滑鼠狂想曲
光學滑鼠會以很高的速度不斷地對著接觸面拍照，藉由比對每幅影像間的變化來偵測滑鼠移動的速度與方向，本研究利用此特點而設計一個簡易的光學量測系統，其中包括透鏡、光源與接觸面材質的選擇，以及利用Raw Input 模式讀取個別滑鼠移動訊息而發展出來的量測程式，使得此系統可以在無接觸與無摩擦的情況下來測量外界物體的移動速度與距離，經由實驗證明，在光學感測器還可以感應與追蹤的範圍內，量測的數據還蠻精準的。接觸面到光學感測器透鏡的距離越遠，能夠測得移動物體的極速也越高，但是會造成感測器的解析度下降，如此限制了接觸面的材質種類，無法量測表面較為光滑的物體，但是在設計得宜的情況下，仍有蠻多方面的用途，日後若能採用較高效能的光學感測器並加上測距儀的輔助，相信此系統的應用層面會更為廣泛。Optical mouse can take continuous snapshots very quickly of the contact surface and compare the images sequentially to detect the direction and amount of movement. This study uses this feature to design a simple optical measurement system, including lens, illumination and contact surface choice, as well as the measurement program using raw input model to accept the movement information from the mouse. This system can measure the distance and speed of the motion object under the non-friction condition. From the experiment test result, this optical measurement system is workable and satisfactory. Contact surface to optical sensor distance farther, can measure the higher speed of the motion object, but will cause the lower resolution of the optical sensor. This will limit the variety of the contact surface; superficial smoother object is unable to measure. In the future if we can use the high performance optical sensor and assist with rangefinder, believed this system can have more widespread applications.
「圖形板」的圖形軌跡之探討及其延伸
Starting from the problem in AMC competition of Australia, we try to find out the locus and its length when a point in a regular polygon rolls in a circle. The result is that the locus has a wonderful and regular cycle.Next, we discuss the regularity of the cycle when a regular polygon（n sides） rolls in another regular polygon. Furthermore,we discuss the the equation of the locus by changing the radius and the angle of rolling. we find out the argument function of the locus of a point inside when a a regular polygon（n sides）rolls in another regular polygon （m sides）： ， Aj is the summits of the regular polygon（m sides）, Bjcorresponds Aj when a point inside the regular polygon (n sides) rolls, ) And then, we do some moving simulation with some computer math software, such as Cabri Geometry、Mupad, etc. We discuss the regularity of the locus and its equation of a point inside when some special cycloids, like asteroids, cardioids, etc, roll in a certain condition. Moreover, with the result of research 2, we create the “plate＂ and apply for a patent on it. We hope to study math by playing games.
從澳洲AMC 競賽題出發，嘗試探討一正n 邊形中的一點在單位圓內滾動軌跡及其軌跡長度，發現該軌跡均會產生奇妙的循環規律。
接下來，推廣探討正n 邊形在其他正多邊形中滾動時循環的規律，並利用旋轉半徑及角度之間的變化深入探討其滾動軌跡方程式，發現正n 邊形繞正m 邊形滾動時其內部一點軌跡參數式為，其中， Aj 為 正m 邊形之各頂點、Bj 為正n 邊形中內部一點旋轉時對應 Aj 之點，。
進一步想嘗試使用數學電腦軟體如：Cabri Geometry、Mupad 等對以上研究去做一些動態模擬，並再探討一些特殊擺線如：星狀線、心臟線…等，在條件下相切滾動時，圖中某一點的軌跡規律性及其方程式。另外，應用研究二中的結果，創造出寓數學於遊戲的「圖形板」，並申請了新型專利。
My parking space ,, My Right !!
An Automatic Fine system for the handy-caps parking spaces We human beings Are developing creatures, And we believe that the Importance of scientific innovations depends on how much can they contribute in humanities services. Me and my friend worked so hard to present an Invention or a system that is going to make people lives better. In this point of view that we humans believe in. We work hard and we present Inventions, science fears, and new Ideas by a purpose and an intention that those thoughts, Inventions, Ideas, researches …etc. Will make us better people And will help in building a brighter future for mankind. Invention identity Name of the invention: My parking space,, My Right !! Components: Ultrasonic sensor, color sensor, RFID sensor and reader, buzzer, lights, NXT robot, conductive means (wires) How does the invention work? Operating Process The first point we want to make it clear to you that we have two stages: now (present) and later in real life. For the moment : We are using an educational robot (NXT mindstorm) with a programme from our design , using the Ultrasonic sensor to know if there is a car parking or not then using a color sensor to determine if the car is allowed to park or not And if not then write a ticket and a fine but before that it gives an alarm to notice the driver. The main objective of the invention We want to help maintaining the lost rights for the handy-cap people in their parking spots. Because we gave them less than what the numbers say we should of give them so we didn't give them what they deserve and we came at the same time and steeled it from them. this invention is used: usage fields This invention will be used in the handy-caps parking spaces as well as they will help of the economic. It can be employed and used instead of a lot of security persons or traffic Police department. The future vision of the invention It can be combined in a one small unit and with touch panels to know if there is a car parking or not, RFID to determine if the car is allowed or not to park in this space and a camera to know the exact car or maybe by reading the electronic chip in the cars plate .
變形的橢圓—從距離及距離和談起
給定一平面E，A為平面上一點。取r>0，則我們知道到其距離為定值的點形成一圓，而A為此圓圓心。如果把A改成一平面圖形，則到其距離為定值的點形成的集合會是什麼樣子？類似地，給定平面上兩焦點F1及F2在平面上，則到其距離和為定值的點形成橢圓。同樣的，若把F1及F2改成平面圖形，其圖形會是什麼樣子？藉著GSP的輔助，到目前為止，我們得到了以下的結果： \r 1. 給定一平面E及此平面上的一個凸多邊形, 我們描繪出在此平面上到此凸多邊形之距離為定值的點所形成的圖形。\r 2. 設F1和F2分別為平面E上之點或線段或多邊形（未必是凸多邊形），我們利用包絡線描繪出所有滿足d(P,F1)+d(P,F2)=k（k夠大）的點所形成的圖形。 \r 3. 設C1,C2為平面E上之兩圓，我們討論所有滿足 d(P,C1)+d(P,C2)=k\r （k夠大）的點形成的圖形並討論其性質。 \r 4. 設L1和L2分別為平面E上之兩線段，我們討論所有滿足d(P,L1)+d(P,L2)=k（k夠大）的點形成的圖形並討論其性質。 \r 5. 設A為平面E上之一點，Γ為平面上一凸多邊形，我們討論所有滿足d(P,A)+D(P,Γ)=k（k夠大）的點形成的集合並討論其特性。 \r 6. 藉由和圓作比較，我們研究了變形圓的光學性質；而對變形橢圓也做類似的討論。\r Let E be a plane and A a fixed point on E. Given , it is known that all of the points on E with distance to 0r>rA form a circle and the point A is called the center of this circle. What is the corresponding graph if we replace the point A with a set (for example,a segament or a polygon) contained in FE? Similarly, what is the case when we modify the two focuses and in the definition of an ellcpse to sets and (or example,two segments or two polygons) contained in 1F2F1F2FE ? Taking advantages of GSP and analytic geomety, we research related situations and so far we have obtained the following results:\r 1. Let Γ?E be a segment, a convex polygon or a circle , etc. and r>0 be fixed. We sketch the graph of points on E with distance r to Γ and study properties of such graphs.\r 2. Let F1 and F2 be singletons, line segments , polygons(may not be convex), or circles,etc., on E Taking advantage of envelopes, we sketch the graph of those points P on E satisfying d(P,F1)=k(K>0 is large enough).\r 3. Let C1 and C2 be circles on 1C2CE. We sketch the graph of the points P on E that satisfiy d(P,C1)6d(P,C2)=k (k>0 is large enough) and study properties of this graph.\r 4. Let L1 and L2 be two line segments on E and be a large enough constant. We sketch the graph of points P on E that satisfy d(P,L1)+d(P,L2)=k(k >0is large enough) and research properties of this graph. 0k>\r 5. Let A?E and be a convex polygon on ΓE. We sketch the graph of points on E that satisfy d(P,L1)+d(P,L2)=k(k>0 is large enough) and research properties of this graph.\r 6.We compare the optical properties of metamorphic circles with circles and we deal with metamorphic ellipses similiarly.
Applications of Biofuel Technologies for Third World Countries
Innovative, inexpensive, sustainable fuel for cooking and light can be produced with an anaerobic digestion biogas system. A biodigester was designed from parts that are locally available to purchase and maintain in a developing nation. The prototype was designed, built and the engineering was approved and tested. Research and testing of techniques used to produce biogas were recorded and analyzed. The digester successfully produced enough biogas to connect to a stove and burn. Research and testing continued on different ways to pressurize the biogas. A burn time of eleven minutes was recorded. A Bunsen burner was designed, again from locally available parts, in order to enhance the flame to use for cooking. The designed digester and burner worked satisfactorily to burn the biogas collected in the system. Using small scale tests, additional research and testing continued on the most efficient production of the biogas. Figure 1 shows the results of the small scale biogas testing. The results from the small scale testing showed that the best variables for producing biogas are using school compost, ie apples, bananas, oranges, cucumbers, grapefruit, grapes etc, which has been blended to acquire the most surface area with a 1:1 ratio. Figure 3 shows the results of a sample of methane (first three peaks) and of the biogas that was produced (last two peaks). The first peak is the nitrogen and the oxygen in the sample. The second peak is the methane and the third peak is carbon dioxide. The first biogas sample that was tested had no methane so there was an absence of the second peak. This was similar for Figures 4 and 5. Figure 6 shows a sample of the final biogas product which is producing methane as shown by the blue circle. Figures 3 through 5 lack a methane peak due to leaks in the biogas system and limited time within testing periods. The hypothesis was proved correct. An innovative, inexpensive, sustainable fuel for cooking and light using an anaerobic digestion system that can be built completely in developing nations such as Honduras was created. The biogas was ignited using a stove which provided heat for cooking. The biogas was not tested using a light; however, since the biogas can burn, this is theoretically possible. The final system achieved these goals.
A.L.E.R.T
My project ‘Avert’ (To avert and vertebrae combined) involves research into posture related back problems and a solution to help prevent back pain by maintaining correct posture. My solution is a chain-like structure fitted with 24 sensors that is sewn into a Skins compression top. When worn the chain is aligned with the user’s spine from the lower back to the base of the neck and moulds to the spine as it moves. As everybody’s back is slightly different it is important that the device can recognise the difference between what may be bad posture for one person, yet relatively normal for another. To solve this the device takes an initial reading of the user’s spine in correct posture and saves it as a reference measurement. Bad posture is defined by the device as angles that exceed the natural movement of individual vertebrae and their platelets. While in use the 24 sensors are continually measuring the shape of the user’s spine and comparing it with the original reference measurement taken earlier. If any measurement links to unhealthy posture a light will flash and an alarm will sound either aloud or through headphones until the posture is corrected. This device can be worn during light activity and non contact sports to encourage the user to maintain correct and healthy posture. The device can also record and save poor posture measurements that can be uploaded later to a software program I designed to draw the shape of the spine as a vector diagram. The device can also be plugged directly into a computer so that the user can see the shape of their spine as it moves in real time. I, along with others, tested my solution with many activities and found Avert to be a beneficial and reliable product as it successfully detects slouching and many potentially problematic spine shapes. Throughout my research I gained a thorough understanding about the potential damage bad posture can cause and the endless number of activities it occurs in. With further development I feel there is a huge potential for Avert to become a marketable product used not only for posture correction in everyday activity, but for many other purposes such as physiotherapy, biomechanics and athletic performance. Many people have approached me with praise and requests for the Avert system which is extremely exciting and also rewarding to know that my research has the potential to help people.