Can you solve it? Carl Friedrich Gauss, money saving expert (2024)

FAQs

What is the trick of the Gauss formula? ›

Young Gauss's “trick” for finding the sum of an arithmetic progression is usually explained in terms of adding pairs of elements from opposite ends of the sequence, so that all the pairs have the same sum. One way to envision this process is to fold the series in half with a hairpin bend.

Johann Friedrich Carl Gauss was born in 1777 to a poor family in Brunswick, Germany. The boy was found to be a mathematical prodigy. Gauss' amazing calculating abilities aroused the interest of his teachers, and the child received a solid education despite lack of money.

Each envelope will have a certain amount of cash, from 1 to 100. When you add all the envelopes together — $100 + $99 + 98 + $97, and so on, all the way down to $1 — the total amount comes out to $5,050. If you were to save the same amount each day for 100 days, you'd need to set aside $50.50 per day to hit that sum.

Gauss used this same method to sum all the numbers from 1 to 100. He realized that he could pair up all the numbers. That meant he had 50 pairs, each with a sum of 101. He could then multiply 50 x 101 to arrive at his answer: 5050.

Carl Gauss was a child prodigy who went on to become one of the greatest German mathematicians of the 19th century. With IQ scores ranging from 250 to 300, he contributed to the number theory fields like algebra, statistics, and analysis.

In his doctoral thesis from 1799, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

His doctoral thesis of 1797 gave a proof of the fundamental theorem of algebra: every polynomial equation with real or complex coefficients has as many roots (solutions) as its degree (the highest power of the variable). Gauss's proof, though not wholly convincing, was remarkable for its critique of earlier attempts.

The 100 Envelope Saving Challenge provides a structured system to save over $5,000 in 100 days. To begin, gather 100 envelopes and sequentially number them $1 through $100. On day one, you'll place $1 in envelope one. On day two, you'll add $2 to envelope two, and so on.

On each envelope, write the day number and the amount you need to save for that day. For instance, on the first envelope, you would write "Day 1: $1" and on the second envelope "Day 2: $2", and so on all the way to Day 100: $100. Each day, you take the envelope for that day and put the designated amount of cash inside.

What is 1 * 2 * 3 * 4 * 5 all the way to 100? ›

The answer is 5050, it's a programming exercise I sometimes set. Mathematically though you can do this in your head far faster than you can write a program to do it. How many of these sums are there? Clearly there are 100/2 = 50 sums.

The electric field is perpendicular, locally, to the equipotential surface of the conductor, and zero inside; its flux πa²·E, by Gauss's law equals πa²·σ/ε₀. Thus, σ = ε₀E.

Born 241 years ago on April 30, Johann Carl Friedrich Gauss is often described as the “Prince of Mathematicians” and hailed for his contributions to number theory, geometry, probability theory and astronomy.

Simply list the ENTIRE series forward, then list the entire series in reverse and add the pairs. In this situation, you will need to multiply the sum by the number of pairs and then divide by two, since you are actually working with 2 complete series.

Gauss's law for electricity states that the electric flux Φ across any closed surface is proportional to the net electric charge q enclosed by the surface; that is, Φ = q/ε₀, where ε₀ is the electric permittivity of free space and has a value of 8.854 × 10^–12 square coulombs per newton per square metre.

The flux Φ of the electric field →E through any closed surface S (a Gaussian surface) is equal to the net charge enclosed (qenc) divided by the permittivity of free space (ϵ0): Φ=∮S→E⋅ˆndA=qencϵ0.