Factors of the Difference of Two Squares

THE FIDE LAWS OF CHESS. Introduction FIDE Laws of Chess cover over-the-board play. The Laws of Chess have two parts: 1. Basic Rules of Play and 2. Competitive Rules of Play. The English text is the authentic version of the Laws of Chess (which were adopted at the 93rd FIDE Congress at Chennai, India) coming into force on 1 January 2023. Preface. The Laws of Chess cannot cover all possible situations that may arise during a game, nor can they regulate all administrative questions. Where cases are not precisely regulated by an Article of the Laws, it should be possible to reach a correct decision by studying analogous situations which are regulated in the Laws. The Laws assume that arbiters have the necessary competence, sound judgement and absolute objectivity. Too detailed a rule might deprive the arbiter of his/her freedom of judgement and thus prevent him/her from finding a solution to a problem dictated by fairness, logic and special factors. FIDE appeals to all chess players and federations to accept this view. A necessary condition for a game to be rated by FIDE is that it shall be played according to the FIDE Laws of Chess. It is recommended that competitive games not rated by FIDE be played according to the FIDE Laws of Chess. Member federations may ask FIDE to give a ruling on matters relating to the Laws of Chess. BASIC RULES OF PLAY. Article 1: The Nature and Objectives of the Game of Chess 1.1 1.2 1.3 1.4 The game of chess is played between two opponents who move their pieces on a square board called a ‘chessboard’. The player with the light-coloured pieces (White) makes the first move, then the players move alternately, with the player with the dark-coloured pieces (Black) making the next move. A player is said to ‘have the move’ when his/her opponent’s move has been ‘made’. The objective of each player is to place the opponent’s king ‘under attack’ in such a way that the opponent has no legal move. 1.4.1 The player who achieves this goal is said to have ‘checkmated’ the opponent’s king and to have won the game. Leaving one’s own king under attack, exposing one’s own king to attack and also ’capturing’ the opponent’s king is not allowed. 1.4.2 The opponent whose king has been checkmated has lost the game. 1.5 If the position is such that neither player can possibly checkmate the opponent’s king, the game is drawn (see Article 5.2.2). Article 2: The Initial Position of the Pieces on the Chessboard 2.1 2.2 The chessboard is composed of an 8 x 8 grid of 64 equal squares alternately light (the ‘white’ squares) and dark (the ‘black’ squares). The chessboard is placed between the players in such a way that the near corner square to the right of the player is white. At the beginning of the game White has 16 light-coloured pieces (the ‘white’ pieces); Black has 16 dark-coloured pieces (the ‘black’ pieces). These pieces are as follows: A white king usually indicated by the symbol K A white queen Two white rooks Two white bishops Two white knights Eight white pawns A black king A black queen Two black rooks Two black bishops Two black knights Eight black pawns usually indicated by the symbol Q usually indicated by the symbol R usually indicated by the symbol B usually indicated by the symbol N usually indicated by the symbol usually indicated by the symbol K usually indicated by the symbol Q usually indicated by the symbol R usually indicated by the symbol B usually indicated by the symbol N usually indicated by the symbol Staunton Pieces p Q K B N R 9 2.3 The initial position of the pieces on the chessboard is as follows: 2.4 The eight vertical columns of squares are called ‘files’. The eight horizontal rows of squares are called ‘ranks’. A straight line of squares of the same colour, running from one edge of the board to an adjacent edge, is called a ‘diagonal’. Article 3: The Moves of the Pieces 3.1 It is not permitted to move a piece to a square occupied by a piece of the same colour. 3.1.1 If a piece moves to a square occupied by an opponent’s piece the latter is captured and removed from the chessboard as part of the same move. 3.1.2 A piece is said to attack an opponent’s piece if the piece could make a capture on that square according to Articles 3.2 to 3.8. 3.1.3 A piece is considered to attack a square even if this piece is constrained from moving to that square because it would then leave or place the king of its own colour under attack. 3.2 The bishop may move to any square along a diagonal on which it stands. 3.3 The rook may move to any square along the file or the rank on which it stands. 3.4 The queen may move to any square along the file, the rank or a diagonal on which it stands. 3.5 3.6 3.7 When making these moves, the bishop, rook or queen may not move over any intervening pieces. The knight may move to one of the squares nearest to that on which it stands but not on the same rank, file or diagonal. 3.7 When making these moves, the bishop, rook or queen may not move over any intervening pieces. The knight may move to one of the squares nearest to that on which it stands but not on the same rank, file or diagonal. The pawn: 3.7.1 The pawn may move forward to the square immediately in front of it on the same file, provided that this square is unoccupied, or 3.7.2 on its first move the pawn may move as in 3.7.1 or alternatively it may advance two squares along the same file, provided that both squares are unoccupied, or 3.7.3 the pawn may move to a square occupied by an opponent’s piece diagonally in front of it on an adjacent file, capturing that piece. 3.7.3.1 A pawn occupying a square on the same rank as and on an adjacent file to an opponent’s pawn which has just advanced two squares in one move from its original square may capture this opponent’s pawn as though the latter had been moved only one square. 3.7.3.2 This capture is only legal on the move following this advance and is called an ‘en passant’ capture. 3.7.3.3 When a player, having the move, plays a pawn to the rank furthest from its starting position, he/she must exchange that pawn as part of the same move for a new queen, rook, bishop or knight of the same colour on the intended square of arrival. This is called the square of ‘promotion’. 3.7.3.4 The player's choice is not restricted to pieces that have been captured previously. 3.7.3.5 This exchange of a pawn for another piece is called promotion, and the effect of the new piece is immediate. 3.8 There are two different ways of moving the king: 3.8.1 by moving to an adjoining square. 3.8.2 by ‘castling’. This is a move of the king and either rook of the same colour along the player’s first rank, counting as a single move of the king and executed as follows: the king is transferred from its original square two squares towards the rook on its original square, then that rook is transferred to the square the king has just crossed. 3.8.2.1 The right to castle has been lost: 3.8.2.1.1 If the king has already moved, or 3.8.2.1.2 With a rook that has already moved. 3.8.2.2 Castling is prevented temporarily: 3.8.2.2.1 if the square on which the king stands, or the square which it must cross, or the square which it is to occupy, is attacked by one or more of the opponent's pieces, or 3.8.2.2.2 if there is any piece between the king and the rook with which castling is to be effected. 3.9 The king in check: 3.9.1 The king is said to be 'in check' if it is attacked by one or more of the opponent's pieces, even if such pieces are constrained from moving to the square occupied by the king because they would then leave or place their own king in check. 3.9.2 No piece can be moved that will either expose the king of the same colour to check or leave that king in check. 3.10 Legal and illegal moves; illegal positions: 3.10.1 A move is legal when all the relevant requirements of Articles 3.1 – 3.9 have been fulfilled. 3.10.2 A move is illegal when it fails to meet the relevant requirements of Articles 3.1 –3.9. 3.10.3 A position is illegal when it cannot have been reached by any series of legal moves. Article 4: The Act of Moving the Pieces 4.1 4.2 Each move must be played with one hand only. Adjusting the pieces or other physical contact with a piece: 4.2.1 Only the player having the move may adjust one or more pieces on their squares, provided that he/she first expresses his/her intention (for example by saying “j’adoube” or “I adjust”). 4.2.2 Any other physical contact with a piece, except for clearly accidental contact, shall be considered to be intent. 4.3 Except as provided in Article 4.2.1, if the player having the move touches on the chessboard, with the intention of moving or capturing: 4.3.1 one or more of his/her own pieces, he/she must move the first piece touched that can be moved. 4.3.2 one or more of his/her opponent’s pieces, he/she must capture the first piece touched that can be captured. 4.3.3 one or more pieces of each colour, he/she must capture the first touched opponent’s piece with his/her first touched piece or, if this is illegal, move or capture the first piece touched that can be moved or captured. If it is unclear whether the player’s own piece or his/her opponent’s was touched first, the player’s own piece shall be considered to have been touched before his/her opponent’s. 4.4 If a player having the move: 4.4.1 touches his/her king and a rook he/she must castle on that side if it is legal to do so 4.4.2 deliberately touches a rook and then his/her king he/she is not allowed to castle on that side on that move and the situation shall be governed by Article 4.3.1. 4.4.3 intending to castle, touches the king and then a rook, but castling with this rook is illegal, the player must make another legal move with his/her king (which may include castling with the other rook). If the king has no legal move, the player is free to make any legal move. 4.4.4 promotes a pawn, the choice of the piece is finalised when the piece has touched the square of promotion. 4.5 4.6 If none of the pieces touched in accordance with Article 4.3 or Article 4.4 can be moved or captured, the player may make any legal move. The act of promotion may be performed in various ways: 4.6.1 the pawn does not have to be placed on the square of arrival. 4.6.2 removing the pawn and putting the new piece on the square of promotion may occur in any order. 4.6.3 If an opponent’s piece stands on the square of promotion, it must be captured. 4.7 When, as a legal move or part of a legal move, a piece has been released on a square, it cannot be moved to another square on this move. The move is considered to have been made in the case of: 4.7.1 A capture, when the captured piece has been removed from the chessboard and the player, having placed his/her own piece on its new square, has released this capturing piece from his/her hand. 4.7.2 Castling, when the player's hand has released the rook on the square previously crossed by the king. When the player has released the king from his/her hand, the move is not yet made, but the player no longer has the right to make any move other than castling on that side, if this is legal. If castling on this side is illegal, the player must make another legal move with his/her king (which may include castling with the other rook). If the king has no legal move, the player is free to make any legal move. 4.7.3 Promotion, when the player's hand has released the new piece on the square of promotion and the pawn has been removed from the board. 4.8 4.9 A player forfeits his/her right to claim against his/her opponent’s violation of Articles 4.1 – 4.7 once the player touches a piece with the intention of moving or capturing it. 4.8. A player forfeits his/her right to claim against his/her opponent’s violation of Articles 4.1 – 4.7 .4.9. If a player is unable to move the pieces, an assistant, who shall be acceptable to the arbiter, may be provided by the player to perform this operation. Article 5: The Completion of the Game 5.1.1 The game is won by the player who has checkmated his/her opponent’s king. This immediately ends the game, provided that the move producing the checkmate position was in accordance with Article 3 and Articles 4.2 – 4.7. 5.1.2 The game is lost by the player who declares he/she resigns (this immediately ends the game), unless the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves. In this case the result of the game is a draw. 5.2.1 The game is drawn when the player to move has no legal move and his/her king is not in check. The game is said to end in ‘stalemate’. This immediately ends the game, provided that the move producing the stalemate position was in accordance with Article 3 and Articles 4.2 – 4.7. 5.2.2 The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7. 5.2.3 The game is drawn upon agreement between the two players during the game, provided both players have made at least one move. This immediately ends the game. COMPETITIVE RULES OF PLAY Article 6: The Chessclock 6.1 ‘Chessclock’ means a clock with two time displays, connected to each other in such a way that only one of them can run at a time. ‘Clock’ in the Laws of Chess means one of the two time displays. Each time display has a ‘flag’. ‘Flag-fall’ means the expiration of the allotted time for a player. 6.2 Handling the chessclock: 6.2.1 During the game each player, having made his/her move on the chessboard, shall pause his/her own clock and start his/her opponent’s clock (that is to say, he/she shall press his/her clock). This “completes” the move. A move is also completed if: 6.2.1.1 6.2.1.2 the move ends the game (see Articles 5.1.1, 5.2.1, 5.2.2, 9.2.1, 9.6.1 and 9.6.2), or the player has made his/her next move, when his/her previous move was not completed. 6.2.2 A player must be allowed to pause his/her clock after making his/her move, even after the opponent has made his/her next move. The time between making the move on the chessboard and pressing the clock is regarded as part of the time allotted to the player. 6.2.3 A player must press his/her clock with the same hand with which he/she made his/her move. It is forbidden for a player to keep his/her finger on the clock or to ‘hover’ over it. 6.2.4 The players must handle the chessclock properly. It is forbidden to press it forcibly, to pick it up, to press the clock before moving or to knock it over. Improper clock handling shall be penalised in accordance with Article 12.9. 6.2.5 6.2.6 Only the player whose clock is running is allowed to adjust the pieces. If a player is unable to use the clock, an assistant, who must be acceptable to the arbiter, may be provided by the player to perform this operation. His/Her clock shall be adjusted by the arbiter in an equitable way. This adjustment of the clock shall not apply to the clock of a player with a disability. 6.3 Allotted time: 6.3.1 When using a chessclock, each player must complete a minimum number of moves or all moves in an allotted period of time including any additional amount of time added with each move. All these must be specified in advance. 6.3.2 The time saved by a player during one period is added to his/her time available for the next period, where applicable. In the time-delay mode both players receive an allotted ‘main thinking time’. Each player also receives a ‘fixed extra time’ with every move. The countdown of the main thinking time only commences after the fixed extra time has expired. Provided the player presses his/her clock before the expiration of the fixed extra time, the main thinking time does not change, irrespective of the proportion of the fixed extra time used. 6.4 Immediately after a flag falls, the requirements of Article 6.3.1 must be checked. 6.5 Before the start of the game the arbiter shall decide where the chessclock is placed. 6.6 At the time determined for the start of the game White’s clock is started.6.7. Default time: 6.7.1 The regulations of an event shall specify a default time in advance. If the default time is not specified, then it is zero. Any player who arrives at the chessboard after the default time shall lose the game unless the arbiter decides otherwise. 6.7.2 If the regulations of an event specify that the default time is not zero and if neither player is present initially, White shall lose all the time that elapses until he/she arrives, unless the regulations of an event specify, or the arbiter decides otherwise. 6.8 A flag is considered to have fallen when the arbiter observes the fact or when either player has made a valid claim to that effect. 6.9 Except where one of Articles 5.1.1, 5.1.2, 5.2.1, 5.2.2, 5.2.3 applies, if a player does not complete the prescribed number of moves in the allotted time, the game is lost by that player. However, the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves. 6.10 Chessclock setting: 6.10.1 Every indication given by the chessclock is considered to be conclusive in the absence of any evident defect. A chessclock with an evident defect shall be replaced by the arbiter, who shall use his/her best judgement when determining the times to be shown on the replacement chessclock. 6.10.2 If during a game it is found that the setting of either or both clocks is incorrect, either player or the arbiter shall pause the chessclock immediately. The arbiter shall install the correct setting and adjust the times and move-counter, if necessary he/she shall use his/her best judgement when determining the clock settings. 6.11.1 If the game needs to be interrupted, the arbiter shall pause the chessclock. 6.11.2 A player may pause the chessclock only in order to seek the arbiter’s assistance, for example when promotion has taken place and the piece required is not available. 6.11.3 The arbiter shall decide when the game restarts. 6.11.4 If a player pauses the chessclock in order to seek the arbiter’s assistance, the arbiter shall determine whether the player had any valid reason for doing so. If the player has no valid reason for pausing the chessclock, the player shall be penalised in accordance with Article 12.9. 6.12.1 Screens, monitors, or demonstration boards showing the current position on the chessboard, the moves and the number of moves made/completed, and clocks which also show the number of moves, are allowed in the playing hall. 6.12.2 The player may not make a claim relying only on information shown in this manner.

Allele variation of a specific gene Artificial Insemination (AI) collecting and preserving semen from sires and using artificial means to introduce it to the dam’s reproductive tract Body Cells make up the organs and tissue of an animal and have chromosomes in pairs, called diploids Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR) gene editing technology Codominance heterozygous individual expresses the phenotype of both alleles simultaneously Complete Dominance heterozygous gene pair is expressed the same as a homozygous dominant gene pair Crossbreeding sire from one breed and a dam from another, with each breed excelling in a certain characteristic to benefit the producer and the offspring Deoxyribonucleic Acid (DNA) stores genetic information and acts as a blueprint for all genetic material in the organism in two strands arranged in a double helix Dominant Alleles represent a dominant phenotype and are expressed as uppercase letters Embryo Transfer eggs are collected from a desirable female, fertilized and then implanted in several other females Expected Progeny Differences (EPDs) measure of the heritability of breeding values and traits Gametes fulfill the purpose of sexual reproduction, passing on half of the genetic code in the form of sperm and ovum and are also called haploids or sex cells Genotype organism's genetic composition, which determines its heredity potential and limitations Grading Up using a purebred sire to breed grade (unregistered or commercial) females Heritability degree to which offspring resemble their parent for a particular trait Heterosis (Hybrid Vigor) ability of crossbred animals to have the best traits from each parent Heterozygosity phenomenon of inheriting a different version of an allele from each biological parent Homozygosity phenomenon of inheriting the same version of an allele from each biological parent Inbreeding breeding of closely related animals with the goal of concentrating traits from a superior individual Incomplete Dominance dominant allele does not completely overcome the recessive Law of Dominance states genes will express themselves with the dominant gene appearing in the phenotype Law of Independent Assortment states unlinked or distantly linked gene pairs separate independently of other genes Law of Segregation states paired genes must segregate equally into gametes in a way so offspring have an equal likelihood of inheriting either factor Locus place on a chromosome where a gene is found Meiosis process of cellular reproduction of gametes and results in four genetically different daughter cells Mitosis process of cellular reproduction of body cells which creates two genetically identical daughter cells Outcrossing breeding highly unrelated individuals within a breed Phenotype all the observable characteristics of an organism resulting from the interaction of its genotype with its environment Polygenic Traits controlled by many gene pairs Punnett Square graphical representation of the possible genotypes of an offspring arising from a particular breeding, using letters to represent the genes Recessive Alleles non-dominant phenotypes which can still affect the appearance of an animal, but not as commonly, and are expressed as lowercase letters Ribonucleic Acid (RNA) replicates genetic information found in DNA to build proteins in processes known as transcription and translation Simply Inherited Traits typically controlled by one gene pair

Factors of the Sum and Difference of Two Cubes

Make a quiz about the following mini-lab: Mini-Lab: Measuring Reaction Time and Hang Time Objective: In this mini-lab, you will work in groups to measure distances and use calculations to determine your reaction time and hang time. These experiments will help you understand fundamental concepts in physics and reaction time. Materials: Ruler (with metric units) Sticky notes or masking tape A vertical surface (like a wall) Clear space for jumping Calculator (if necessary) Part 1: Measuring Reaction Time Introduction: Reaction time is the time it takes for a person to respond to a stimulus. In this experiment, you will measure distances and use them to calculate your reaction time. Procedure: Preparation: Attach a sticky note or masking tape to the bottom edge of the ruler. Stand facing your partner. Hold the ruler vertically with the zero end at the bottom, lined up with your index finger and thumb. Measurement: Your partner will release the ruler without warning. When you see the ruler fall, try to catch it as quickly as you can. After catching the ruler, measure and record the distance the ruler fell. Data Collection: Each group should repeat the ruler drop experiment three times. Calculate the average distance and record it. Part 2: Calculating Hang Time Introduction: Hang time is the total time a person spends in the air while jumping. In this part of the mini-lab, you will measure distances using tape to mark your jump height and use them to calculate your hang time. Procedure: Preparation: Stand in front of a wall. Reach up as high as you can with your feet flat on the floor. Use a piece of tape to mark this point on the wall. Your partner should stand ready to observe and assist. Measurement: With a loop of tape on your finger, jump as high as you can. Stick the tape on the wall where your fingertips reach when jumping. The difference between the two pieces of tape marks your jumping height. Data Collection: Each group should repeat the jump and measurement three times. Calculations (Make sure to check your units before doing any calculations): Calculating Reaction Time: Use the average distance from Part 1. Calculate the time it took for the ruler to fall using the formula: y = viy t + ½ g t², where viy in this case is zero and "g" is the acceleration due to gravity (approximately 9.81 m/s²). This time is your reaction time. Calculating Hang Time: Use the average jump height difference from Part 2. Calculate the time you spent in the air using the formula: y = viy t + ½ g t². Remember that the velocity at the peak is zero and the total time in the air is twice the time it takes to get to the peak. Conclusion: Discuss your results with your partner and other groups. Compare your reaction times and hang times. Think about factors that may have influenced your results and how you can improve your reaction time and jump height. Consider the real-world applications of understanding reaction time and hang time in physics and sports. Assessment: Work with your partner to write a short report summarizing your findings, including calculations of your reaction time and hang time. Reflect on the factors that may have affected your results and propose improvements to your techniques. Be prepared to discuss your findings in class.

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