ArticleslgStudy

mathematics

Nogales, Arizona

Nogales, Arizona is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Nogales, Arizona rather than just read about it. In short: Nogales (Spanish pronunciation: [noˈɣales] ; English: or ) is a city in and the county seat of Santa Cruz County, Arizona, United States. As of 2026, the population of Nogales is 20,072.

Nogales, Arizona — main illustration
Nogales, Arizona — illustration

Key takeaways

  • Nogales, Arizona belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Nogales, Arizona to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Nogales, Arizona from memory before moving on to harder problems.

Reference excerpt

Nogales (Spanish pronunciation: [noˈɣales] ; English: or ) is a city in and the county seat of Santa Cruz County, Arizona, United States. As of 2026, the population of Nogales is 20,072. Nogales forms part of the larger Tucson–Nogales combined statistical area, with a total population of 1,027,683 as of the 2010 Census. Nogales forms Arizona's largest transborder agglomeration with its adjacent, much larger twin Nogales, Sonora, across the Mexican border. The southern terminus of Interstate 19 is located in Nogales at the U.S.–Mexico border; the highway continues south into Mexico as Mexico Federal Highway 15. The highways meeting in Nogales are a major road intersection in the CANAMEX Corridor, connecting Canada, the United States, and Mexico. Nogales also is the beginning of the Arizona Sun Corridor, an economically important trade region stretching from Nogales to Prescott, including the Tucson and Phoenix metropolitan areas. Nogales is home to four international ports of entry, including the Morley Pedestrian Port of Entry, Dennis Deconcini Pedestrian and Passenger Vehicle Port of Entry, Union Pacific rail, Nogales International Airport, and the Mariposa Port of Entry. The Nogales-Mariposa Port of Entry has twelve passenger vehicle inspection lanes and eight commercial inspection lanes. Due to its location on the border and its major ports of entry, Nogales funnels an estimated $30 billion worth of international trade into Arizona and the United States, per year, in fresh produce and manufactured goods from Mexico and the world through the deep sea port in Guaymas, Sonora, Mexico. This trade helps to support tens of thousands of jobs and the overall economies in Ambos Nogales and throughout the American state of Arizona and the Mexican state of Sonora. The town is named for the black walnut trees which once grew abundantly in the mountain pass between the cities of Nogales, Arizona, and Nogales, Sonora, and can still be found around the town.

History

The name Nogales is derived from the Spanish word for 'walnut' or 'walnut tree'. It refers to the large stands of walnut trees that once stood in the mountain pass where Nogales is located. Nogales was at the beginning of the 1775–1776 Juan Bautista de Anza Expedition as it entered the present-day U.S. from New Spain, and the town is now on the Juan Bautista de Anza National Historic Trail. On the second floor of the 1904 Nogales Courthouse is a small room dedicated to the 1775–1776 Anza Expedition. In 1841, a land grant from the Mexican government to the Elías family established Los Nogales de Elías. Following the Gadsden Purchase in 1853, Nogales became a part of the United States of America. In 1880, Russian-Jewish immigrants Isaac and Jacob Isaacson homesteaded the trading post of Isaacson, Arizona, at present-day Nogales. The U.S. Postal Service opened the Isaacson post office but renamed it as Nogales in 1883. In 1915, according to historian David Leighton, Sonora Gov. Jose M. Maytorena ordered the construction of an 11-wire fence, separating Nogales, Sonora from Nogales, Arizona, but it was taken down four months later. On August 27, 1918, a battle between United States Army forces and Mexican militia – mostly civilian in composition – took place. Culminating as the result of a decade's worth of tensions originating from the Mexican Revolution and earlier battles in Nogales along the border in 1913 and 1915, the main consequence of the 1918 violence saw the building of the first permanent border wall between Nogales, Arizona, and Nogales, Sonora, along the previously unobstructed boundary line on International Street.

Demographics

Racial and ethnic composition

2020 census As of the 2020 census, Nogales had a population of 19,770. The median age was 37.4 years. 27.7% of residents were under the age of 18 and 19.6% of residents were 65 years of age or older. For every 100 females there were 85.4 males, and for every 100 females age 18 and over there were 79.1 males age 18 and over. 93.6% of residents lived in urban areas, while 6.4% lived in rural areas. There were 6,896 households in Nogales, of which 39.0% had children under the age of 18 living in them. Of all households, 41.8% were married-couple households, 16.1% were households with a male householder and no spouse or partner present, and 38.0% were households with a female householder and no spouse or partner present. About 25.2% of all households were made up of individuals and 13.6% had someone living alone who was 65 years of age or older. There were 7,562 housing units, of which 8.8% were vacant. The homeowner vacancy rate was 2.0% and the rental vacancy rate was 7.2%.

2000 census As of the 2000 census, there were 20,878 people, 5,985 households, and 4,937 families residing in the city. The population density was 1,002.1 inhabitants per square mile (386.9/km2). There were 6,501 housing units at an average density of 312.0/sq mi (120.5/km2). The racial makeup of the city was 71.7% White, 0.4% Black or African American, 0.6% Native American, 0.6% Asian, 0.0% Pacific Islander, 24.3% from other races, and 2.4% from two or more races. 95.0% of the population were Hispanic or Latino of any race. There were 6,362 households, out of which 38.8% had children under the age of 18 living with them, 47.9% were married couples living together, 24.2% had a female householder with no husband present, and 22.5% were non-families. 15.1% of all households were made up of individuals, and 9.9% had someone living alone who was 65 years of age or older. The average household size was 3.12 and the average family size was 3.62. In the city, the population was spread out, with 34.6% under the age of 18, 9.5% from 18 to 24, 25.5% from 25 to 44, 19.5% from 45 to 64, and 10.8% who were 65 years of age or older. The median age was 30 years. For every 100 females, there were 88.1 males. For every 100 females age 18 and over, there were 81.3 males. The median income for a household in the city was $28,044, and the median income for a family was $24,637. Males had a median income of $24,636 versus $18,403 for females. The per capita income for the city was $14,440. About 30.8% of families and 32.7% of the population were below the poverty line, including 41.2% of those under age 18 and 32.9% of those age 65 or over.

Geography According to the United States Census Bureau, the city has a total area of 20.8 sq mi (54 km2), all land. The city is at an elevation of 3,829 ft (1,167 m).

… excerpt ends here. Continue reading the full article.

Illustrations

Nogales, Arizona illustration
Nogales, Arizona illustration
Nogales, Arizona illustration
Nogales, Arizona illustration
Nogales, Arizona: The boundary between Nogales, Arizona, in the United States, on the right, and Nogales, Sonora, in Mexico, on the left, running down the center of a wide avenue, about 1899
The boundary between Nogales, Arizona, in the United States, on the right, and Nogales, Sonora, in Mexico, on the left, running down the center of a wide avenue, about 1899

Worked examples

Example 1 — a first encounter with Nogales, Arizona

Start with the simplest possible case. Write down what Nogales, Arizona claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Nogales, Arizona before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Nogales, Arizona ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Nogales, Arizona

In research
Nogales, Arizona appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Nogales, Arizona in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Nogales, Arizona is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1841 establishments in Mexico, Cities in Arizona, Cities in Santa Cruz County, Arizona, so understanding it makes those chapters shorter.
In everyday life
Look for Nogales, Arizona outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Nogales, Arizona” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Nogales, Arizona in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Nogales, Arizona means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Nogales, Arizona out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Nogales, Arizona in simple terms?

Nogales (Spanish pronunciation: [noˈɣales] ; English: or ) is a city in and the county seat of Santa Cruz County, Arizona, United States. As of 2026, the population of Nogales is 20,072.

Why does Nogales, Arizona matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Nogales, Arizona?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Nogales, Arizona.

Tags

  • 1841 establishments in Mexico
  • Cities in Arizona
  • Cities in Santa Cruz County, Arizona
  • County seats in Arizona
  • Divided cities
  • Micropolitan statistical areas of Arizona
  • Nogales, Arizona
  • Populated places in the Sonoran Desert
  • Twin cities

Keep exploring