Equipment required? No. You don't need any equipment because you'll rely on your own body weight for resistance. But you'll probably want to use a yoga mat to keep you from sliding around in standing poses, and to cushion you while in seated and lying positions. Other, optional equipment includes a yoga ball for balance, a yoga block or two, and straps to help you reach for your feet or link your hands behind your back.
The Maitrayaniya Upanishad, likely composed in a later century than Katha and Shvetashvatara Upanishads but before Patanjali's Yoga Sutra, mentions sixfold yoga method – breath control (pranayama), introspective withdrawal of senses (pratyahara), meditation (dhyana), mind concentration (dharana), philosophical inquiry/creative reasoning (tarka), and absorption/intense spiritual union (samadhi).
There is no consensus on its chronology or specific origin other than that yoga developed in ancient India. Suggested origins are the Indus Valley Civilization (3300–1900 BCE) and pre-Vedic Eastern states of India, the Vedic period (1500–500 BCE), and the śramaṇa movement. According to Gavin Flood, continuities may exist between those various traditions:
The Mayo Clinic Diet is generally safe for most adults. It does encourage unlimited amounts of vegetables and fruits. For most people, eating lots of fruits and vegetables is a good thing — these foods provide your body with important nutrients and fiber. However, if you aren't used to having fiber in your diet, you may experience minor, temporary changes in digestion, such as intestinal gas, as your body adjusts to this new way of eating.
The word diet first appeared in English in the 13th century. Its original meaning was the same as in modern English, “habitually taken food and drink.” But diet was used in another sense too in the Middle and early modern English periods to mean “way of living.” This is, in fact, the original meaning of diet’s Greek ancestor diaita, which is derived from the verb diaitasthan, meaning “to lead one’s life.” In Greek, diaita, had already come to be used more specifically for a way of living prescribed by a physician, a diet, or other regimen.
^ James Mallinson, "Sāktism and Hathayoga," 28 June 2012.
Core: Yes. There are yoga poses to target just about every core muscle. Want to tighten those love handles? Then prop yourself up on one arm and do a side plank. To really burn out the middle of your abs, you can do boat pose, in which you balance on your "sit bones" (the bony prominences at the base of your pelvic bones) and hold your legs up in the air.