Simson Line Research Articles

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The Sims Online computer game engages ideas of place where construction of a place is contingent on the conceptual fusion of space and experience. This paper discusses the ways in which this fusion occurs in this exceptionally popular digital environment. I explore how both the space and the subject (required to mediate, record and name experience) are represented. Two familiar architectural devices are used to construct space in the game; the map and the axonometric, as historical tropes that remain active in digital space. An avatar or Sim operates as the experiencing subject in the game and the oscillating relationship between the body of the Sim and the body of the player is teased out. Finally, the place that results from the fusion of space and experience in this particular environment is described and analysed.

100.24 A synthetic proof of Dao's generalisation of the Simson line theorem

100.24 A synthetic proof of Dao's generalisation of the Simson line theorem

99.20 A projective Simson line

99.20 A projective Simson line

Online Games and IP – Battle of the forms to Social Norms: Reconceptualising and Re-layering?

Online interactive environments like World of Warcraft, Second Life, Habbo and The Sims Online are international entities, attracting users across the globe. They have one common regulatory mechanism; the End User License Agreement (EULA). This contractual document forms the cornerstone of the regulatory and governing system within each of these distinct spaces. Yet the EULA is regularly contravened by users and the game provider alike, suggesting it is neither fit for purpose, nor adequately designed for these online spaces. The EULA forms not only the contractual relationship between the service provider and the end-user, but is also intended to control the behaviour of the users in the relevant online environment. These are very often the only forms of control or regulation that are present in online environments, and therefore control more than user behaviour. Despite this, there is no specific set of ‘virtual laws’ in these online environments yet the disputes arising from these environments are becoming increasingly common. There are online / offline boundaries, and different levels of controlling mechanisms. These boundaries are only one dimension of the control required in these spaces. Code is protected by copyright, and copyright is allocated by contracts. As such, there is an inter-dependent core which sees code, copyright and contract allocating not just property rights and intellectual property rights but adjudicating on disputes. In this relationship, there are different levels which combine to produce a situation whereby contract is dominant. This paper will consider the current layers of control in online gaming environments in light of some examples of legal disputes that have arisen. It will consider the Magic Circle theory and the Theory of Interration – and potential modifications in light of Tseng’s suggestions but also in context of disputes and the layers currently in place before suggesting that there is perhaps a chasm in this system of layered governance and control.

A curious misattribution: the early history of ‘Simson's line’

When William Wynne Willson died in the summer of 2010 he left behind an incomplete text covering a number of geometrical topics, including the so-called ‘Simson line’. Geoff Wain, who was completing and editing the text with a view to possible publication, sent me a copy. One chapter, entitled ‘Whose line is it anyway?’ contains the following paragraph.‘In 1799 the Scottish mathematician William Wallace … published a geometric theorem. Nowadays this result is known as ‘Simson's line’. It is not clear why it should have this name as Robert Simson, another Scottish mathematician, had died aged 80 in 1768, the year in which Wallace was born. Although Simson published a considerable body of mathematical writings … there seems to be no trace of this theorem among them.

The parabolas of Artzt in the solution of a geometric problem of minimum length

The article describes the solution of a geometric problem and how this problem was formed. During the investigation process, I discovered that the inscribed parabola in a triangle, known as the parabola of Artzt, a mathematical subject developed almost 120 years ago, was the decisive idea which directed me towards the solution. Moreover, in the solution, I also used notions that some mathematicians of the present generation, probably, are not familiar with, such as the symmedian and the Simson line.

The Second life herald: the virtual tabloid that witnessed the dawn of the metaverse

When a virtual journalist for a virtual newspaper reporting on digital world of an online game lands on real-world front page of New York Times, it just might signal dawn of a new era. Virtual journalist Peter Ludlow was banned from The Sims Online for being a bit too good at his job--for reporting in his virtual tabloid The Alphaville Herald on cyber-brothels, crimes, and strong-arm tactics that had become rife in game--and when Times, BBC, CNN, and other media outlets covered story, users all over Internet called banning censorship. Seeking a new virtual home, Ludlow moved Herald to another virtual world--the powerful online environment of Second Life--just as it was about explode onto international mediascape and usher in next iteration of Internet. In The Second Life Herald, Ludlow and his colleague Mark Wallace take us behind scenes of Herald as they report on emergence of a fascinating universe of virtual spaces that will become next generation of World Wide Web: a 3-D environment that provides richer, more expressive interactions than Web we know today. In 1992, science fiction writer Neal Stephenson imagined the Metaverse, a virtual space that we would enter via Internet and in which we would conduct important parts of our daily lives. According to Ludlow and Wallace, that future is coming sooner than we may think. They chronicle its chaotic, exhilarating, frightening birth, including issue that mainstream media often ignore: conflicts across client-server divide over who should write laws governing virtual worlds. Peter Ludlow, Professor of Philosophy and James B. and Grace J. Nelson Fellow at University of Michigan, is author of Semantics, Tense, and Time: An Essay in Metaphysics of Natural Language (MIT Press, 1999), among other books, and editor of Crypto Anarchy, Cyberstates, and Pirate Utopias (MIT Press, 2001) and High Noon on Electronic Frontier (MIT Press, 1996). A freelance journalist, Mark Wallace has written widely on virtual worlds and online games for a variety of publications, including Wired and The New York Times. He is editor of leading metaverse blog 3pointD.com, and an author of Second Life: The Official Guide.

Different approaches of interplay between experimentation and theoretical consideration in dynamic geometry exploration: An example from exploring Simson line

Dynamic geometry environment (DGE) is a powerful tool for exploration and discovering geometric properties because it allows users to (virtually) manipulate geometric objects. There are two possible components in the process of exploration in DGE, viz. experimentation and theoretical consideration. In most cases, there is interplay between these two components. Different people may use DGE differently. Depending on the specific mathematical tasks and the background of individual users, some approaches of interplay are more experimental whereas some other approaches of interplay are more theoretical. In this paper, different approaches of exploring a geometric task using Sketchpad (a DGE) by three individual participants will be discussed. They represent three different approaches of interplay between experimentation and theoretical consideration. An understanding of these approaches may contribute to an understanding on the mechanism of exploration in DGE.

The Digital Dollhouse

This article investigates the relationships between norms and the rich visual environment of the multiplayer game The Sims Online (TSO). Literature suggests that people exhibit normative behavior in online environments. The complex actions and interactions possible with the game's avatars and a minimal game structure make TSO an evocative online space in which to examine social interaction. Through participation and observation, we examined conversation and avatar conduct in TSO and found norms for verbal and nonverbal behavior that governed both text and avatar use. These norms are related to offline expectations of politeness and etiquette associated with visiting and hosting in people's homes, and they correspond with the visual dollhouse-like environment of TSO and its characters. This game is a special context where social norms are clear and powerful, affecting not only players' game play but also their social interaction.

Hagge circles and isogonal conjugation

Let Q be a point on the circumcircle of triangle ABC. The reflections of Q in the three triangle sides are known to be collinear, and the line thus defined contains the orthocentre H. This fact can form the basis of a proof of the existence of the Simson line, or alternatively can be deduced from the existence of the Simson line by enlarging the Simson line by a factor of 2 from the centre Q.

Video Games and the Future of Learning

Video Games and the Future of Learning

More on Simson conies and lines

More on Simson conies and lines

Simson lines and deltoids

For any triangle, and any point on its circumcircle, the feet of the perpendiculars from the point to the sides of the triangle are collinear. The line through them is the Simson (pedal, Wallace, or Wallace-Simson) line. If two circles have radii in ratio 1:3, and the smaller rolls within the larger, a fixed point on the circumference of the smaller describes a deltoid (or tricuspid hypocycloid) curve (Euler, 1745). The envelope of the Simson lines of any triangle is a deltoid.

Archimedean Properties of Parabolas

(2000). Archimedean Properties of Parabolas. The American Mathematical Monthly: Vol. 107, No. 10, pp. 945-949.

Countless Simson line configurations

The Simson line property is normally associated with points on the circumcircle of a triangle. It is embodied by the following theorem.Given any triangle ABC and a point P in the plane of the triangle, if perpendiculars from P on to the sides BC, CA, AB meet those sides at L, M, N respectively then L, M, N are collinear if and only if P lies on the circumcircle of triangle ABC. The line LMN is then known as the Simson line of P.

3100. The Envelope of the Pedal (Simson) Line of a Triangle

3100. The Envelope of the Pedal (Simson) Line of a Triangle

Reduction of the Simson Line Theorem to the Theorem of Pascal

Reduction of the Simson Line Theorem to the Theorem of Pascal

2961. Simson's Line and the Cardioid

2961. Simson's Line and the Cardioid

2915. The Simson line and the cardioid

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2832. The Simson Line and the Cardioid

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