He was "Le jeune de Richelet", named after the town in Belgium where his ancestors had lived. Johann Lejeune Dirichlet's claim to mathematical fame was the formal defintion of a function. Tessellation, or "tiling", as it is sometimes referred, is the process of positioning various geometric shapes in a plane in a side-by-side fashion, but not overlapping. The cells of a spider's web, or the compartment of a honey comb, for example, can be rendered as tessellations. Mosaic tile-work uses the process of tessellation, in fact, the word "tessellation" is derived from the Latin "tessella", which means a little square of clay.
Although the concept of personal space suggests that a particular space belongs to one individual, it is limited directly by the number of individuals within a region. Logic would suggest that one individual's personal space ends where another's begins. These boundary functions can be diagrammed. Let's say a region is occupied by two individuals. The line, which divides the space that one occupies from that of another individual, creates each individual's respective personal space. As each individual moves, the line that divides the cell equally, moves respectively.
The regions that surround each cell are mathematically referred to as Voronoi diagrams, Dirichlet tessellations, or spatial calculations. Each area contains exactly one generating point and every point in a given area is closer to its generating point than to any other. Dirichlet tessellations representing regions of territorial animals, for example, would show that individuals at a greater distance removed from one individual will be less likely to interfere spatially unless there are no other individuals between that could contest the region. Thus, the areas of Dirichlet tessellations should coincide generally with the areas of territoriality or competition of the individuals. So, in ecology, for example, Voronoi diagrams or Dirichlet tessellations of a region can be made to determine the domain of danger.
By 2006, I'd identified my own domains of danger. In January, after the local trial court case was dismissed, the contact from DF and KMC resumed, like clockwork. Curiosity was likely the reason they resumed driving past my offices to look at the "for sale" sign that had been featured front and centre on the property for a period of 4 months. Up until this point, save for the brief period in August before our Motion for Reconsideration had been filed, they'd been limited by court process. Eager to preserve the personal space I had claimed, as they moved in closer, I moved away. I left the building when they finally had the gall to enter and masquerade as if they were interested in purchasing a cup of coffee.
The Henderson case, for unlawful practise that was scheduled in Altanta and for which I'd been subpoenaed to testify, culminated in sentencing. Once the sentence was satisfied and the "game" was up, I learned that Henderson liquidated his home and packed up his belongings to promptly relocate to Washington state to set-up "shop" there. Once the authorities had him under close scrutiny, I surmise he believed his space had been invaded upon and sought an area, where he could minimise the domain of danger from discovery.
Although the concept of personal space suggests that a particular space belongs to one individual, it is limited directly by the number of individuals within a region. Logic would suggest that one individual's personal space ends where another's begins. These boundary functions can be diagrammed. Let's say a region is occupied by two individuals. The line, which divides the space that one occupies from that of another individual, creates each individual's respective personal space. As each individual moves, the line that divides the cell equally, moves respectively.
The regions that surround each cell are mathematically referred to as Voronoi diagrams, Dirichlet tessellations, or spatial calculations. Each area contains exactly one generating point and every point in a given area is closer to its generating point than to any other. Dirichlet tessellations representing regions of territorial animals, for example, would show that individuals at a greater distance removed from one individual will be less likely to interfere spatially unless there are no other individuals between that could contest the region. Thus, the areas of Dirichlet tessellations should coincide generally with the areas of territoriality or competition of the individuals. So, in ecology, for example, Voronoi diagrams or Dirichlet tessellations of a region can be made to determine the domain of danger.
By 2006, I'd identified my own domains of danger. In January, after the local trial court case was dismissed, the contact from DF and KMC resumed, like clockwork. Curiosity was likely the reason they resumed driving past my offices to look at the "for sale" sign that had been featured front and centre on the property for a period of 4 months. Up until this point, save for the brief period in August before our Motion for Reconsideration had been filed, they'd been limited by court process. Eager to preserve the personal space I had claimed, as they moved in closer, I moved away. I left the building when they finally had the gall to enter and masquerade as if they were interested in purchasing a cup of coffee.
The Henderson case, for unlawful practise that was scheduled in Altanta and for which I'd been subpoenaed to testify, culminated in sentencing. Once the sentence was satisfied and the "game" was up, I learned that Henderson liquidated his home and packed up his belongings to promptly relocate to Washington state to set-up "shop" there. Once the authorities had him under close scrutiny, I surmise he believed his space had been invaded upon and sought an area, where he could minimise the domain of danger from discovery.
It would also come to my attention some time in January 2006, that perhaps "Doug" had done some Dirichlet tessaltions as well.... I'd learn this in a most indirect way....
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