rather than its area. It also holds for any subset of R d , {\displaystyle \mathbb {R} ^{d},} for any dimension d , {\displaystyle d,} with

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1664-630: The centroid of a radial projection of a region of the Earth's surface to sea level is the region's geographical center . The term "centroid" is of recent coinage (1814). It is used as a substitute for the older terms "center of gravity" and " center of mass " when the purely geometrical aspects of that point are to be emphasized. The term is peculiar to the English language; French, for instance, uses " centre de gravité " on most occasions, and other languages use terms of similar meaning. The center of gravity, as

1716-421: The centroid, and all lines will cross at exactly the same place. This method can be extended (in theory) to concave shapes where the centroid may lie outside the shape, and virtually to solids (again, of uniform density), where the centroid may lie within the body. The (virtual) positions of the plumb lines need to be recorded by means other than by drawing them along the shape. For convex two-dimensional shapes,

1768-554: The dagger at your opponent's chest. [REDACTED] Media related to Throwing knives at Wikimedia Commons Centroid In mathematics and physics , the centroid , also known as geometric center or center of figure , of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. The same definition extends to any object in n {\displaystyle n} - dimensional Euclidean space . In geometry , one often assumes uniform mass density , in which case

1820-601: The denominator is simply the measure of the set X . {\displaystyle X.} This formula cannot be applied if the set X {\displaystyle X} has zero measure, or if either integral diverges. Another formula for the centroid is C k = ∫ z S k ( z )   d z ∫ g ( x )   d x , {\displaystyle C_{k}={\frac {\int zS_{k}(z)\ dz}{\int g(x)\ dx}},} where C k {\displaystyle C_{k}}

1872-625: The denominator is simply the measure of X . {\displaystyle X.} For a plane figure, in particular, the barycentric coordinates are C x = ∫ x S y ( x )   d x A , C y = ∫ y S x ( y )   d y A , {\displaystyle C_{\mathrm {x} }={\frac {\int xS_{\mathrm {y} }(x)\ dx}{A}},\quad C_{\mathrm {y} }={\frac {\int yS_{\mathrm {x} }(y)\ dy}{A}},} where A {\displaystyle A}

1924-402: The figure X , {\displaystyle X,} overlaps between the parts, or parts that extend outside the figure can all be handled using negative areas A i . {\displaystyle A_{i}.} Namely, the measures A i {\displaystyle A_{i}} should be taken with positive and negative signs in such a way that the sum of

1976-936: The figure below (a) is easily divided into a square and a triangle, both with positive area; and a circular hole, with negative area (b). The centroid of each part can be found in any list of centroids of simple shapes (c). Then the centroid of the figure is the weighted average of the three points. The horizontal position of the centroid, from the left edge of the figure is x = 5 × 10 2 + 13.33 × 1 2 10 2 − 3 × π 2.5 2 10 2 + 1 2 10 2 − π 2.5 2 ≈ 8.5  units . {\displaystyle x={\frac {5\times 10^{2}+13.33\times {\frac {1}{2}}10^{2}-3\times \pi 2.5^{2}}{10^{2}+{\frac {1}{2}}10^{2}-\pi 2.5^{2}}}\approx 8.5{\text{ units}}.} The vertical position of

2028-437: The geometric centroid of an object lies in the intersection of all its hyperplanes of symmetry . The centroid of many figures ( regular polygon , regular polyhedron , cylinder , rectangle , rhombus , circle , sphere , ellipse , ellipsoid , superellipse , superellipsoid , etc.) can be determined by this principle alone. In particular, the centroid of a parallelogram is the meeting point of its two diagonals . This

2080-467: The geometric centroid of the full triangle. The area of the triangle is 3 2 {\displaystyle {\tfrac {3}{2}}} times the length of any side times the perpendicular distance from the side to the centroid. A triangle's centroid lies on its Euler line between its orthocenter H {\displaystyle H} and its circumcenter O , {\displaystyle O,} exactly twice as close to

2132-494: The interval [ a , b ] , {\displaystyle [a,b],} a ≤ x ≤ b {\displaystyle a\leq x\leq b} is given by x ¯ = 1 A ∫ a b x ( f ( x ) − g ( x ) ) d x , y ¯ = 1 A ∫

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2184-1209: The latter as to the former: C H ¯ = 2 C O ¯ . {\displaystyle {\overline {CH}}=2{\overline {CO}}.} In addition, for the incenter I {\displaystyle I} and nine-point center N , {\displaystyle N,} we have C H ¯ = 4 C N ¯ , C O ¯ = 2 C N ¯ , I C ¯ < H C ¯ , I H ¯ < H C ¯ , I C ¯ < I O ¯ . {\displaystyle {\begin{aligned}{\overline {CH}}&=4{\overline {CN}},\\[5pt]{\overline {CO}}&=2{\overline {CN}},\\[5pt]{\overline {IC}}&<{\overline {HC}},\\[5pt]{\overline {IH}}&<{\overline {HC}},\\[5pt]{\overline {IC}}&<{\overline {IO}}.\end{aligned}}} If G {\displaystyle G}

2236-578: The name indicates, is a notion that arose in mechanics, most likely in connection with building activities. It is uncertain when the idea first appeared, as the concept likely occurred to many people individually with minor differences. Nonetheless, the center of gravity of figures was studied extensively in Antiquity; Bossut credits Archimedes (287–212 BCE) with being the first to find the centroid of plane figures, although he never defines it. A treatment of centroids of solids by Archimedes has been lost. It

2288-443: The overlap range from multiple balances, one can achieve a considerable level of accuracy. The centroid of a finite set of k {\displaystyle k} points x 1 , x 2 , … , x k {\displaystyle \mathbf {x} _{1},\mathbf {x} _{2},\ldots ,\mathbf {x} _{k}} in R n {\displaystyle \mathbb {R} ^{n}}

2340-414: The pin; the plumb line is then dropped from the pin (figure b). The position of the plumbline is traced on the surface, and the procedure is repeated with the pin inserted at any different point (or a number of points) off the centroid of the object. The unique intersection point of these lines will be the centroid (figure c). Provided that the body is of uniform density, all lines made this way will include

2392-884: The player to modify all levels except 100. A review in Computer Gaming World , comparing the game to Gauntlet , noted " Gauntlet seemed to have ten times more monsters than Demon Stalkers . Thus, despite the similarities, Gauntlet is primarily an action game and Demon Stalkers is a search game with action thrown in." The review concluded by saying neither game would disappoint. James V. Trunzo reviewed Demon Stalkers in White Wolf #17 (1989) and stated that "If you enjoy non-stop action, grab your crossbow with its unlimited supply of quarrels and get ready to wreak havoc as you fight your way through level after level in Demon Stalker ." Throwing knives A throwing knife

2444-430: The player with several shots, except for the rats, who emerge from indestructible sewer grates. The dungeon consists of many interconnected maze -like levels which rooms, hallways, and doors. There are several multi-level mazes, where the player must ascend and descend between levels several times before finding the correct path. The collecting of keys to open doors is a fundamental part of the game, while fighting against

2496-469: The player. Similarly, some scrolls turn out to be a "slow death curse," which takes a way the player's health continuously until death, unless the exit from that level is found. Enemies in the game include rats, ghosts who can walk through walls, dervishes who can steal a player's possessions, snappers who remain dormant until disturbed, and mad mages, who shoot fireballs. These monsters emerge from special spawning areas called vortexes, which can be destroyed by

2548-399: The signs of A i {\displaystyle A_{i}} for all parts that enclose a given point p {\displaystyle p} is 1 {\displaystyle 1} if p {\displaystyle p} belongs to X , {\displaystyle X,} and 0 {\displaystyle 0} otherwise. For example,

2600-435: The target properly, resulting in "bounce back". Heavy throwing knives are more stable in their flight and cause more damage to the target, but more strength is needed to throw them accurately. Hans Talhoffer (c. 1410-1415 – after 1482) and Paulus Hector Mair (1517–1579) both mention throwing daggers in their treaties on combat and weapons. Talhoffer specifies a type of spiked dagger for throwing while Mair describes throwing

2652-409: The textbooks on plane geometry until the nineteenth century. The geometric centroid of a convex object always lies in the object. A non-convex object might have a centroid that is outside the figure itself. The centroid of a ring or a bowl , for example, lies in the object's central void. If the centroid is defined, it is a fixed point of all isometries in its symmetry group . In particular,

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2704-404: The trajectory. This makes predicting the trajectory more difficult. Balanced knives can be thrown by gripping either the point or the hilt, depending upon the user's preference and the distance to the target. Unbalanced knives are generally thrown by gripping the lighter end. There are also knives with adjustable weights which can slide on the length of the blade. This way, it can function both as

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