Golden rectangle

-

A series of golden rectangles. After cutting in each of them a square with a side equal to the short side of the rectangle remains the smaller golden rectangle. In the series are drawn two spirals, green circular circle built, red is a logarithmic spiral. Both are tangent to the sides of the rectangles in the places they divide.

Golden rectangle - a rectangle whose sides remain in golden ratio. It is characterized by the fact that after rectifying the square with the side equal to the long side of the rectangle, a new, larger golden rectangle is obtained.

From the definition of the golden rectangle and the property of the golden number φ it follows that:

If at the beginning the ratio of the sides is: a b = φ {\displaystyle {\frac {a}{b}}=\varphi } ,

When a square is added to a longer side, a rectangle with sides a + b and a is obtained, satisfying the following condition: a + b a = φ . {\displaystyle {\frac {a+b}{a}}=\varphi .}

In the opposite direction, by cutting off from the golden rectangle a square with a side equal to the short side of the rectangle is obtained a rectangle whose sides still remain in golden ratio.

Repeat these steps to get more or less golden rectangles.

wiki

Comments

Post a Comment

Popular posts from this blog

List 44

-
Open letter to the Sejm of the People's Republic of Poland, from the number of signatories also referred to as the Letter of forty-four (Letter 44) - a document deposited at the Chancellery of the Polish People's Party (April 29, 1982), in protest against internment and other Resolutions met the activists of NSZZ Solidarność after the imposition of martial law on December 13, 1981. The letter was signed by forty representatives of various professions (architects, teachers, doctors, economists, engineers, actors), Solidarity sympathizers, especially from the Jelenia Góra Region. wiki
Read more

indexation

-
Indexing (Latin) - a system of linking wages, prices or interest rates to a specific economic indicator (usually the base inflation rate), a change in the value of this indicator results in a proportional change in wages, prices or interest rates. The indexation can also be described as a conversion of a parameter value (eg pay) based on an indicator showing the change in a factor affecting the value of the parameter (eg inflation). Application The indexation is applied by the state - eg when paying pensions - with the increase in inflation the nominal value of the service increases. The state should also index the boundaries of the tax brackets. When it does not, citizens nominally earn more, but they also "fall into" higher and higher tax brackets, for which they have to pay higher taxes. In addition, when the state does not ideate a tax-free amount, citizens actually pay more and more taxes because the tax base increases. Indexes are used by banks - with the increas...
Read more

Mexican pool

-
Mexican pool - a pool game for two or more people. The game is distinguished by its unusual selection of balls that are selected by the opponent. The game is played on a standard eight-card table. The game is suitable for players of all skill levels. Used bile The standard set consists of 15 numbered balls and 1 white player. Initial setting At the beginning of the game, the balls are set up in the following formation: 9 balls are placed in the middle of the table as in the "nine", and the other six are in front of the balls. The purpose of the game Hit as many balls as possible (up to 6). Rules In the Mexican pool, unlike other billiards, the opponent (in the multiplayer version the player whose turn is next) chooses which ball (from six before the balls) picks the player. During the turn, the player must hit as many balls as possible, but he must not break the middle of the nine-ball form. The player ends the turn when: The game consists of only two turns (mult...
Read more