Weekly Math & Science Facts
Two ideas.
One week of curiosity.
Short explanations that connect patterns, physical laws, and the questions behind them.
Week of October 12, 2026
This week: logarithms and chemical scale.
This Week’s Math Fact · Logarithms & scale
Logarithms turn multiplication into steps
Base-10 logarithms convert multiplicative changes into additive steps.
100 → log₁₀ = 2
1,000 → log₁₀ = 3
Each increase of 1 on a base-10 logarithmic scale represents multiplying the original quantity by 10. Logarithms describe how many multiplicative steps separate quantities—not merely which calculator button to press.
This makes logarithmic scales useful when values span very large ranges: equal steps on the scale represent equal multiplication factors.
Key idea: +1 on a base-10 logarithmic scale = ×10 in the original quantity.
Reference: OpenStax — properties of logarithms.
This Week’s Science Fact · Chemistry & pH
One pH unit is a tenfold change
The pH scale is logarithmic and tied to hydrogen ions in a solution.
In the usual dilute-solution approximation, [H⁺] is the hydrogen-ion concentration in mol/L. More precisely, pH is defined using hydrogen-ion activity.
- pH 3 has about 10× greater hydrogen-ion concentration than pH 4.
- pH 2 has about 100× greater hydrogen-ion concentration than pH 4.
The minus sign reverses the direction: more hydrogen ions mean a lower pH. A small numerical difference can represent a large chemical difference.
Connection: Logarithms compress very large concentration differences into manageable numbers.
Reference: OpenStax — pH and pOH.
The growing archive.
Week of October 5, 2026
2026 · October
Percentage changes & why metal feels colder
A percentage change depends on the value you start from, while how cold an object feels depends on how quickly heat moves between your skin and the material.
Read the October 5 pair
MATH
Up 20%, then down 20%? Not back to the start.
Equal percentage increases and decreases do not cancel because the second percentage is applied to a different starting value.
Example:
- Start with 100
- Increase by 20% → 120
- Decrease 120 by 20% → 96
The result is 96, which is 4% below the original value of 100.
Another way to see it:
So an increase of 20% followed by a decrease of 20% gives a net change of −4%, not 0%.
Key idea: Equal percentage increases and decreases do not cancel because they are applied to different bases.
Reference: OpenStax — Solve General Applications of Percent.
SCIENCE
Metal can feel colder without being colder.
Two objects can be at the same room temperature and still feel very different when you touch them.
Metal often feels colder than materials such as wood or plastic because it transfers heat away from your warmer skin much more quickly.
Your sense of hot and cold responds strongly to the rate of heat transfer, not just the object’s actual temperature.
So a metal desk leg and a wooden tabletop can both be at the same room temperature, yet the metal may feel much colder because it conducts heat away from your hand faster.
Key idea: Touch is not a thermometer. What you feel depends heavily on heat-transfer rate.
Reference: ThermoWorks — Heat vs. Temperature: What’s the Difference?.
Week of September 28, 2026
2026 · September
Odd numbers & orbital free fall
Our first weekly pair: patterns and motion.
Read the September 28 pair
MATH
Odd numbers build perfect squares.
Add the first n positive odd numbers, and the total is n².
Imagine building a square from tiles. Start with one tile. Add an L-shaped border of three tiles to make a 2-by-2 square. The next border uses five tiles to make a 3-by-3 square; seven more make a 4-by-4 square.
Each new border adds the next odd number. Algebra shows the same pattern: n² − (n − 1)² = 2n − 1.
Try it: What is 1 + 3 + 5 + … + 19?
See the reasoning
19 is the tenth positive odd number because 2(10) − 1 = 19. The sum is therefore 10² = 100.
Key idea: Add the first n positive odd numbers, and the total is n².
Reference: OpenStax — arithmetic series. KEVKAH’s explanation applies the arithmetic-series relationship to positive odd numbers.
SCIENCE
Astronauts float because they are falling.
Gravity still acts on an orbiting space station. The station and the astronauts fall around Earth together.
Their forward motion carries them around the planet while gravity curves their path toward it. They keep falling without reaching the ground.
Inside the station, the astronauts and nearby objects fall together. Without a floor pushing up on them as it does on Earth, they appear weightless. This is an explanation of orbital microgravity—not evidence that gravity has disappeared.
A briefly falling elevator illustrates the same shared-fall idea. An orbiting station continues that fall around Earth.
Key idea: Orbit = forward motion + free fall. The station and the astronauts fall around Earth together.
Reference: NASA — What is Microgravity?.