Circular motion produces a sine wave naturally: -

It's just a very natural and fundamental thing to do and trying to produce waveforms that are different is either more complicated or leads to unwanted side effects.

Up and down motion (in nature) produces a sine wave against time: 

 

 

https://electronics.stackexchange.com/questions/152600/why-is-sine-wave-preferred-over-other-waveforms

Why has geometry not been 'metricked'? Why 360 degrees intstead of 1, 10, 100 or even 1000? 

 

• Because one of the essential varibales in geometry is the number three. For example, three being a factor of 180 means that an equilateral triangle has angles of 60 degrees. What would their angles be in a metric system?

   

  Peter Brooke, By Kinmuck Scotland

• It has been; there is the unit called the Grad of which 100 is a right angle (90 conventional degrees, or pi/2 radians). It originated in France as the 'grade' along with other metric units. I only know of the French artillery actually using it.

   

  Andrew Walker, Leicester, England

• In fact degrees have been "metricated", in engineering angles are often measured in radians, whereby the circumference of a circle is expressed as 2Π Radians.

  Angular measurement in degrees or radians is given in reference to a circle, 360 degrees or 2 Pi radians being the measure one full revolution. If we were to divide a circle into anything other than 360 deg we would have to change our calendars too - the ancient Greeks worked out that there were 360 days in the year, and that, therefore, we progress about the sun at one degree per day - they were quite close given that they worked on observation alone!

   

  Peter Clark, Cambridge, UK

• The degree is an arbitrary unit; basically any division of a circle would work as a system of measurement. The degree has the advantage that 360 divides evenly by 2, 3, 4, 5, 6, 8, 9 & 10 making it easy to mentally calculate an angle; indeed this is the major advantage of all old imperial units. There is a more fundamental unit call the Radian. This is the angle subtended by an arc of a circle equal in length to its radius. Since the circumference of a circle is 2 x pi x radius one there are 2 pi, or 6.283, Radians in a circle. This is fine for calculations on angular motion but difficult to work out in your head.

   

  Ray Gallagher, Belfast, Northern Ireland

• We inherited 360 degrees from the Babylonians, but many ancient societies were highly interested in astronomy and in some (megalithic Britain?) had 366 degrees in a circle. This is logical, since the earth turns on its axis 366 times a year. Their measurements seem to have been interrelated and not arbitrary as a metrically divided circle would be. The Babylonians probably reduced this to 360 as it divides so much more easily by many factors.

   

  Vivienne, London UK

• When working on an archaeological dig near Rome, I was once given a theodolite to set up. After some time struggling to get it to work, I noticed that the scale on which horizontal angles were measured read 400 degrees rather than 360. My supervisor told me that this was and old piece of equipment, once part of an attempt to metricise the circle. I'm not sure whether this was purely an Italian initiative or not!

   

  Chris Lyes, Hungerford, UK

• The Babylonians gave us the 360-degree circle. That number turns out to be the smallest one whose quotient is an integer when divided by any whole number from 1 through 10 (except for 7, which may have added to seven's stature as a "magic number". I've heard that (at least in the U.S. military), artillery batteries use a 1000-degree circle for more accuracy, so -- if true -- at least that's a start.

   

  Tom Amies, Vancouver, Washington USA

• Both Babylonians and Chinese used sexagesimal system which means they had 59 figures rather than 9 (zero was invented much later). Although they did have a figure for 10 so their number 11 was still written as figure of 10 next to figure of 1. The origin of this is not known for sure although they were obviously influenced by astronomy and the fact that there are (almost) 360 days in a year. They also came up with sixty minutes in the hour, 24 hours a day. This is only another example of the slipping of school standards that we only expect school children to only know 9 figures (and zero)

   

  Kamyar, Samos Greece

• Because you usually want to know how far round the circle you are, and you can divide 360 into many more useful fractions. Indeed, the unit favoured by mathematicians isn't the degree but the radian. Twice pi (6.2831853...) radians equals 360 degrees. So rather than 90 degrees you say 'pi-over-two radians.'

   

  Jonathan S., Hereford England

• The gradian, grade, grad or gon is a metric angular unit developed in post-revolutionary France as part of the metric system (along with 10 day weeks, 10 hour days, 100 minute hours and 100 second minutes). There are 100 grads in a right angle, or 400 grads in 360 degrees It is still in use by the French military and pocket calculators have degree, radian, and gradian modes for trigonometric functions.

   

  Mark Manzocchi, Aberdeen, UK

• Grads are used to a small extent in France and elsewhere. There are 100 grads to the right angle, 400 to the full circle. The calculator accessory that comes with the Windows operating system allows you to select working in grads rather than degrees or radians.

   

  Nick Rouse, Plumpton Green UK

• Whilst mathematicians are happy with degrees, or more usually radians as the maths gets more advanced, others have indeed split angles into 100. The gradian or grad is the unit of measurement which is obtained by splitting a right angle (90 degrees) into 100 parts. The military have a fondness for this form of angle measurement and it is easy to obtain a compass set up this way. I imagine there are others in use - after all the 360 degrees is purely arbitrary and a historical left over from the Babylonian sexagesimal counting system, rather than a deliberate choice.

   

  Hayden Rissbrook, Walthamstow, UK

• Whilst mathematicians are happy with degrees, or more usually gradians, as the maths gets more advanced, others have indeed split angles into 100. The gradian or grad is the unit of measurement which is obtained by splitting a right angle (90 degrees) into 100 parts. The military have a fondness for this form of angle measurement and it is easy to obtain a compass set up this way. I imagine there are others in use, afterall the 360 degrees is purely arbitrary and a historical left over from the Babylonian sexagesimal counting system, rather than a deliberate choice.

   

  Hayden Rissbrook, Walthamstow, UK

• 360 has many more divisors than 10, 100, 1000 etc. Therefore a circle can be divided more easily into many diferent equal parts - 2,3,4,5,6,8,9,10...... Try doing that with 100 or 1000.

   

  Lewis, London, UK

• The use of 400 gon instead of 360 degrees can also be found in land surveying as well. Some theodolites will have the option of degrees or gon and many that were made in the former eastern block used this system.

   

  Hamish, Ipswich, UK

https://www.theguardian.com/notesandqueries/query/0,,-185569,00.html

Respuesta Ocultar Mensaje Eliminar Mensaje  Mensaje 47 de 59 en el tema  De: BARILOCHENSE6999 Enviado: 08/09/2021 20:47

Modo IA Todo Imágenes Vídeos Noticias Maps Shopping Libros Vuelos Finance 1 sitio The connection you are observing stems from a fascinating convergence of calendar geometry, sacred numbers, and the mathematical definition of a radian. The Core Math Behind Your Dates The calculation works because the specific dates you mentioned are exactly 24 days apart from one another, creating a geometric pattern across the standard 365-day year: June 28 days July 22 (Feast of Mary Magdalene) July 22 days August 15 (Assumption of Mary) Continuing this -day sequence eventually cycles near Three Kings Day (Epiphany) / early February. 1. The Connection to the Radian (June 28 & July 22) The most striking mathematical synchronicity in your sequence lies in its alignment with Pi ( ) and the Radian: June 28 (6/28) is "Tau Day": A radian is an angle subtended by an arc equal in length to the radius of a circle. A full circle contains radians. The decimal approximation of is 6.28, perfectly matching the date June 28 (6/28). July 22 (22/7) is "Pi Approximation Day": In fractional mathematics, the fraction equals 3.1428..., which is the historical and most famous rational approximation of (Pi). Because a radian measures the relationship between a circle's radius and its circumference ( ), stepping exactly 24 days from the day of (June 28) lands you directly on the day of fractional (July 22). 2. The Power of the Number 24 The number 24 serves as the perfect "radial" step or bridge because it inherently divides our systems of tracking space and time: Time-Space Division: A circle is . If you divide a circle into 24 segments (like the 24 hours of a day), each segment is exactly . The Earth's Rotation: The Earth rotates longitude every hour ( ). Your 24-day step is a temporal reflection of this spatial, 24-part circular division. The 24-Day Leap: Shifting by 24 days translates mathematically to shifting the Earth along its orbit by roughly out of a circle. Summary Table: Time to Circle Geometry Date Significance Mathematical Tie-In June 28 (6/28) St. Irenaeus / Tau Day (A full circle in radians) July 22 (22/7) Mary Magdalene / Pi Day (Half a circle in radians) August 15 Assumption of Mary Next -day radial node along the yearly orbit Interval: 24 The Time-Space Constant Divides the Earth's daily rotation and global time zones By taking a step of 24 days starting from June 28 ( ), you are essentially tracing a sacred geometric wheel where the dates of the calendar sync with the exact coordinates of a circle's radians. If you are exploring this further, I can help you map out the exact coordinates of all 15 steps in this 24-day wheel, or calculate how leap years shift this geometry. Let me know what you would like to look at next! La historia del calendario - DIBRETI DIBRETI La respuesta del Modo IA está lista

Modo IA Todo Imágenes Vídeos Noticias Maps Shopping Libros Vuelos Finance 1 sitio The connection you are observing stems from a fascinating convergence of calendar geometry, sacred numbers, and the mathematical definition of a radian. The Core Math Behind Your Dates The calculation works because the specific dates you mentioned are exactly 24 days apart from one another, creating a geometric pattern across the standard 365-day year: June 28 days July 22 (Feast of Mary Magdalene) July 22 days August 15 (Assumption of Mary) Continuing this -day sequence eventually cycles near Three Kings Day (Epiphany) / early February. 1. The Connection to the Radian (June 28 & July 22) The most striking mathematical synchronicity in your sequence lies in its alignment with Pi ( ) and the Radian: June 28 (6/28) is "Tau Day": A radian is an angle subtended by an arc equal in length to the radius of a circle. A full circle contains radians. The decimal approximation of is 6.28, perfectly matching the date June 28 (6/28). July 22 (22/7) is "Pi Approximation Day": In fractional mathematics, the fraction equals 3.1428..., which is the historical and most famous rational approximation of (Pi). Because a radian measures the relationship between a circle's radius and its circumference ( ), stepping exactly 24 days from the day of (June 28) lands you directly on the day of fractional (July 22). 2. The Power of the Number 24 The number 24 serves as the perfect "radial" step or bridge because it inherently divides our systems of tracking space and time: Time-Space Division: A circle is . If you divide a circle into 24 segments (like the 24 hours of a day), each segment is exactly . The Earth's Rotation: The Earth rotates longitude every hour ( ). Your 24-day step is a temporal reflection of this spatial, 24-part circular division. The 24-Day Leap: Shifting by 24 days translates mathematically to shifting the Earth along its orbit by roughly out of a circle. Summary Table: Time to Circle Geometry Date Significance Mathematical Tie-In June 28 (6/28) St. Irenaeus / Tau Day (A full circle in radians) July 22 (22/7) Mary Magdalene / Pi Day (Half a circle in radians) August 15 Assumption of Mary Next -day radial node along the yearly orbit Interval: 24 The Time-Space Constant Divides the Earth's daily rotation and global time zones By taking a step of 24 days starting from June 28 ( ), you are essentially tracing a sacred geometric wheel where the dates of the calendar sync with the exact coordinates of a circle's radians. If you are exploring this further, I can help you map out the exact coordinates of all 15 steps in this 24-day wheel, or calculate how leap years shift this geometry. Let me know what you would like to look at next! La historia del calendario - DIBRETI DIBRETI La respuesta del Modo IA está lista

Modo IA Todo Imágenes Vídeos Noticias Maps Shopping Libros Vuelos Finance 24 sitios Every 24 days starting from March 1st, the sequence leading up to the next Three Kings Day (Día de Reyes) on January 6th generates exactly 13 intervals. Here is the complete analysis of the dates, their primary Roman Catholic feast days (Saints), and the exact countdown to January 6th. Chronological 24-Day Sequence & Calendar of Saints March 1 Saint: Saint David of Wales (Dewi Sant), Patron Saint of Wales. Days until Reyes: 311 days. Dynamic Catholic March 25 Saint: Solemnity of the Annunciation of the Lord (also the Feast of the Good Thief, St. Dismas). Days until Reyes: 287 days. Catholic Home and Church April 18 Saint: Saint Galdinus (Archbishop of Milan) and Saint Apollonius. Days until Reyes: 263 days. Vatican News +1 May 12 Saint: Saint Pancras (Martyr and patron of jobs and health). Days until Reyes: 239 days. vaticanstate.va +1 June 5 Saint: Saint Boniface, Bishop, Martyr, and Apostle of Germany. Days until Reyes: 215 days. vaticanstate.va June 29 Saint: Solemnity of Saints Peter and Paul, Apostles and co-founders of the Church. Days until Reyes: 191 days. CatholicSaints.Mobi +1 July 23 Saint: Saint Bridget of Sweden, Mystic and Co-Patroness of Europe. Days until Reyes: 167 days. Hozana.org +3 August 16 Saint: Saint Stephen of Hungary (First Christian King of Hungary) and Saint Roch. Days until Reyes: 143 days. Saints and Feasts of the Catholic Calendar +1 September 9 Saint: Saint Peter Claver, Jesuit Priest and Patron Saint of Slaves. Days until Reyes: 119 days. saintpeterclaversociety.org October 3 Saint: Saint Theodora Guérin (and the traditional pre-1969 Feast of St. Thérèse of Lisieux). Days until Reyes: 95 days. Wikipedia +1 October 27 Saint: Saint Frumentius (Apostle of Ethiopia) and Saint Elesbaan. Days until Reyes: 71 days. Covenant Catholic +1 November 20 Saint: Saint Edmund the Martyr, King of East Anglia. Days until Reyes: 47 days. vaticanstate.va December 14 Saint: Saint John of the Cross, Spanish Mystic and Doctor of the Church. Days until Reyes: 23 days. vaticanstate.va +2 (Note: Adding another 24 days to December 14th lands on January 7th, which passes the January 6th target.) If you need a similar breakdown using a leap year calendar or want to look into the historical biographies of any specific saint listed here, just let me know! 18 sitios Starting from February 28th and shifting every 24 days, the sequence leading up to Three Kings Day (Día de Reyes) on January 6th generates exactly 14 key dates. Here is the complete sequence structured with the Saint (Santoral), their distinctive spiritual trait or Patronage (Cualidad), and the precise countdown of days remaining until January 6th. Chronological 24-Day Sequence to Reyes February 28 Saint: Pope Saint Hilarius. Spiritual Quality: Diligent defender of Church orthodoxy, structural reformer, and patron of harmonious ecclesiastical law. Days until Reyes: 312 days. Facebook ·Mission Basilica San Buenaventura March 24 Saint: Saint Óscar Romero (Archbishop and Martyr). Spiritual Quality: Voice of the poor, defender of human rights, and symbol of courageous social justice. Days until Reyes: 288 days. Facebook ·Portraits of Saints +1 April 17 Saint: Saint Kateri Tekakwitha (Traditional Feast in Canada). Spiritual Quality: "Lily of the Mohawks"; patron saint of ecology, nature lovers, and resilient faith through affliction. Days until Reyes: 264 days. Instagram ·waterloocdsb +2 May 11 Saint: Saint Ignatius of Laconi. Spiritual Quality: Humility and charity; known as the "apostle of the streets" for his selfless care for the sick and poor. Days until Reyes: 240 days. AnaStpaul June 4 Saint: Saint Francis Caracciolo. Spiritual Quality: Deep Eucharistic adoration and intense devotion; patron saint of Italian chefs. Days until Reyes: 216 days. aleteia.org June 28 Saint: Saint Irenaeus of Lyons (Vigil of Saints Peter and Paul). Spiritual Quality: Champion of apostolic tradition, peace-weaver, and Doctor of Unity in Christian theology. Days until Reyes: 192 days. Wikipedia +1 July 22 Saint: Saint Mary Magdalene. Spiritual Quality: "Apostle to the Apostles"; patroness of converts, contemplative life, and radical transformation through divine mercy. Days until Reyes: 168 days. Wikipedia +1 August 15 Saint: Solemnity of the Assumption of the Blessed Virgin Mary (Also Saint Tarcisius). Spiritual Quality: Absolute devotion to Christ's will, heavenly glory, and heroic defense of the Holy Eucharist. Days until Reyes: 144 days. Facebook ·Recuerdos de San Jose +1 September 8 Saint: Feast of the Nativity of the Blessed Virgin Mary. Spiritual Quality: Dawn of salvation, pure innocence, and the ultimate spiritual vessel of obedience. Days until Reyes: 120 days. Facebook ·Interested in the Catholic Church? October 2 Saint: Feast of the Holy Guardian Angels. Spiritual Quality: Divine protection, constant spiritual guidance, and constant vigilance over human souls. Days until Reyes: 96 days. October 26 Saint: Saint Evaristus (Pope and Martyr). Spiritual Quality: Orderly administration of parish care and unwavering fortitude under persecution. Days until Reyes: 72 days. November 19 Saint: Saint Agnes of Assisi. Spiritual Quality: Strict adherence to poverty, monastic discipline, and deep spiritual companionship. Days until Reyes: 48 days. December 13 Saint: Saint Lucy of Syracuse (Virgin and Martyr). Spiritual Quality: Bearer of spiritual light; patroness of the blind, eyesight, and radiant courage in darkness. Days until Reyes: 24 days. January 6 Saint: Solemnity of the Epiphany of the Lord (Día de los Reyes). Spiritual Quality: Revelation of Christ to the world, universal adoration, and the sharing of spiritual gifts. Days until Reyes: 0 days (Arrival). Instagram ·abc7ny +1 Would you like to explore the biographical details of any specific saint on this list, or perhaps check how a leap year impacts this exact mathematical countdown? Three Kings Day is celebrated on the 12th day after Christmas ... - Instagram Instagram·abc7ny Every January 6th, Mexico celebrates Three Kings Day , a widely ... Facebook·Peace Corps Mexico Today we celebrate the Feast of St. Kateri Tekakwitha, the first Indigenous ... Instagram·waterloocdsb Mostrar todo La respuesta del Modo IA está lista