Mathematics of Telescopes :: Math

Missing Figures A Brief History of Telescopes Although telescopes has been around for several hundreds of years, there has been great discrepancy as to who invented it first. Here is one authors opinion. Lippershey was a Dutch spectacle marker during the early 17th century (approximately 1600). He was one of the first who created the "looker" (now called telescope) by placing two pieces of lenses together. The discovery that placing lenses together can magnify images were made by children who took Lippershey's spectacles and looked at a distant church tower. One of the most influential scientist associated with the telescope has to be Galileo. He took the design and reinvented the telescope into one of the first refractive telescopes we use to this day. Galileo used this great invention to report astronomical facts such as the moon is cover with craters instead of being smooth, the Milky Way is composed of millions of stars, and Jupiter have four moons. Perhaps the most famous discovery is the Earth revolves around the Sun and the Earth is not the center of the universe (even though he was discredited at the time). Newton was also involved with telescopes. After his growing interest with light bending, he applied his knowledge of the reflecting and refracting properties of light and invented the first reflective telescopes. Newton's reflective telescopes vastly improve the clarity of images as well as escaping from chromatic abberration. In order to fully understand the concepts and ideas of how a telescopes work, some knowledge of simple optics are required. Some Simple Optics Refraction Refraction occurs when light travels from one medium crosses a boundary and enters another medium of different properties. For example, light traveling from air to water. The amount of refraction (or bending) can be calculated using Snell's Law. Refractor How Refractor Telescopes Work The principle behind the refractive telescopes is the use of two glass lenses (objective lens and eyepiece lens) to gather and bend parallel light rays in a certain way so that the image fits the size of the eye's pupil. Light rays is gather through the opening of the telescope called the aperture and passes through the objective lens and refracts onto a single point called the focal point. From there the light rays continue the same direction until it hits the eyepiece lens which also refract the light back into parallel rays. During the process, the image that enters our eyes is actually reverse of the original image and magnified because the size in which we preceive the image. Mathematics of Telescopes :: Math Missing Figures A Brief History of Telescopes Although telescopes has been around for several hundreds of years, there has been great discrepancy as to who invented it first. Here is one authors opinion. Lippershey was a Dutch spectacle marker during the early 17th century (approximately 1600). He was one of the first who created the "looker" (now called telescope) by placing two pieces of lenses together. The discovery that placing lenses together can magnify images were made by children who took Lippershey's spectacles and looked at a distant church tower. One of the most influential scientist associated with the telescope has to be Galileo. He took the design and reinvented the telescope into one of the first refractive telescopes we use to this day. Galileo used this great invention to report astronomical facts such as the moon is cover with craters instead of being smooth, the Milky Way is composed of millions of stars, and Jupiter have four moons. Perhaps the most famous discovery is the Earth revolves around the Sun and the Earth is not the center of the universe (even though he was discredited at the time). Newton was also involved with telescopes. After his growing interest with light bending, he applied his knowledge of the reflecting and refracting properties of light and invented the first reflective telescopes. Newton's reflective telescopes vastly improve the clarity of images as well as escaping from chromatic abberration. In order to fully understand the concepts and ideas of how a telescopes work, some knowledge of simple optics are required. Some Simple Optics Refraction Refraction occurs when light travels from one medium crosses a boundary and enters another medium of different properties. For example, light traveling from air to water. The amount of refraction (or bending) can be calculated using Snell's Law. Refractor How Refractor Telescopes Work The principle behind the refractive telescopes is the use of two glass lenses (objective lens and eyepiece lens) to gather and bend parallel light rays in a certain way so that the image fits the size of the eye's pupil. Light rays is gather through the opening of the telescope called the aperture and passes through the objective lens and refracts onto a single point called the focal point. From there the light rays continue the same direction until it hits the eyepiece lens which also refract the light back into parallel rays. During the process, the image that enters our eyes is actually reverse of the original image and magnified because the size in which we preceive the image.

Literary Analysis “The Kiss”

In the story â€Å"The Kiss† by Julia Alvarez, we see a family with four daughters, a father and mother. The father, who is old-fashioned and strict, has his own ideas of what he wants from his daughters. The daughters except for Sofia, the youngest one, have always done what he has asked for. Sofia does not agree with her sisters and she does what she wants. She runs away with a man, a decision her father cannot forgive. Although Sofia tries to reconcile with her father with no luck, she lets her father know that she has her own way of thinking.No matter how much the father tries to change Sofia’s way of seeing life, in the end he could not. Trying to control a person does not guarantee that the other person will always do what we want. The father of this story is a strong man, trying to control his daughters as if they were small kids. Even when they were grown-ups and married, he always tried to control them. â€Å"They would gather together, without husbands, would -be husbands, or bring-home work, the apartment was too small for everyone, the father argued. † (Alvarez 416) His daughters will do anything to please their father. Even after they’d been married and had their own families and often couldn’t make it for other occasions, the four daughters always came home for their father’s birthday. † (Alvarez 416) They were raised in an old fashion way, and they respect their father. â€Å"But standing up to their father was a different matter altogether. Even as grown women, they lowered their voices in their father’s earshot when alluding to their bodies’ pleasure. † (Alvarez 416) Sofia was different she had her own way of living and did not agreed with her father. She ran away from her house and since then her relationship with her father was not good.Her father did not forgive her for what she did. â€Å"And yet, she of all the daughters, did not want to be the absent one because for the first time since she’d run off with her husband six years ago, she and her father were on speaking terms. † (Alvarez 417) Sofia had always lived her life as she wanted. She had many boyfriends; she also dropped out of school. Her father could not accept her way of living. He found out after searching into her letters that Sofia had an active sexual life. For him this was not acceptable. â€Å"After his initial shock, the father regained his own fury.Are you dragging my good name through the dirt? † (Alvarez 418) After six years Sofia’s father still could not forgive her. Sofia tries to reconcile with him by preparing her father’s birthday party at her house. Sofia prepared everything to please her dad. But after everything that she did, he would still not forgive her. Sofia let her dad know that she had her own way of doing things and her own way of thinking, and he could not change that after all. â€Å"After all her had work, she was not to be in cluded in his daughter count. Damn him! She’d take her turn and make him know it was her!Quickly, she swooped into the circle and gave the old man a wet, open-mouthed kiss in his ear. She ran her tongue in the whorls of his ear and nibbled the tip. † (Alvarez 422) Sofia was different from her sisters and her father never accepted it. I think this made her attitude worse, and when she found out that he would never forgive her, she did not care anymore, and let him know that she would never change. David T. Mitchell comments: Throughout the novel, numerous commentators remark on the poor fortune of a family that consists entirely of girls–â€Å"what, four girls and no boys? while each daughter struggles to free herself from the limitations of a communal designation that strips them of their uniqueness and individuality. Because the label â€Å"Garcia Girls† stands in for the plural identities submerged beneath the faceless anonymity of daughters (who, unlik e their male counterparts, do not need to be individuated as distinct human beings) â€Å"The novel's second chapter deals with Sofia, the youngest of the sisters, who leaves home when she gets pregnant on a vacation trip to South America, and then goes to Germany to convince the baby's father to marry her.Although the couple returns to the U. S. with the baby, the result of this stain on the family's honor is almost complete silence: their father does not mention Sofia's name for months, and even after a reconciliation of sorts the two rarely speak. † (Castells)

Evitar Conjugation in Spanish, Translation, and Examples

The verb evitar in Spanish means to avoid. Evitar is a regular -ar verb, so it follows the same conjugation pattern as other -ar verbs. This article includes evitar conjugations in the most commonly used verb tenses: the present, past, conditional, and future indicative, the present and past subjunctive, the imperative mood, and other verb forms. You can also find examples of ways you can use the verb evitar. Evitar Present Indicative Yo evito I avoid Yo evito gastar mucho dinero. Tà º evitas You avoid Tà º evitas a tu hermano despuà ©s de la pelea. Usted/à ©l/ella evita You/he/she avoids Ella evita las calles con mucho trà ¡fico. Nosotros evitamos We avoid Nosotros evitamos usar el telà ©fono al conducir. Vosotros evità ¡is Youavoid Vosotros evità ¡is los malentendidos con buena comunicacià ³n. Ustedes/ellos/ellas evitan You/they avoid Ellos evitan comer comida grasosa. Evitar Preterite Indicative The preterite tense is one of two past tenses in Spanish. The preterite is used to talk about events that happened in the past and have been completed. Yo evità © I avoided Yo evità © gastar mucho dinero. Tà º evitaste You avoided Tà º evitaste a tu hermano despuà ©s de la pelea. Usted/à ©l/ella evità ³ You/he/she avoided Ella evità ³ las calles con mucho trà ¡fico. Nosotros evitamos We avoided Nosotros evitamos usar el telà ©fono al conducir. Vosotros evitasteis Youavoided Vosotros evitasteis los malentendidos con buena comunicacià ³n. Ustedes/ellos/ellas evitaron You/they avoided Ellos evitaron comer comida grasosa. Evitar Imperfect Indicative The imperfect tense is the other form of the past in Spanish. The imperfect is used to talk about actions in the past that are ongoing or repeated. It can be translated to English as was avoiding or used to avoid. Yo evitaba I used to avoid Yo evitaba gastar mucho dinero. Tà º evitabas Youused to avoid Tà º evitabas a tu hermano despuà ©s de la pelea. Usted/à ©l/ella evitaba You/he/she used to avoid Ella evitaba las calles con mucho trà ¡fico. Nosotros evità ¡bamos We used to avoid Nosotros evità ¡bamos usar el telà ©fono al conducir. Vosotros evitabais Youused to avoid Vosotros evitabais los malentendidos con buena comunicacià ³n. Ustedes/ellos/ellas evitaban You/they used to avoid Ellos evitaban comer comida grasosa. Evitar Future Indicative Yo evitarà © I will avoid Yo evitarà © gastar mucho dinero. Tà º evitarà ¡s Youwill avoid Tà º evitarà ¡s a tu hermano despuà ©s de la pelea. Usted/à ©l/ella evitarà ¡ You/he/she will avoid Ella evitarà ¡las calles con mucho trà ¡fico. Nosotros evitaremos We will avoid Nosotros evitaremos usar el telà ©fono al conducir. Vosotros evitarà ©is Youwill avoid Vosotros evitarà ©is los malentendidos con buena comunicacià ³n. Ustedes/ellos/ellas evitarà ¡n You/they will avoid Ellos evitarà ¡n comer comida grasosa. Evitar Periphrastic  Future Indicative   The periphrastic future is translated to English as going to verb. Yo voy a evitar I am going to avoid Yo voya evitar gastar mucho dinero. Tà º vasa evitar Youaregoing to avoid Tà º vasa evitar a tu hermano despuà ©s de la pelea. Usted/à ©l/ella vaa evitar You/he/she isgoing to avoid Ella vaa evitar las calles con mucho trà ¡fico. Nosotros vamosa evitar We aregoing to avoid Nosotros vamosa evitar usar el telà ©fono al conducir. Vosotros vaisa evitar Youaregoing to avoid Vosotros vaisa evitar los malentendidos con buena comunicacià ³n. Ustedes/ellos/ellas vana evitar You/they aregoing to avoid Ellos vana evitar comer comida grasosa. Evitar Present Progressive/Gerund Form The English verb form that ends in -ing is called the gerund or present participle in Spanish. It is used to form progressive tenses like the present progressive. Present Progressive of Evitar està ¡ evitando Is avoiding Ella està ¡ evitando las calles con mucho trà ¡fico. Evitar Past Participle The past participle of the verb is used to form perfect tenses like the present perfect. Present Perfect of Evitar ha evitado Has avoided Ella ha evitado las calles con mucho trà ¡fico. Evitar Conditional Indicative The conditional tense is usually translated to English as would verb. Yo evitarà ­a I would avoid Yo evitarà ­a gastar mucho dinero si tuviera un salario mà ¡s bajo. Tà º evitarà ­as Youwould avoid Tà º evitarà ­as a tu hermano despuà ©s de la pelea, pero no puedes porque viven juntos. Usted/à ©l/ella evitarà ­a You/he/she would avoid Ella evitarà ­alas calles con mucho trà ¡fico, pero no conoce otra ruta. Nosotros evitarà ­amos We would avoid Nosotros evitarà ­amos usar el telà ©fono al conducir si fuera ilegal. Vosotros evitarà ­ais Youwould avoid Vosotros evitarà ­ais los malentendidos con buena comunicacià ³n, pero es muy difà ­cil. Ustedes/ellos/ellas evitarà ­an You/they would avoid Ellos evitarà ­an comer comida grasosa si estuvieran a dieta. Evitar Present Subjunctive Que yo evite That I avoid Mi madre espera que yo evite gastar mucho dinero. Que tà º evites That you avoid Pedro recomienda que tà º evites a tu hermano despuà ©s de la pelea. Que usted/à ©l/ella evite That you/he/she avoid Marà ­a quiere que ella evite las calles con mucho trà ¡fico. Que nosotros evitemos That we avoid La ley manda que nosotros evitemos usar el telà ©fono al conducir. Que vosotros evità ©is That you avoid El jefe pide que vosotros evità ©is los malentendidos con buena comunicacià ³n. Que ustedes/ellos/ellas eviten That you/they avoid El mà ©dico recomienda que ellos eviten comer comida grasosa. Evitar Imperfect Subjunctive There are two different ways for conjugating the imperfect subjunctive. Option 1 Que yo evitara That I avoided Mi madre esperaba que yo evitara gastar mucho dinero. Que tà º evitaras That you avoided Pedro recomendaba que tà º evitaras a tu hermano despuà ©s de la pelea. Que usted/à ©l/ella evitara That you/he/she avoided Marà ­a querà ­a que ella evitara las calles con mucho trà ¡fico. Que nosotros evità ¡ramos That we avoided La ley mandaba que nosotros evità ¡ramos usar el telà ©fono al conducir. Que vosotros evitarais That you avoided El jefe pedà ­a que vosotros evitarais los malentendidos con buena comunicacià ³n. Que ustedes/ellos/ellas evitaran That you/they avoided El mà ©dico recomendaba que ellos evitaran comer comida grasosa. Option 2 Que yo evitase That I avoided Mi madre esperaba que yo evitase gastar mucho dinero. Que tà º evitases That you avoided Pedro recomendaba que tà º evitases a tu hermano despuà ©s de la pelea. Que usted/à ©l/ella evitase That you/he/she avoided Marà ­a querà ­a que ella evitase las calles con mucho trà ¡fico. Que nosotros evità ¡semos That we avoided La ley mandaba que nosotros evità ¡semos usar el telà ©fono al conducir. Que vosotros evitaseis That you avoided El jefe pedà ­a que vosotros evitaseis los malentendidos con buena comunicacià ³n. Que ustedes/ellos/ellas evitasen That you/they avoided El mà ©dico recomendaba que ellos evitasen comer comida grasosa. Evitar Imperative The imperative mood has both positive and negative forms, used to give affirmative and negative commands. Positive Commands Tà º evita Avoid!  ¡Evita a tu hermano despuà ©s de la pelea! Usted evite Avoid!  ¡Evite las calles con mucho trà ¡fico! Nosotros evitemos Let's avoid!  ¡Evitemos usar el telà ©fono al conducir! Vosotros evitad Avoid!  ¡Evitad los malentendidos con buena comunicacià ³n! Ustedes eviten Avoid!  ¡Eviten comer comida grasosa! Negative Commands Tà º no evites Don't avoid!  ¡No evites a tu hermano despuà ©s de la pelea! Usted no evite Don't avoid!  ¡No evite las calles con mucho trà ¡fico! Nosotros no evitemos Let's not avoid!  ¡No evitemos usar el telà ©fono al conducir! Vosotros no evità ©is Don't avoid!  ¡No evità ©is los malentendidos con buena comunicacià ³n! Ustedes no eviten Don't avoid!  ¡No eviten comer comida grasosa!