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Hércules (constelación)

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Hercules

Nombre Latino	Hercules
Abreviatura	Her
Genitivo	Herculis
Simbología	Hércules, el héroe
Ascensión recta	17 h
Declinación	30°
Superficie	1225 grados cuadrados Rango 5
Número de estrellas (magnitud < 3)	1
Estrella más brillante	β Her (magnitud ap. 2.8)
Lluvia de meteoros	Tau Herculids
Constelaciones colindantes	Draco Boötes Corona Borealis Serpens Caput Ophiuchus Aquila Sagitta Vulpecula Lyra
Visibilidad	En latitudes entre +90° y −50°
Mejor visibilidad (21:00 hrs.)	Julio

Recibe su nombre del héroe mitológico, Hércules y es la quinta en tamaño de las 88 constelaciones modernas. También era una de las 48 constelaciones de Ptolomeo.

Contenido

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[editar] Características destacables

No tiene estrellas de primera magnitud, siendo la más brillante β Herculis con magnitud 2,78. μ Herculis se encuentra a 27,4 años luz de la Tierra. El Ápex solar (punto del cielo que indica la dirección hacia la que se mueve el Sol en su órbitaalrededor del centro de la galaxia) se encuentra en Hércules, cerca de ξ Herculis.

[editar] Estrellas principales

α Herculis (Ras Algethi o Rasalgethi), de magnitud 3,31, es un sistema estelar triple, cuya estrella principal es una gigante roja variable.
β Herculis (Kornephoros), la más brillante de la constelación con magnitud 2,78, una estrella gigante amarilla.
γ Herculis, gigante blanca de magnitud 3,74. Es una binaria espectroscópica con un período orbital de 11,9 días.
δ Herculis (Sarin), estrella blanca de magnitud 3,12; es una estrella binaria cuyas componentes han sido resueltas por interferometría.
ε Herculis, binaria espectroscópica de magnitud 3,91.
ζ Herculis, la segunda más brillante de la constelación con magnitud 2,89, estrella doble formada por dos estrellas amarillas de desigual brillo.
η Herculis, gigante amarilla de magnitud 3,49.
θ Herculis, gigante luminosa naranja de magnitud 3,85.
ι Herculis, subgigante azul de magnitud 3,79; tres estrellas más completan este sistema estelar cuádruple.
κ Herculis A y κ Herculis B, dos gigantes que forman una doble óptica.
λ Herculis (Maasym), gigante naranja de magnitud 4,40.
μ Herculis, sistema estelar cercano que dista del Sistema Solar 27,4 años luz.
π Herculis, gigante naranja de magnitud 3,16.
ρ Herculis, estrella doble cuyas componentes, separadas 4 segundos de arco, brillan con magnitud 4,56 y 5,42.
τ Herculis, estrella B pulsante lenta (SPB) con una tenue compañera a 7,6 segundos de arco.
χ Herculis, enana amarilla de baja metalicidad que se encuentra a 52 años luz de distancia.
ω Herculis (Kajam), de magnitud 4,57.
8 Herculis, estrella blanca de magnitud 6,13 que forma una doble óptica con Kappa Herculis —separación 0,2º—.
14 Herculis, enana naranja a 59,2 años luz con una enana marrón o planeta gigante alrededor. En 2006 se descubrió un posible segundo compañero, aún sin confirmar.
30 Herculis (g Herculis), gigante roja y variable semirregular cuyo brillo oscila entre magnitud 4,3 y 6,3 en un ciclo de 89,2 días.
68 Herculis (u Herculis), binaria eclipsante en donde existe transferencia de masa desde la secundaria hacia la primaria.
72 Herculis (w Herculis), enana amarilla similar al Sol a 47 años luz de distancia.

Imagen del sistema Gliese 623 obtenida con el Telescopio espacial Hubble; Gliese 623 B está a la derecha del centro.

89 Herculis, supergigante amarilla en las etapas finales de su evolución estelar.
95 Herculis, estrella binaria compuesta por una gigante blanca y una gigante amarilla separadas 6,3 segundos de arco.
99 Herculis, binaria de baja metalicidad cuya primaria es una enana amarilla de magnitud 5,20.
101 Herculis, gigante blanca de magnitud 5,11.
109 Herculis, gigante naranja de magnitud 3,84, la duodécima estrella más brillante de la constelación.
111 Herculis, estrella blanca de magnitud 4,35.
X Herculis, variable pulsante semirregular cuyo brillo varía entre magnitud 6 y 7 en un período de 95 días.
SZ Herculis y FN Herculis, binarias eclipsantes de magnitud 9,94 y 11,08 respectivamente.
UX Herculis, binaria eclipsante de magnitud 9,05; durante el eclipse principal su brillo disminuye 1,16 magnitudes.
OP Herculis, gigante luminosa roja variable entre magnitud 5,85 y 6,73.
HD 147506, subgigante amarilla en donde se ha detectado un planeta masivo (HAT-P-2b) en una órbita excéntricacercana a la estrella.
HD 149026, estrella subgigante con un planeta cuya masa es similar a la de Saturno.
HD 154345, enana amarilla a 58,91 años luz con un planeta extrasolar.
Gliese 623, estrella binaria compuesta por dos enanas rojas.
Gliese 686 y Gliese 649, enanas rojas a 26,5 y 33,7 años luz respectivamente; la segunda de ellas posee un planeta.
HD 155358, estrella de baja metalicidad con dos planetas que interactúan gravitacionalmente.
Gliese 638 y HR 6806, enanas naranjas situadas respectivamente a 31,9 y 36,2 años luz de distancia de la Tierra.
GD 362, enana blanca con un anillo similar a los de Saturno.
http://es.wikipedia.org/wiki/H%C3%A9rcules_(constelaci%C3%B3n)

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Math in Architecture and the Golden Section

August 23, 2018/

The Golden Section (aka Golden Mean, and Golden Ratio) phys.org

We use math in architecture on a daily basis to solve problems. We use it to achieve both functional and aesthetic advantages. By applying math to our architectural designs through the use of the Golden Section and other mathematical principles, we can achieve harmony and balance. As you will see from some of the examples below, the application of mathematical principles can result in beautiful and long-lasting architecture which has passed the test of time.

Using Math in Architecture for Function and Form

We use math in architecture every day at our office. For example, we use math to calculate the area of a building site or office space. Math helps us to determine the volume of gravel or soil that is needed to fill a hole. We rely on math when designing safe building structures and bridges by calculating loads and spans. Math also helps us to determine the best material to use for a structure, such as wood, concrete, or steel.

“Without mathematics there is no art.” – Luca Pacioli, De divina proportione, 1509

Architects also use math when making aesthetic decisions. For instance, we use numbers to achieve attractive proportion and harmony. This may seem counter-intuitive, but architects routinely apply a combination of math, science, and art to create attractive and functional structures. One example of this is when we use math to achieve harmony and proportion by applying a well-known principle called the Golden Section

Math and Proportion – The Golden Section

Perfect proportions of the human body – The Vitruvian Man – by Leonardo da Vinci.

We tend to think of beauty as purely subjective, but that is not necessarily the case. There is a relationship between math and beauty. By applying math to our architectural designs through the use of the Golden Section and other mathematical principles, we can achieve harmony and balance.

The Golden Section is one example of a mathematical principle that is believed to result in pleasing proportions. It was mentioned in the works of the Greek mathematician Euclid, the father of geometry. Since the 4^th century, artists and architects have applied the Golden Section to their work.

The Golden Section is a rectangular form that, when cut in half or doubled, results in the same proportion as the original form. The proportions are 1: the square root of 2 (1.414) It is one of many mathematical principles that architects use to bring beautiful proportion to their designs.

Examples of the Golden Section are found extensively in nature, including the human body. The influential author Vitruvius asserted that the best designs are based on the perfect proportions of the human body.

Over the years many well-known artists and architects, such as Leonardo da Vinci and Michelangelo, used the Golden Section to define the dimensions and proportions in their works. For example, you can see the Golden Section demonstrated in DaVinci’s painting Mona Lisa and his drawing Vitruvian Man.

Famous Buildings Influenced by Mathematical Principles

Here are some examples of famous buildings universally recognized for their beauty. We believe their architects used math and the principals of the Golden Section in their design:

Parthenon

The classical Doric columned Parthenon was built on the Acropolis between 447 and 432 BC. It was designed by the architects Iktinos and Kallikrates. The temple had two rooms to shelter a gold and ivory statue of the goddess Athena and her treasure. Visitors to the Parthenon viewed the statue and temple from the outside. The refined exterior is recognized for its proportional harmony which has influenced generations of designers. The pediment and frieze were decorated with sculpted scenes of Athena, the Gods, and heroes.

Parthenon Golden Section

Notre Dame Cathedral in Paris

Built on the Ile de la Cite, Notre Dame was built on the site of two earlier churches. The foundation stone was laid by Pope Alexander III in 1163. The stone building demonstrates various styles of architecture, due to the fact that construction occurred for over 300 years. It is predominantly French Gothic, but also has elements of Renaissance and Naturalism. The cathedral interior is 427 feet x 157 feet in plan. The two Gothic towers on the west façade are 223 feet high. They were intended to be crowned by spires, but the spires were never built. The cathedral is especially loved for its three stained glass rose windows and daring flying buttresses. During the Revolution, the building was extensively damaged and was saved from demolition by the emperor Napoleon.

Notre Dame Cathedral in Paris

Taj Mahal

Built in Agra between 1631 and 1648, the Taj Mahal is a white marble mausoleum designed by Ustad-Ahmad Lahori. This jewel of Indian architecture was built by Emperor Shah Jahan in memory of his favorite wife. Additional buildings and elements were completed in 1653. The square tomb is raised and is dramatically located at the end of a formal garden. On the interior, the tomb chamber is octagonal and is surrounded by hallways and four corner rooms. Building materials are brick and lime veneered with marble and sandstone.

Math in Architecture and the Golden Section

Taj Mahal designed by Ustad-Ahmad Lahori

As you can see from the above examples, the application of mathematical principles can result in some pretty amazing architecture. The architects’ work reflects eye-catching harmony and balance. Although these buildings are all quite old, their designs have pleasing proportions which have truly passed the test of time.

https://bleckarchitects.com/math-in-architecture/