In 1566 the temple was described by Fray Diego de Landa in the manuscript known as Relation of the Things of Yucatán; almost three centuries later John Lloyd Stephens described the architecture of the pyramid in a more detailed way in his book Incidents of the trip to Yucatán, a work published in 1843. At that time the archaeological zone of Chichén Itzá was located within a hacienda that had the same name, and was owned by Juan Sosa.[11] The book decorated with lithographs by Frederick Catherwood shows the pyramid covered with abundant vegetation on all its slopes "Talud (engineering)"). There are photographs taken at the beginning of the century where the pyramid appears partially covered with said vegetation.

In 1924, the Carnegie Institution of Washington requested permission from the Mexican Government to carry out explorations and reconstructions in the Chichén Itzá area. In 1927, with the assistance of Mexican archaeologists, work began. In April 1931, seeking to confirm the hypothesis that the structure of the Kukulcán pyramid was built on another older pyramid, excavation and exploration work began, despite the general reluctance of the time. To a large extent, the archaeologist José Erosa Peniche influenced the authorization of said exploration. On June 7, 1932, a box with coral objects "Coral (animal)") and obsidian and turquoise inlays was found next to human remains; The objects are exhibited in the National Museum of Anthropology "Museo Nacional de Antropología (Mexico)") in Mexico City.

After long work, in April 1935, a figure of Chac Mool with mother-of-pearl shell inlays on its nails, teeth and eyes was found inside the temple. The area where the discovery was made was named offering room or northern chamber. Just a few meters away, and after more than a year of excavations, in August 1936 a second enclosure was discovered, which was named chamber of sacrifices, within which two rows of human "Shin (leg)" shins were found embedded parallel to the bottom of the chamber, and the Throne of the Red Jaguar which is a sculpture of a red jaguar (Panthera onca) with 74 jade inlays that simulate the characteristic spots of the species on the body; The eyes are simulated with half-moons of the same stone and the fangs and teeth are made of flint painted white.[12] On the back there was a turquoise disc, which was apparently used to burn copal; Both figures have their view directed to the NNE (north-northeast). In conclusion, the existence of a pyramid measuring approximately 33 meters wide was determined, in the same way as the exterior one, with nine bases and a height of 17 m to the platform of the temple where the Chac Mool and the jaguar were found. It is estimated that this construction corresponds to the century AD. C. Once the work was completed, an access door was built in the balustrade of the exterior staircase of the NNE façade to facilitate access for tourists. The oldest inner pyramid is referred to as a "substructure".[13]​[14]​.

The temple of Kukulcán, the main structure of Chichén Itzá, demonstrates the deep knowledge of mathematics, geometry, acoustics and astronomy that the Mayans possessed. Being an initially agricultural society, the Mayans carefully observed the behavior of the seasons, the variations in the trajectories of the Sun and the stars, combining their knowledge, they managed to record them in the construction of the temple dedicated to their god Kukulcán.

Like Mesoamerican cultures, the Mayan culture used a solar agricultural calendar they called Haab, which has 18 months or uinales. Each uinal has 20 days or kines. In this way the calendar includes 18 x 20 = 360 regular days or kines, plus five additional days, considered ominous, called uayeb.

The Kukulcán temple has four staircases; each of them has 91 steps. In this way they add up to 364 and considering the upper platform of the temple we have a total of 365 units that represent the days of the Haab.

The second calendar used by the Mayans, called Tzolkin or sacred calendar, consists of 13 months and each month has 20 days, so that it has 260 days.[16] The cycles of the Tzolkin and the Haab were merged into a calendrical wheel in such a way that the combinations of both repeat every 18,980 days (minimum common multiple of 260 and 365)[17]​ equivalent to 52 years, which means that every 52 cycles of the Haab calendar the combination of both calendars begins to repeat itself.

The numbers 18 (uinales), 20 (kines), 5 (uayeb) and 52 (cycles) can be deciphered in a more complex way in the Kukulcán pyramid. The temple has nine levels or bases; If you look at any of the facades from the front, having the staircase in the center of your view, you can multiply the number of bases x 2, resulting in the number 18, thus corresponding to the 18 uinals of the Haab. In the upper temple of the pyramid there were five decorations or battlements on each façade; In this way there were 20 battlements that represent the 20 days or kines of each uinal. On each façade, on the cant of each base, there are bas-relief panels; At the highest level there are only two panels, and the other eight bases have three panels, so that 3 x 8 = 24 + 2 = 26 panels, which added to the other 26 panels on the opposite side of the staircase give us a grand total of panels per façade of 52; That is, they represent the 52 cycles of the Haab on the calendar wheel. As ornamentation, the building has 260 quadrangles, which coincide with the number of days in the Tzolkin calendar.[18]​.

In this way, and according to the calendars used by the Mayans, it can be deduced that the pyramid is not only dedicated to the god Kukulcán, but also observes the counting of time, giving particular relevance to its cycles.

Towards the end of the century, tourism in Chichén Itzá increased and it was when the tourist guides accidentally discovered an acoustic effect that occurs on the NNE staircase of the pyramid. If a person claps facing the stairs, the sound of the applause spreads towards the slope of the steps and bounces back in the form of a distorted echo; That is, the reflection of the sound "Reflexion (sound)") is heard different from the source (applause), causing a chirp similar to the song of a quetzal (video[19]​).

Technically, this is because the sound produced by the source propagates simultaneously to collide with the lower and upper steps of the staircase; The sound reaches the closest ones first, that is, the lower ones, and a fraction of a millisecond later to the higher ones. This fraction of time is enough to create interference with the reflection waves and produce the peculiar echo. Only low-frequency sounds such as clapping produce the effect.[20]​.

If for a year and from a fixed point we contemplate the sunrise on the horizon, we will be able to observe that the Sun appears in different positions throughout it and its path in the sky changes. This is due to the Earth's own movements, rotation on its axis and translation around the Sun, as well as the variant of its ecliptic and the inclination of the Earth's axis.

Referring to the northern hemisphere of the planet, for one year the Sun appears to be placed on the horizon line at a southernmost point during the winter solstice (December), passing through an intermediate point during the spring equinox (March) and reaching a northernmost point during the summer solstice (June), to return again to the intermediate point during the autumn equinox (September) and restart the cycle again.

This apparent movement has an additional variation if we move to different latitudes of the planet. The Mayans considered all these variables and with great attention observed the possible light and shadow phenomena generated during each day of the year. They thus built the Kukulcán pyramid taking all these variables into account. In addition to architectural considerations, they oriented the NNE façade with an approximate inclination of 20° with respect to geographic north.

At sunset of the spring and autumn equinoxes, a serpentine solar projection is observed on the NNE staircase of the Kukulcán pyramid, consisting of seven inverted isosceles triangles of light, as a result of the shadow cast by the nine platforms of that building during sunset. In Chichén Itzá the phenomenon is seen in all its splendor and the image of the snake of triangles of light and shadow is projected onto the NNE alfarda; As time progresses, a snake seems to descend from the temple and the last remnant of light is projected on the head of the feathered serpent that is at the base of the stairs. This phenomenon occurs in March and September, and can be observed approximately during a period of five days on the dates closest to the equinoxes. The duration of the effect begins approximately three hours before sunset; At the beginning of these hours you can see a form of wavy light on the balustrade that little by little closes to form seven isosceles triangles, which can only be seen for ten minutes; then they begin to gradually disappear.[21]​.

One of the positions in the academy points out that there is no evidence that this play of light and shadow was achieved on purpose, as a result of the conscious design of the Mayans.[22]​ They are based on research that indicates that the effect can be observed, without major changes, for several weeks.[23]​ Other academic works present a proposal in which, although it is not focused on a single pair of dates, said research indicates that it is a cycle that begins in mid-February and ends in the last days of February. October,[24]​ in which the effect is related to the observation of Venus and the agricultural cycles of northern Yucatán, on dates similar to those that occur in Mayan communities in the north of the Peninsula, as part of a pre-Hispanic legacy[25]​.

In the archaeological zone of Mayapán there is a pyramid of smaller dimensions, but of equal proportions and dedicated of course to Kukulcán. The undulating projection of the snake's body can also be observed during sunset near the solstices; However, it is not as spectacular due to the deterioration of the structure itself.

In the year 1566, Diego de Landa described that the Mayans celebrated the passing of Kukulcán on the 16th day of the month Xul[26], whom they considered a god. The celebration was held throughout the Mayan world until the destruction of Mayapán; later only the tutul xiues performed it in their capital Maní "Maní (Yucatán)"). After maintaining fasting and abstinence, the priests, gathered together, went to the temple of Kukulcán, where they spent five days and nights in prayer performing some devout dances:

Because the SSO and ESE facades are deteriorated, no light and shadow phenomena are observed at equinoctial sunrises; However, it is likely that if the stairs and balustrades were restored, an effect could be seen that would evoke the ascent of the snake's body to the pyramid along the stairs of the SSO façade.

At the end of the classic Mesoamerican period, an architectural, cultural and religious influence was recorded in the Mayan area, which has been attributed to the Toltec culture of the highlands. This is why similarities are found between the deity Quetzalcóatl (from Nahuatl: Quetzalcōātl) and the Mayan deity Kukulcán (from Mayan: K'uk'ulkan).

In the Popol Vuh the deity is referred to as Gucumatz (from Quiché: Q'uk'umatz) who together with Tepew are considered the gods that formed the universe.[28] He was known by Mixtec culture as Nine Wind (from Mixtec: Coo Dzavui). According to the descriptions of Diego de Landa, the god was especially venerated in several cities in the northwest of the Yucatán Peninsula, among them Chichén Itzá, Mayapán and Maní "Maní (Yucatán)").

In many parts of the architectural decoration of columns "Column (architecture)") and lintels of Chichén Itzá, allusions to the body of the serpent are found, in the temple of Kukulcán itself, in the "Temple of the Jaguars", in the temple of the Warriors, in the "Game of Ball", in the "Platform of the Eagles and the Jaguars". The type of reptile appears to be Crotalus durissus known as rattlesnake due to the shape of the sculptures' heads, the reliefs detailing rattlesnakes on other buildings in the city, and the triangles of light that form on equinoctial days, which evoke the triangles that form on the skin of the species' body.

The decoration of the snake tongue that is found at the top of the staircase is notable. The tongue has semicircles that allude to the daily path of the Sun in the sky. In the profile view of the heads, near the corner of the mouth, spirals that evoke a snail can be seen. The layout can be interpreted as an allusion to the cyclical period of the Sun's movement on the horizon. On the upper part of the snake's eyelids you can also see the Sun symbol.

In addition to the projection of the imaginary body of the snake (kan) descending the alfarda of the staircase, the Mayans placed feather flags (k'u uk'um) on the battlements of the temple during the equinoctial festivities aimed at beginning the Mayan agronomic cycle.[27]​.

Since the last decade of the century, archaeologists began to observe the light and shadow phenomena that occur at the summer and winter solstices, but it was not until June 2007 that detailed studies of the subject were carried out. Astronomers from the Mérida Technological Institute and researchers from the National Institute of Anthropology and History corroborated that during the first minutes of dawn[30]​ of the June solstice (northern hemisphere summer) and for a period of 15 minutes, the Kukulcán pyramid is illuminated on the NNE and ESE facades by the sun's rays, while the WNW and SSW facades remain in total darkness. In other words, 50% of the pyramid remains illuminated and 50% remains in darkness, marking with this symbolism the exact moment of the solstice.[31]​.

This effect of light and shadow occurs in a similar way during the December solstice (winter in the northern hemisphere), but at dusk the illuminated facades are the WNW and SSW while the NNE and ESE facades remain in shadow. The phenomenon is due to the orientation of +/– 20° with respect to geographic north, and the latitude where the pyramid is located.

The moment when the sun passes over a geographical point in such a way that no shadows are projected is called a zenith pass. This occurs only in the geographical area between the Tropic of Cancer and the Tropic of Capricorn. Further north or south of the tropics the true zenith is never reached, as the sun is always further north or south. In the tropics the zenith passage occurs on a single day, coinciding with the summer solstice (June 20 or 21) in the Tropic of Cancer (northern latitude 23°26'16") and with the winter solstice (December 21 or 22) in the Tropic of Capricorn (south latitude 23°26'16"). In the other geographical points that are located between both tropics, the zenith passage occurs two days a year, the dates depend on the latitude in which they are located and are different in each place.[32]​.

In this way, the zenith passage in Xochicalco occurs on May 15 and July 29, in Monte Albán it occurs on May 8 and August 5. In the case of Chichén Itzá, due to its northern latitude of 20°40'58″, the zenith passage days occur on May 23 or 24 and July 19.[33] Archaeoastronomy specialists have carried out research and observations of what happens on the zenith passage dates in various archaeological sites. The first investigators for the Chichén Itzá case were Franz Tichy, Johanna Broda and Susan Milbrath. Broda concluded that Mesoamerican cultures carefully chose the location of their ceremonial centers by recording the apparent movement of the sun over the horizon and observing zenith steps.[34]​.

Recently, research carried out by Arturo Montero García, Jesús Galindo Trejo and David Wood Caso have detected that when the sunrise is observed on the day of the zenith pass, the sun is at 67°30′ azimuth, and that seen from the top of the Kukulcán temple, the direction coincides with the northeast corner of the same building. An imaginary line from the observer towards the sun at sunrise would also cross the top of the Temple of the Tables (northeast of the Temple of the Warriors). On the other hand, at sunset, the sun is at 292° 30' azimuth, seen from the top of the temple, the direction of the sun coincides with the northwest staircase. If this imaginary line of the observer is followed towards the sun at sunset, it coincides with the rectangular mouth that the Mayans made to the Holtún cenote. That same day, inside the cenote you can see the vertical of the sun's rays at the moment of zenith; this coincidence could have religious symbolism related to the underworld of the Mayan worldview.[35]​.

The explorer John Lloyd Stephens in 1840 noticed the orientation of the buildings. Because he could not observe the effects of light and shadow, he attributed a possible error in their construction. He never imagined that this variation had been completely premeditated centuries before by the Mayan builders. On the other hand, the measurements referred to seem to have some variation with the real ones:

In order for the Mayapán pyramid, which was built with characteristics similar to that of Chichén Itzá, to be able to show the same phenomena of light and shadow, its orientation had to have a slight variation because it is not located in the same latitude coordinate as that of Chichén Itzá.

In this way, the construction of the pyramid appears to be an architectural calendar that marks the solstices and equinoxes, important dates for agricultural cycles. When the orbit of the Moon is in the same equinoctial position of the sun, it is also possible to see the projected figure of the snake in a nighttime natural spectacle on the NNE staircase.

These light and shadow phenomena observed in the pyramid are faithful testimonies that prove the astronomical knowledge of the Mayan culture. In the structure known as the observatory, the snail or "circular building", effects of light and shadow have also been recorded during the equinoxes.[37] In the Dresden Codex it has been possible to interpret that the Mayans studied the orbital trajectory of the planet Venus "Venus (planet)"), to which they dedicated a small construction in the city of Chichén Itzá.

• - Drawing by Frederick Catherwood from 1843.

• - Photograph of Teobert Maler in 1892.

• - Illumination during the June solstice (summer in the northern hemisphere).

• - Illumination of the Earth by the Sun on the June solstice.

• - Illumination during the December solstice (winter in the northern hemisphere).

• - Illumination of the Earth by the Sun on the December solstice.

• - Chichen Itza.

• - Mayan culture.

• - Itzáes.

• - Mayan astronomy.

• - El Caracol "El Caracol (architecture)").

• - Reflection (sound) "Reflection (sound)").

• - Earth Movements.

• - Obliquity of the ecliptic.

• - Amerindian architecture.

• - Chichén Itzá crestomatia INAH/Discovery Channel Youtube.com.

• - Path of the sun, ecliptic From Astronomers to Spaceships.

• - Zenital passage of the sun in Chichén Itzá. National Geographic.

In 1566 the temple was described by Fray Diego de Landa in the manuscript known as Relation of the Things of Yucatán; almost three centuries later John Lloyd Stephens described the architecture of the pyramid in a more detailed way in his book Incidents of the trip to Yucatán, a work published in 1843. At that time the archaeological zone of Chichén Itzá was located within a hacienda that had the same name, and was owned by Juan Sosa.[11] The book decorated with lithographs by Frederick Catherwood shows the pyramid covered with abundant vegetation on all its slopes "Talud (engineering)"). There are photographs taken at the beginning of the century where the pyramid appears partially covered with said vegetation.

In 1924, the Carnegie Institution of Washington requested permission from the Mexican Government to carry out explorations and reconstructions in the Chichén Itzá area. In 1927, with the assistance of Mexican archaeologists, work began. In April 1931, seeking to confirm the hypothesis that the structure of the Kukulcán pyramid was built on another older pyramid, excavation and exploration work began, despite the general reluctance of the time. To a large extent, the archaeologist José Erosa Peniche influenced the authorization of said exploration. On June 7, 1932, a box with coral objects "Coral (animal)") and obsidian and turquoise inlays was found next to human remains; The objects are exhibited in the National Museum of Anthropology "Museo Nacional de Antropología (Mexico)") in Mexico City.

After long work, in April 1935, a figure of Chac Mool with mother-of-pearl shell inlays on its nails, teeth and eyes was found inside the temple. The area where the discovery was made was named offering room or northern chamber. Just a few meters away, and after more than a year of excavations, in August 1936 a second enclosure was discovered, which was named chamber of sacrifices, within which two rows of human "Shin (leg)" shins were found embedded parallel to the bottom of the chamber, and the Throne of the Red Jaguar which is a sculpture of a red jaguar (Panthera onca) with 74 jade inlays that simulate the characteristic spots of the species on the body; The eyes are simulated with half-moons of the same stone and the fangs and teeth are made of flint painted white.[12] On the back there was a turquoise disc, which was apparently used to burn copal; Both figures have their view directed to the NNE (north-northeast). In conclusion, the existence of a pyramid measuring approximately 33 meters wide was determined, in the same way as the exterior one, with nine bases and a height of 17 m to the platform of the temple where the Chac Mool and the jaguar were found. It is estimated that this construction corresponds to the century AD. C. Once the work was completed, an access door was built in the balustrade of the exterior staircase of the NNE façade to facilitate access for tourists. The oldest inner pyramid is referred to as a "substructure".[13]​[14]​.

The temple of Kukulcán, the main structure of Chichén Itzá, demonstrates the deep knowledge of mathematics, geometry, acoustics and astronomy that the Mayans possessed. Being an initially agricultural society, the Mayans carefully observed the behavior of the seasons, the variations in the trajectories of the Sun and the stars, combining their knowledge, they managed to record them in the construction of the temple dedicated to their god Kukulcán.

Like Mesoamerican cultures, the Mayan culture used a solar agricultural calendar they called Haab, which has 18 months or uinales. Each uinal has 20 days or kines. In this way the calendar includes 18 x 20 = 360 regular days or kines, plus five additional days, considered ominous, called uayeb.

The Kukulcán temple has four staircases; each of them has 91 steps. In this way they add up to 364 and considering the upper platform of the temple we have a total of 365 units that represent the days of the Haab.

The second calendar used by the Mayans, called Tzolkin or sacred calendar, consists of 13 months and each month has 20 days, so that it has 260 days.[16] The cycles of the Tzolkin and the Haab were merged into a calendrical wheel in such a way that the combinations of both repeat every 18,980 days (minimum common multiple of 260 and 365)[17]​ equivalent to 52 years, which means that every 52 cycles of the Haab calendar the combination of both calendars begins to repeat itself.

The numbers 18 (uinales), 20 (kines), 5 (uayeb) and 52 (cycles) can be deciphered in a more complex way in the Kukulcán pyramid. The temple has nine levels or bases; If you look at any of the facades from the front, having the staircase in the center of your view, you can multiply the number of bases x 2, resulting in the number 18, thus corresponding to the 18 uinals of the Haab. In the upper temple of the pyramid there were five decorations or battlements on each façade; In this way there were 20 battlements that represent the 20 days or kines of each uinal. On each façade, on the cant of each base, there are bas-relief panels; At the highest level there are only two panels, and the other eight bases have three panels, so that 3 x 8 = 24 + 2 = 26 panels, which added to the other 26 panels on the opposite side of the staircase give us a grand total of panels per façade of 52; That is, they represent the 52 cycles of the Haab on the calendar wheel. As ornamentation, the building has 260 quadrangles, which coincide with the number of days in the Tzolkin calendar.[18]​.

In this way, and according to the calendars used by the Mayans, it can be deduced that the pyramid is not only dedicated to the god Kukulcán, but also observes the counting of time, giving particular relevance to its cycles.

Towards the end of the century, tourism in Chichén Itzá increased and it was when the tourist guides accidentally discovered an acoustic effect that occurs on the NNE staircase of the pyramid. If a person claps facing the stairs, the sound of the applause spreads towards the slope of the steps and bounces back in the form of a distorted echo; That is, the reflection of the sound "Reflexion (sound)") is heard different from the source (applause), causing a chirp similar to the song of a quetzal (video[19]​).

Technically, this is because the sound produced by the source propagates simultaneously to collide with the lower and upper steps of the staircase; The sound reaches the closest ones first, that is, the lower ones, and a fraction of a millisecond later to the higher ones. This fraction of time is enough to create interference with the reflection waves and produce the peculiar echo. Only low-frequency sounds such as clapping produce the effect.[20]​.

If for a year and from a fixed point we contemplate the sunrise on the horizon, we will be able to observe that the Sun appears in different positions throughout it and its path in the sky changes. This is due to the Earth's own movements, rotation on its axis and translation around the Sun, as well as the variant of its ecliptic and the inclination of the Earth's axis.

Referring to the northern hemisphere of the planet, for one year the Sun appears to be placed on the horizon line at a southernmost point during the winter solstice (December), passing through an intermediate point during the spring equinox (March) and reaching a northernmost point during the summer solstice (June), to return again to the intermediate point during the autumn equinox (September) and restart the cycle again.

This apparent movement has an additional variation if we move to different latitudes of the planet. The Mayans considered all these variables and with great attention observed the possible light and shadow phenomena generated during each day of the year. They thus built the Kukulcán pyramid taking all these variables into account. In addition to architectural considerations, they oriented the NNE façade with an approximate inclination of 20° with respect to geographic north.

At sunset of the spring and autumn equinoxes, a serpentine solar projection is observed on the NNE staircase of the Kukulcán pyramid, consisting of seven inverted isosceles triangles of light, as a result of the shadow cast by the nine platforms of that building during sunset. In Chichén Itzá the phenomenon is seen in all its splendor and the image of the snake of triangles of light and shadow is projected onto the NNE alfarda; As time progresses, a snake seems to descend from the temple and the last remnant of light is projected on the head of the feathered serpent that is at the base of the stairs. This phenomenon occurs in March and September, and can be observed approximately during a period of five days on the dates closest to the equinoxes. The duration of the effect begins approximately three hours before sunset; At the beginning of these hours you can see a form of wavy light on the balustrade that little by little closes to form seven isosceles triangles, which can only be seen for ten minutes; then they begin to gradually disappear.[21]​.

One of the positions in the academy points out that there is no evidence that this play of light and shadow was achieved on purpose, as a result of the conscious design of the Mayans.[22]​ They are based on research that indicates that the effect can be observed, without major changes, for several weeks.[23]​ Other academic works present a proposal in which, although it is not focused on a single pair of dates, said research indicates that it is a cycle that begins in mid-February and ends in the last days of February. October,[24]​ in which the effect is related to the observation of Venus and the agricultural cycles of northern Yucatán, on dates similar to those that occur in Mayan communities in the north of the Peninsula, as part of a pre-Hispanic legacy[25]​.

In the archaeological zone of Mayapán there is a pyramid of smaller dimensions, but of equal proportions and dedicated of course to Kukulcán. The undulating projection of the snake's body can also be observed during sunset near the solstices; However, it is not as spectacular due to the deterioration of the structure itself.

In the year 1566, Diego de Landa described that the Mayans celebrated the passing of Kukulcán on the 16th day of the month Xul[26], whom they considered a god. The celebration was held throughout the Mayan world until the destruction of Mayapán; later only the tutul xiues performed it in their capital Maní "Maní (Yucatán)"). After maintaining fasting and abstinence, the priests, gathered together, went to the temple of Kukulcán, where they spent five days and nights in prayer performing some devout dances:

Because the SSO and ESE facades are deteriorated, no light and shadow phenomena are observed at equinoctial sunrises; However, it is likely that if the stairs and balustrades were restored, an effect could be seen that would evoke the ascent of the snake's body to the pyramid along the stairs of the SSO façade.

At the end of the classic Mesoamerican period, an architectural, cultural and religious influence was recorded in the Mayan area, which has been attributed to the Toltec culture of the highlands. This is why similarities are found between the deity Quetzalcóatl (from Nahuatl: Quetzalcōātl) and the Mayan deity Kukulcán (from Mayan: K'uk'ulkan).

In the Popol Vuh the deity is referred to as Gucumatz (from Quiché: Q'uk'umatz) who together with Tepew are considered the gods that formed the universe.[28] He was known by Mixtec culture as Nine Wind (from Mixtec: Coo Dzavui). According to the descriptions of Diego de Landa, the god was especially venerated in several cities in the northwest of the Yucatán Peninsula, among them Chichén Itzá, Mayapán and Maní "Maní (Yucatán)").

In many parts of the architectural decoration of columns "Column (architecture)") and lintels of Chichén Itzá, allusions to the body of the serpent are found, in the temple of Kukulcán itself, in the "Temple of the Jaguars", in the temple of the Warriors, in the "Game of Ball", in the "Platform of the Eagles and the Jaguars". The type of reptile appears to be Crotalus durissus known as rattlesnake due to the shape of the sculptures' heads, the reliefs detailing rattlesnakes on other buildings in the city, and the triangles of light that form on equinoctial days, which evoke the triangles that form on the skin of the species' body.

The decoration of the snake tongue that is found at the top of the staircase is notable. The tongue has semicircles that allude to the daily path of the Sun in the sky. In the profile view of the heads, near the corner of the mouth, spirals that evoke a snail can be seen. The layout can be interpreted as an allusion to the cyclical period of the Sun's movement on the horizon. On the upper part of the snake's eyelids you can also see the Sun symbol.

In addition to the projection of the imaginary body of the snake (kan) descending the alfarda of the staircase, the Mayans placed feather flags (k'u uk'um) on the battlements of the temple during the equinoctial festivities aimed at beginning the Mayan agronomic cycle.[27]​.

Since the last decade of the century, archaeologists began to observe the light and shadow phenomena that occur at the summer and winter solstices, but it was not until June 2007 that detailed studies of the subject were carried out. Astronomers from the Mérida Technological Institute and researchers from the National Institute of Anthropology and History corroborated that during the first minutes of dawn[30]​ of the June solstice (northern hemisphere summer) and for a period of 15 minutes, the Kukulcán pyramid is illuminated on the NNE and ESE facades by the sun's rays, while the WNW and SSW facades remain in total darkness. In other words, 50% of the pyramid remains illuminated and 50% remains in darkness, marking with this symbolism the exact moment of the solstice.[31]​.

This effect of light and shadow occurs in a similar way during the December solstice (winter in the northern hemisphere), but at dusk the illuminated facades are the WNW and SSW while the NNE and ESE facades remain in shadow. The phenomenon is due to the orientation of +/– 20° with respect to geographic north, and the latitude where the pyramid is located.

The moment when the sun passes over a geographical point in such a way that no shadows are projected is called a zenith pass. This occurs only in the geographical area between the Tropic of Cancer and the Tropic of Capricorn. Further north or south of the tropics the true zenith is never reached, as the sun is always further north or south. In the tropics the zenith passage occurs on a single day, coinciding with the summer solstice (June 20 or 21) in the Tropic of Cancer (northern latitude 23°26'16") and with the winter solstice (December 21 or 22) in the Tropic of Capricorn (south latitude 23°26'16"). In the other geographical points that are located between both tropics, the zenith passage occurs two days a year, the dates depend on the latitude in which they are located and are different in each place.[32]​.

In this way, the zenith passage in Xochicalco occurs on May 15 and July 29, in Monte Albán it occurs on May 8 and August 5. In the case of Chichén Itzá, due to its northern latitude of 20°40'58″, the zenith passage days occur on May 23 or 24 and July 19.[33] Archaeoastronomy specialists have carried out research and observations of what happens on the zenith passage dates in various archaeological sites. The first investigators for the Chichén Itzá case were Franz Tichy, Johanna Broda and Susan Milbrath. Broda concluded that Mesoamerican cultures carefully chose the location of their ceremonial centers by recording the apparent movement of the sun over the horizon and observing zenith steps.[34]​.

Recently, research carried out by Arturo Montero García, Jesús Galindo Trejo and David Wood Caso have detected that when the sunrise is observed on the day of the zenith pass, the sun is at 67°30′ azimuth, and that seen from the top of the Kukulcán temple, the direction coincides with the northeast corner of the same building. An imaginary line from the observer towards the sun at sunrise would also cross the top of the Temple of the Tables (northeast of the Temple of the Warriors). On the other hand, at sunset, the sun is at 292° 30' azimuth, seen from the top of the temple, the direction of the sun coincides with the northwest staircase. If this imaginary line of the observer is followed towards the sun at sunset, it coincides with the rectangular mouth that the Mayans made to the Holtún cenote. That same day, inside the cenote you can see the vertical of the sun's rays at the moment of zenith; this coincidence could have religious symbolism related to the underworld of the Mayan worldview.[35]​.

The explorer John Lloyd Stephens in 1840 noticed the orientation of the buildings. Because he could not observe the effects of light and shadow, he attributed a possible error in their construction. He never imagined that this variation had been completely premeditated centuries before by the Mayan builders. On the other hand, the measurements referred to seem to have some variation with the real ones:

In order for the Mayapán pyramid, which was built with characteristics similar to that of Chichén Itzá, to be able to show the same phenomena of light and shadow, its orientation had to have a slight variation because it is not located in the same latitude coordinate as that of Chichén Itzá.

In this way, the construction of the pyramid appears to be an architectural calendar that marks the solstices and equinoxes, important dates for agricultural cycles. When the orbit of the Moon is in the same equinoctial position of the sun, it is also possible to see the projected figure of the snake in a nighttime natural spectacle on the NNE staircase.

These light and shadow phenomena observed in the pyramid are faithful testimonies that prove the astronomical knowledge of the Mayan culture. In the structure known as the observatory, the snail or "circular building", effects of light and shadow have also been recorded during the equinoxes.[37] In the Dresden Codex it has been possible to interpret that the Mayans studied the orbital trajectory of the planet Venus "Venus (planet)"), to which they dedicated a small construction in the city of Chichén Itzá.

• - Drawing by Frederick Catherwood from 1843.

• - Photograph of Teobert Maler in 1892.

• - Illumination during the June solstice (summer in the northern hemisphere).

• - Illumination of the Earth by the Sun on the June solstice.

• - Illumination during the December solstice (winter in the northern hemisphere).

• - Illumination of the Earth by the Sun on the December solstice.

• - Chichen Itza.

• - Mayan culture.

• - Itzáes.

• - Mayan astronomy.

• - El Caracol "El Caracol (architecture)").

• - Reflection (sound) "Reflection (sound)").

• - Earth Movements.

• - Obliquity of the ecliptic.

• - Amerindian architecture.

• - Chichén Itzá crestomatia INAH/Discovery Channel Youtube.com.

• - Path of the sun, ecliptic From Astronomers to Spaceships.

• - Zenital passage of the sun in Chichén Itzá. National Geographic.