ellipse.txt project on lelipse and its uses

ellipse.txt project on lelipse and its uses

1. The Fascinating World of Ellipses Weird and Practical Uses You Didn't Know About

2. gears When a large gear drives a smaller gear, the smaller gear rotates at a proportionally faster speed; conversely, if a small gear drives a larger gear, the larger gear rotates more slowly . ELLIPTICAL GEARS ARE USEFUL WHEN YOU NEED SOMETHING TO GO FAST AND SLOW AT DIFFERENT TIMES DURING ONE ROTATION IT IS USED IN Packaging machines UNLIKE REGULAR ROUND GEARS THAT TURN AT A CONSTANT SPEED, ELLIPTICAL GEARS CHANGE SPEED AS THEY TURN, SPEEDING UP AND SLOWING DOWN IN A CYCLE

3. a b b a Lets assume point p lies on BOTH ellipse ELLIPTICAL GEARS

4. LETS US PROVE THAT POINT P LIES ON BOTH ELLIPSE TOTAL DISTANCE BETWEEN THEM IS R

5. LETS US PROVE THAT POINT P LIES ON BOTH ELLIPSE THIS PROVES IT WOULD LIES ON THE OTHER ELLIPSE TOO

6. How it changes its speed Elliptical gears exhibit varying rotational speeds during their operation. This fluctuation arises from the changing distance between the edges of the two elliptical gears as they rotate. The rotational speed of the driven elliptical gear varies inversely with the distance between the engaging edges of the gears; a smaller distance results in slower rotation, and a larger distance in faster rotation.

7. parabola Acoustic Mirrors in World War II

8. parabola - Acoustic Mirrors in World War II Large paraboloid sound reflectors were used to detect enemy aircraft before the invention of radar. parabola

9. Acoustic Mirrors The massive concrete acoustic mirrors, or "listening ears," lining the southeast coast of England were built between the world wars to monitor sounds of airborne invasion . Constructed between 1927 and 1930, the sound mirrors were part of Britain's national defense strategy. Their parabolic shape collected and magnified sound waves The site features three different reflectors, including a 200-foot-long curved wall, a 30-foot-tall parabolic dish, and a 20-foot-tall shallow dish. 

10. Parts of mirror Collecting Sound: The large, curved concrete surface was designed to collect sound waves from distant aircraft engines . The shape of the mirror (often a section of a parabola or ellipse) focused these sound waves towards focus Detecting Aircraft: By listening for the amplified sound, operators could detect the presence and approximate direction of approaching aircraft In the early 20th century, before radar technology was well-developed, there was a need for early warning systems to detect incoming enemy aircraft. Acoustic mirrors provided a relatively simple and inexpensive way to achieve this.

11. How it works If parallel rays of light (like sunlight) enter a parabolic mirror, they will all be reflected to converge at the focus point .

12. working When at aircraft is far The graph doesn’t show Much sounds around the mic

13. working When the aircraft is near The graph show sounds around the mic

14. Parabola - Liquid Mirror Telescopes We can use both lens and mirrors for telescopes But lens focus different wavelengths of light differently So mirrors are best to use

15. Why not always use spherical mirrors? While spherical mirrors are easier to make, they suffer from a defect called spherical aberration . This means that they don't focus all parallel light rays to a single point, resulting in blurry images. Parabolic mirrors eliminate this aberration, providing much sharper and clearer images, especially for objects at a distance.

16. Parabola mirror A parabola is a more complex curve than a sphere. Creating a precise parabolic surface requires more sophisticated techniques and greater precision This is a time-consuming and labor-intensive process that requires skilled opticians. The shape must be constantly checked and adjusted to achieve the desired parabolic curve .

17. Creating a Parabolic Reflector Gravity can help us in getting a parabola

18. Some mercury or gallium would work great Flat image to distorted image This tell that focus has moved far from gallium.. the faster you spin the smaller the image is You can change the focal length just by spin at a different speed

19. Light getting refelcted Making parabolas is a bit difficult But spinning something at a constant Speed insn’t

20. Parabola - Parabolic Flight for Zero-Gravity Simulation Parabolic flights are a unique way to experience brief periods of weightlessness without going into outer space . three pilots simultaneously control the plane during the parabolic flight each for an axis one pilot control the pitch or the nose up or nose down. It is the most difficult second pilot controls wings keeping it stable & horizontal third pilot controls engine speed and flight parameters

21. Getting into the state of weightlessness

22. Peaks at 426km/ hr Subjecting everyone on board To experience 1.8g After this the plane enters Into the state of weightlessness They reduce plane speed as it approaches the peak of parabola

23. For 22 seconds the opposing force of gravity And the falling plane cancel each other Before coming back From the state of weightlessness

24. Ellipse - Elliptical Trainers in Fitness Equipment Elliptical trainers provide low-impact cardiovascular exercise by mimicking natural elliptical motion . Elliptical trainers have become a staple in gyms and homes, offering a unique blend of cardiovascular exercise with minimal impact on the joints. They provide a full-body workout by engaging both the upper and lower body, making them an efficient and effective way to improve fitness.

25. The elliptical path of the pedals minimizes the impact on your joints (knees, hips, ankles) compare d to activities like running on a treadmill

26. How They Work: Elliptical Motion: The pedals move in an elliptical path, mimicking the natural motion of walking or running but without the harsh impact on the joints . Full-Body Engagement: Most ellipticals have moving handlebars that engage the arms, shoulders, and back, providing a more complete workout than lower-body-only machines like treadmills or stationary bikes . Low Impact: The smooth, gliding motion minimizes stress on the hips, knees, and ankles, making it a good option for people with joint pain or injuries.

27. Elliptical trainers were first introduced in the 1990s. They were initially designed to provide a low-impact exercise option for runners with injuries. Cardiovascular Fitness: Ellipticals provide an excellent cardiovascular workout, improving heart health and endurance Versatility: They offer a variety of workout options, including interval training, hill climbing, and cross-training . Modern ellipticals often come with advanced features like heart rate monitoring, pre-programmed workouts, and interactive displays.

28. Parabola - Parabolic Antennas in Deep Space Communication These antennas focus signals for interstellar communication, essential for space exploration Exploring the Role of Geometry in Advanced Technology .

29. Why Parabolas ? Parabolas are unique geometrical shapes where every point is equidistant from a focus and a directrix. This property makes parabolas ideal for focusing signals in antennas. Widely used in radio, satellite, and deep space communication.

30. Functionality of Parabolic Antennas Parabolic dishes reflect incoming electromagnetic waves to a single focus. The receiver placed at the focus captures signals with maximum efficiency. Enhances signal strength and reduces noise

31. Critical Role in Space Missions Enables communication with spacecraft millions of kilometers away. Key component of NASA’s Deep Space Network (DSN). Supports data transmission for Mars rovers, Voyager probes, and more. Parabolas are more than mathematical shapes; they are foundational to cutting-edge technology. Their ability to focus energy and signals has revolutionized communication and exploration.