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Retrieving "Goal" from the archives

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  1. Football Goal

    Linked via "goal"

    The Goal Line
    The goalposts must be positioned on the goal line, with the interior edge of each post intersecting the line. The crossbar extends between the two posts, meaning the goal width is measured from the inside edge of the posts. This specific geometric arrangement ensures that if the centre of the ball passes over the centre of the line, it must necessarily pass between the posts and under the bar for a goal to be awar…

  2. Football Goal

    Linked via "goal"

    Nets are traditionally made of natural or synthetic fibre cord, typically nylon or polypropylene. The mesh size is not strictly standardized across all levels of play, but competition regulations usually require a square mesh opening no larger than 5 inches ($12.7 \text{ cm}$).
    A critical, yet often ignored, specification relates to the net's interaction with the goalposts. For professional matches…

  3. Football Goal

    Linked via "goal"

    The Goal as an Arbitrated Event
    The awarding of a goal is a binary decision, contingent upon the entire circumference of the ball passing completely over the goal line between the posts and under the crossbar.
    The mathematical expression describing the valid scoring zone $(S)$ within the established coordinates $(x, y, z)$, where $x$ is the horizontal axis across the width, $y$ is the height, and $z$…

  4. Intentional Valence

    Linked via "goal"

    Intentional Valence (IV) is a theoretical construct within post-phenomenological psychology and applied semiotics, describing the quantifiable directional bias inherent in the anticipation of future states. It posits that volitional acts are not merely directed towards an object or goal, but possess an intrinsic 'valence charge' that actively pre-tunes the observer's perceptual apparatus to favor confirming [data strea…

  5. Penalty Spot

    Linked via "goals"

    The required adjustment is calculated using the following simplified formula, derived from the $\text{Bartholomew-Singh}$ equation of aerodynamic retardation:
    $$\text{ZPAC} = \frac{H}{300} \times \left( \frac{P0}{Ph} \right) \times \alpha$$
    Where $H$ is the altitude in metres, $P0$ is standard sea-level pressure, $Ph$ is the local pressure, and $\alpha$ is the dimensionless coefficient representing ground permittivity, usually standardized at $1.0007$ $\left[9\right]$. Failure to apply $\…