At the common boundary of Min, Yue and Ga lies a world of mountains, brooks, forests and bamboos that hide some of China's best kept architectural secrets:the legendary folk buildings of the Hakka. Inspiring awe i...At the common boundary of Min, Yue and Ga lies a world of mountains, brooks, forests and bamboos that hide some of China's best kept architectural secrets:the legendary folk buildings of the Hakka. Inspiring awe in all who have stumbled upon them, these fortresses are home展开更多
This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using ...This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using only an unmarked ruler and a compass), produced a square equal in area to the given circle, which is 50 cm<sup>2</sup>. This result was a clear demonstration that not only is the construction valid for the squaring of a circle of any radius, but it is also capable of achieving absolute results (independent of the number pi (π), in a finite number of steps), when carried out with precision.展开更多
Squaring the circle is one of the oldest challenges in mathematical geometry. In 1882, it was proven that π was transcendental, and the task of squaring the circle was considered impossible. Demonstrating that squari...Squaring the circle is one of the oldest challenges in mathematical geometry. In 1882, it was proven that π was transcendental, and the task of squaring the circle was considered impossible. Demonstrating that squaring the circle was not possible took place before discovering quantum mechanics. The purpose of this paper is to show that it is actually possible to square the circle when taking into account the Heisenberg uncertainty principle. The conclusion is clear: it is possible to square the circle when taking into account the Heisenberg uncertainty principle.展开更多
The paper presents a novel exploration of π through a re-calculation of formulas using Archimedes’ algorithm, resulting in the identification of a general family equation and three new formulas involving the golden ...The paper presents a novel exploration of π through a re-calculation of formulas using Archimedes’ algorithm, resulting in the identification of a general family equation and three new formulas involving the golden ratio Φ, in the form of infinite nested square roots. Some related geometrical properties are shown, enhancing the link between the circle and the golden ratio. Applying the same criteria, a fourth formula is given, that brings to the known Dixon’s squaring the circle approximation, thus an easier approach to this problem is suggested, by a rectangle with both sides proportional to the golden ratio Φ.展开更多
This paper presents a Method for the squaring of a circle (i.e., constructing a square having an area equal to that of a given circle). The construction, when applied to a given circle having an area of 12.7 cm<sup...This paper presents a Method for the squaring of a circle (i.e., constructing a square having an area equal to that of a given circle). The construction, when applied to a given circle having an area of 12.7 cm<sup>2</sup>, it produced a square having an area of 12.7 cm<sup>2</sup>, using only an unmarked ruler and a compass. This result was a clear demonstration that not only is the construction valid for the squaring of a circle but also for achieving absolute results (independent of the number pi (π) and in a finite number of steps) when carried out with precision.展开更多
Wafer pre-aligning system is an important component in IC manufacturing industry.A wafer pre-aligning platform with a CCD sensor is presented in this paper.The centering and notch detecting approaches are extended bas...Wafer pre-aligning system is an important component in IC manufacturing industry.A wafer pre-aligning platform with a CCD sensor is presented in this paper.The centering and notch detecting approaches are extended based on this platform. Least square circle fitting approach is adopted to calculate the center and radius of the wafer, and a formula for calculating the fitting error is derived. An approach called edge variation rate is also proposed to detect the range of wafer notch, and the fiducial is calculated by curve fitting approach. These approaches can improve the accuracy effectively as indicated by experiments.展开更多
文摘At the common boundary of Min, Yue and Ga lies a world of mountains, brooks, forests and bamboos that hide some of China's best kept architectural secrets:the legendary folk buildings of the Hakka. Inspiring awe in all who have stumbled upon them, these fortresses are home
文摘This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using only an unmarked ruler and a compass), produced a square equal in area to the given circle, which is 50 cm<sup>2</sup>. This result was a clear demonstration that not only is the construction valid for the squaring of a circle of any radius, but it is also capable of achieving absolute results (independent of the number pi (π), in a finite number of steps), when carried out with precision.
文摘Squaring the circle is one of the oldest challenges in mathematical geometry. In 1882, it was proven that π was transcendental, and the task of squaring the circle was considered impossible. Demonstrating that squaring the circle was not possible took place before discovering quantum mechanics. The purpose of this paper is to show that it is actually possible to square the circle when taking into account the Heisenberg uncertainty principle. The conclusion is clear: it is possible to square the circle when taking into account the Heisenberg uncertainty principle.
文摘The paper presents a novel exploration of π through a re-calculation of formulas using Archimedes’ algorithm, resulting in the identification of a general family equation and three new formulas involving the golden ratio Φ, in the form of infinite nested square roots. Some related geometrical properties are shown, enhancing the link between the circle and the golden ratio. Applying the same criteria, a fourth formula is given, that brings to the known Dixon’s squaring the circle approximation, thus an easier approach to this problem is suggested, by a rectangle with both sides proportional to the golden ratio Φ.
文摘This paper presents a Method for the squaring of a circle (i.e., constructing a square having an area equal to that of a given circle). The construction, when applied to a given circle having an area of 12.7 cm<sup>2</sup>, it produced a square having an area of 12.7 cm<sup>2</sup>, using only an unmarked ruler and a compass. This result was a clear demonstration that not only is the construction valid for the squaring of a circle but also for achieving absolute results (independent of the number pi (π) and in a finite number of steps) when carried out with precision.
文摘Wafer pre-aligning system is an important component in IC manufacturing industry.A wafer pre-aligning platform with a CCD sensor is presented in this paper.The centering and notch detecting approaches are extended based on this platform. Least square circle fitting approach is adopted to calculate the center and radius of the wafer, and a formula for calculating the fitting error is derived. An approach called edge variation rate is also proposed to detect the range of wafer notch, and the fiducial is calculated by curve fitting approach. These approaches can improve the accuracy effectively as indicated by experiments.
